diff --git a/.github/workflows/CompatHelper.yml b/.github/workflows/CompatHelper.yml
index b17575afa..c13c749eb 100644
--- a/.github/workflows/CompatHelper.yml
+++ b/.github/workflows/CompatHelper.yml
@@ -1,16 +1,35 @@
 name: CompatHelper
+
 on:
   schedule:
-    - cron: '00 00 * * *'
+    - cron: 0 0 * * *
   workflow_dispatch:
+
 jobs:
   CompatHelper:
     runs-on: ubuntu-latest
     steps:
-      - name: Pkg.add("CompatHelper")
-        run: julia -e 'using Pkg; Pkg.add("CompatHelper")'
-      - name: CompatHelper.main()
+      - uses: actions/checkout@v2
+      - name: "Install CompatHelper"
+        run: |
+          import Pkg
+          name = "CompatHelper"
+          uuid = "aa819f21-2bde-4658-8897-bab36330d9b7"
+          version = "2"
+          Pkg.add(; name, uuid, version)
+        shell: julia --color=yes {0}
+      - name: "Run CompatHelper"
+        run: |
+          import CompatHelper
+          subdirs = ["", "test", "docs"]
+          for f in readdir("examples"; join=true)
+              if isdir(f)
+                  push!(subdirs, joinpath("examples", basename(f)))
+              end
+          end
+          @info "CompatHelper directories" subdirs
+          CompatHelper.main(; subdirs=subdirs)
+        shell: julia --color=yes {0}
         env:
           GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
           COMPATHELPER_PRIV: ${{ secrets.DOCUMENTER_KEY }}
-        run: julia -e 'using CompatHelper; CompatHelper.main(; subdirs = ["", "docs", "test"])'
diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index d9d9ad787..8eeb12b4b 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -6,7 +6,7 @@ on:
   pull_request:
 jobs:
   test:
-    name: Julia ${{ matrix.version }} - ${{ matrix.os }} - ${{ matrix.arch }} - ${{ github.event_name }}
+    name: Julia ${{ matrix.version }} - ${{ matrix.group }}
     runs-on: ${{ matrix.os }}
     continue-on-error: ${{ matrix.version == 'nightly' }}
     strategy:
@@ -18,10 +18,14 @@ jobs:
           - 'nightly'
         os:
           - ubuntu-latest
-          - macOS-latest
-          - windows-latest
         arch:
           - x64
+        group:
+          - 'Transform'
+          - 'BaseKernels'
+          - 'Kernels'
+          - 'MultiOutput'
+          - 'Others'
     steps:
       - uses: actions/checkout@v2
       - uses: julia-actions/setup-julia@v1
@@ -40,10 +44,26 @@ jobs:
             ${{ runner.os }}-
       - uses: julia-actions/julia-buildpkg@v1
       - uses: julia-actions/julia-runtest@v1
+        with:
+          coverage: ${{ matrix.version == '1' && matrix.os == 'ubuntu-latest' }}
+        env:
+          GROUP: ${{ matrix.group }}
       - uses: julia-actions/julia-processcoverage@v1
-      - name: Send coverage
         if: matrix.version == '1' && matrix.os == 'ubuntu-latest'
+      - name: Coveralls parallel
+        if: matrix.version == '1' && matrix.os == 'ubuntu-latest'
+        uses: coverallsapp/github-action@master
+        with:
+          github-token: ${{ secrets.GITHUB_TOKEN }}
+          path-to-lcov: ./lcov.info
+          flag-name: run-${{ matrix.group }}
+          parallel: true
+  finish:
+    needs: test
+    runs-on: ubuntu-latest
+    steps:
+      - name: Send coverage
         uses: coverallsapp/github-action@master
         with:
-            github-token: ${{ secrets.GITHUB_TOKEN }}
-            path-to-lcov: ./lcov.info
+          github-token: ${{ secrets.github_token }}
+          parallel-finished: true
diff --git a/.github/workflows/docs.yml b/.github/workflows/docs.yml
index e47f93896..2b57c0c99 100644
--- a/.github/workflows/docs.yml
+++ b/.github/workflows/docs.yml
@@ -19,6 +19,8 @@ jobs:
         run: julia --project=docs/ -e 'using Pkg; Pkg.develop(PackageSpec(path=pwd())); Pkg.instantiate()'
       - name: Build and deploy
         env:
+          GKSwstype: nul # turn off GR's interactive plotting for notebooks
           GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} # For authentication with GitHub Actions token
           DOCUMENTER_KEY: ${{ secrets.DOCUMENTER_KEY }} # For authentication with SSH deploy key
+          JULIA_DEBUG: Documenter # Print `@debug` statements (https://github.com/JuliaDocs/Documenter.jl/issues/955)
         run: julia --project=docs/ docs/make.jl
diff --git a/.gitignore b/.gitignore
index 3bd1d529e..eefb4afce 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,6 +1,6 @@
 *.json
 *.cov
-Manifest.toml
+/Manifest.toml
+/test/Manifest.toml
 coverage/
-src/update_v0.8.0
 .DS_store
diff --git a/Project.toml b/Project.toml
index 6d5a50658..3e3387030 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "KernelFunctions"
 uuid = "ec8451be-7e33-11e9-00cf-bbf324bd1392"
-version = "0.10.5"
+version = "0.10.7"
 
 [deps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
diff --git a/docs/.gitignore b/docs/.gitignore
index 90fb8a549..909052372 100644
--- a/docs/.gitignore
+++ b/docs/.gitignore
@@ -1,4 +1,3 @@
 build/
 site/
-
-#Temp to avoid to many changes
+src/examples/
diff --git a/docs/Manifest.toml b/docs/Manifest.toml
new file mode 100644
index 000000000..bd968e75c
--- /dev/null
+++ b/docs/Manifest.toml
@@ -0,0 +1,355 @@
+# This file is machine-generated - editing it directly is not advised
+
+[[AbstractFFTs]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "485ee0867925449198280d4af84bdb46a2a404d0"
+uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
+version = "1.0.1"
+
+[[ArgTools]]
+uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
+
+[[Artifacts]]
+uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
+
+[[Base64]]
+uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
+
+[[ChainRulesCore]]
+deps = ["Compat", "LinearAlgebra", "SparseArrays"]
+git-tree-sha1 = "be770c08881f7bb928dfd86d1ba83798f76cf62a"
+uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+version = "0.10.9"
+
+[[Compat]]
+deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
+git-tree-sha1 = "dc7dedc2c2aa9faf59a55c622760a25cbefbe941"
+uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
+version = "3.31.0"
+
+[[CompilerSupportLibraries_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
+
+[[CompositionsBase]]
+git-tree-sha1 = "f3955eb38944e5dd0fabf8ca1e267d94941d34a5"
+uuid = "a33af91c-f02d-484b-be07-31d278c5ca2b"
+version = "0.1.0"
+
+[[DataAPI]]
+git-tree-sha1 = "ee400abb2298bd13bfc3df1c412ed228061a2385"
+uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
+version = "1.7.0"
+
+[[DataStructures]]
+deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
+git-tree-sha1 = "4437b64df1e0adccc3e5d1adbc3ac741095e4677"
+uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
+version = "0.18.9"
+
+[[Dates]]
+deps = ["Printf"]
+uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
+
+[[DelimitedFiles]]
+deps = ["Mmap"]
+uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
+
+[[Distances]]
+deps = ["LinearAlgebra", "Statistics", "StatsAPI"]
+git-tree-sha1 = "abe4ad222b26af3337262b8afb28fab8d215e9f8"
+uuid = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
+version = "0.10.3"
+
+[[Distributed]]
+deps = ["Random", "Serialization", "Sockets"]
+uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
+
+[[DocStringExtensions]]
+deps = ["LibGit2"]
+git-tree-sha1 = "a32185f5428d3986f47c2ab78b1f216d5e6cc96f"
+uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
+version = "0.8.5"
+
+[[Documenter]]
+deps = ["Base64", "Dates", "DocStringExtensions", "IOCapture", "InteractiveUtils", "JSON", "LibGit2", "Logging", "Markdown", "REPL", "Test", "Unicode"]
+git-tree-sha1 = "47f13b6305ab195edb73c86815962d84e31b0f48"
+uuid = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+version = "0.27.3"
+
+[[Downloads]]
+deps = ["ArgTools", "LibCURL", "NetworkOptions"]
+uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
+
+[[FillArrays]]
+deps = ["LinearAlgebra", "Random", "SparseArrays"]
+git-tree-sha1 = "a603e79b71bb3c1efdb58f0ee32286efe2d1a255"
+uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
+version = "0.11.8"
+
+[[Functors]]
+deps = ["MacroTools"]
+git-tree-sha1 = "a7bb2af991c43dcf5c3455d276dd83976799634f"
+uuid = "d9f16b24-f501-4c13-a1f2-28368ffc5196"
+version = "0.2.1"
+
+[[IOCapture]]
+deps = ["Logging", "Random"]
+git-tree-sha1 = "f7be53659ab06ddc986428d3a9dcc95f6fa6705a"
+uuid = "b5f81e59-6552-4d32-b1f0-c071b021bf89"
+version = "0.2.2"
+
+[[InteractiveUtils]]
+deps = ["Markdown"]
+uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
+
+[[JLLWrappers]]
+deps = ["Preferences"]
+git-tree-sha1 = "642a199af8b68253517b80bd3bfd17eb4e84df6e"
+uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
+version = "1.3.0"
+
+[[JSON]]
+deps = ["Dates", "Mmap", "Parsers", "Unicode"]
+git-tree-sha1 = "81690084b6198a2e1da36fcfda16eeca9f9f24e4"
+uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
+version = "0.21.1"
+
+[[KernelFunctions]]
+deps = ["ChainRulesCore", "Compat", "CompositionsBase", "Distances", "FillArrays", "Functors", "LinearAlgebra", "Random", "Requires", "SpecialFunctions", "StatsBase", "StatsFuns", "TensorCore", "Test", "ZygoteRules"]
+path = ".."
+uuid = "ec8451be-7e33-11e9-00cf-bbf324bd1392"
+version = "0.10.6"
+
+[[Kronecker]]
+deps = ["FillArrays", "LinearAlgebra", "NamedDims", "SparseArrays", "StatsBase"]
+git-tree-sha1 = "90e082a267982069e624ea0f825d324c86a01b4e"
+uuid = "2c470bb0-bcc8-11e8-3dad-c9649493f05e"
+version = "0.4.3"
+
+[[LibCURL]]
+deps = ["LibCURL_jll", "MozillaCACerts_jll"]
+uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"
+
+[[LibCURL_jll]]
+deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
+uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"
+
+[[LibGit2]]
+deps = ["Base64", "NetworkOptions", "Printf", "SHA"]
+uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"
+
+[[LibSSH2_jll]]
+deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
+uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"
+
+[[Libdl]]
+uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
+
+[[LinearAlgebra]]
+deps = ["Libdl"]
+uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+
+[[LogExpFunctions]]
+deps = ["DocStringExtensions", "LinearAlgebra"]
+git-tree-sha1 = "1ba664552f1ef15325e68dc4c05c3ef8c2d5d885"
+uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
+version = "0.2.4"
+
+[[Logging]]
+uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
+
+[[MacroTools]]
+deps = ["Markdown", "Random"]
+git-tree-sha1 = "6a8a2a625ab0dea913aba95c11370589e0239ff0"
+uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
+version = "0.5.6"
+
+[[Markdown]]
+deps = ["Base64"]
+uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
+
+[[MbedTLS_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
+
+[[Missings]]
+deps = ["DataAPI"]
+git-tree-sha1 = "4ea90bd5d3985ae1f9a908bd4500ae88921c5ce7"
+uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
+version = "1.0.0"
+
+[[Mmap]]
+uuid = "a63ad114-7e13-5084-954f-fe012c677804"
+
+[[MozillaCACerts_jll]]
+uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
+
+[[NamedDims]]
+deps = ["AbstractFFTs", "LinearAlgebra", "Pkg", "Requires", "Statistics"]
+git-tree-sha1 = "572b7af3ee53328eec29392d3b133804925595a1"
+uuid = "356022a1-0364-5f58-8944-0da4b18d706f"
+version = "0.2.34"
+
+[[NetworkOptions]]
+uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
+
+[[OpenSpecFun_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
+uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
+version = "0.5.5+0"
+
+[[OrderedCollections]]
+git-tree-sha1 = "85f8e6578bf1f9ee0d11e7bb1b1456435479d47c"
+uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
+version = "1.4.1"
+
+[[PDMats]]
+deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse"]
+git-tree-sha1 = "4dd403333bcf0909341cfe57ec115152f937d7d8"
+uuid = "90014a1f-27ba-587c-ab20-58faa44d9150"
+version = "0.11.1"
+
+[[Parsers]]
+deps = ["Dates"]
+git-tree-sha1 = "c8abc88faa3f7a3950832ac5d6e690881590d6dc"
+uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
+version = "1.1.0"
+
+[[Pkg]]
+deps = ["Artifacts", "Dates", "Downloads", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
+uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
+
+[[Preferences]]
+deps = ["TOML"]
+git-tree-sha1 = "00cfd92944ca9c760982747e9a1d0d5d86ab1e5a"
+uuid = "21216c6a-2e73-6563-6e65-726566657250"
+version = "1.2.2"
+
+[[Printf]]
+deps = ["Unicode"]
+uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
+
+[[REPL]]
+deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
+uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
+
+[[Random]]
+deps = ["Serialization"]
+uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+
+[[Requires]]
+deps = ["UUIDs"]
+git-tree-sha1 = "4036a3bd08ac7e968e27c203d45f5fff15020621"
+uuid = "ae029012-a4dd-5104-9daa-d747884805df"
+version = "1.1.3"
+
+[[Rmath]]
+deps = ["Random", "Rmath_jll"]
+git-tree-sha1 = "bf3188feca147ce108c76ad82c2792c57abe7b1f"
+uuid = "79098fc4-a85e-5d69-aa6a-4863f24498fa"
+version = "0.7.0"
+
+[[Rmath_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "68db32dff12bb6127bac73c209881191bf0efbb7"
+uuid = "f50d1b31-88e8-58de-be2c-1cc44531875f"
+version = "0.3.0+0"
+
+[[SHA]]
+uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
+
+[[Serialization]]
+uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
+
+[[SharedArrays]]
+deps = ["Distributed", "Mmap", "Random", "Serialization"]
+uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
+
+[[Sockets]]
+uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
+
+[[SortingAlgorithms]]
+deps = ["DataStructures"]
+git-tree-sha1 = "2ec1962eba973f383239da22e75218565c390a96"
+uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
+version = "1.0.0"
+
+[[SparseArrays]]
+deps = ["LinearAlgebra", "Random"]
+uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+
+[[SpecialFunctions]]
+deps = ["ChainRulesCore", "LogExpFunctions", "OpenSpecFun_jll"]
+git-tree-sha1 = "a50550fa3164a8c46747e62063b4d774ac1bcf49"
+uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
+version = "1.5.1"
+
+[[Statistics]]
+deps = ["LinearAlgebra", "SparseArrays"]
+uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+
+[[StatsAPI]]
+git-tree-sha1 = "1958272568dc176a1d881acb797beb909c785510"
+uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
+version = "1.0.0"
+
+[[StatsBase]]
+deps = ["DataAPI", "DataStructures", "LinearAlgebra", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
+git-tree-sha1 = "2f6792d523d7448bbe2fec99eca9218f06cc746d"
+uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
+version = "0.33.8"
+
+[[StatsFuns]]
+deps = ["LogExpFunctions", "Rmath", "SpecialFunctions"]
+git-tree-sha1 = "30cd8c360c54081f806b1ee14d2eecbef3c04c49"
+uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
+version = "0.9.8"
+
+[[SuiteSparse]]
+deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]
+uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"
+
+[[TOML]]
+deps = ["Dates"]
+uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
+
+[[Tar]]
+deps = ["ArgTools", "SHA"]
+uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
+
+[[TensorCore]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
+uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
+version = "0.1.1"
+
+[[Test]]
+deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
+uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[[UUIDs]]
+deps = ["Random", "SHA"]
+uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
+
+[[Unicode]]
+uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
+
+[[Zlib_jll]]
+deps = ["Libdl"]
+uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
+
+[[ZygoteRules]]
+deps = ["MacroTools"]
+git-tree-sha1 = "9e7a1e8ca60b742e508a315c17eef5211e7fbfd7"
+uuid = "700de1a5-db45-46bc-99cf-38207098b444"
+version = "0.2.1"
+
+[[nghttp2_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
+
+[[p7zip_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
diff --git a/docs/Project.toml b/docs/Project.toml
index 3f90d2da6..4f10fcafa 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -1,7 +1,12 @@
 [deps]
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+KernelFunctions = "ec8451be-7e33-11e9-00cf-bbf324bd1392"
+Kronecker = "2c470bb0-bcc8-11e8-3dad-c9649493f05e"
 PDMats = "90014a1f-27ba-587c-ab20-58faa44d9150"
 
 [compat]
 Documenter = "0.27"
+KernelFunctions = "0.10"
+Kronecker = "0.4"
 PDMats = "0.11"
+julia = "1.3"
diff --git a/docs/README.md b/docs/README.md
new file mode 100644
index 000000000..32e47f700
--- /dev/null
+++ b/docs/README.md
@@ -0,0 +1,63 @@
+# How to build the docs locally
+
+If you just want to modify or add an example, you can [build just the example](../examples/README.md) without having to build the full documentation locally.
+
+If you want to build the documentation, navigate to this (docs/) directory and open a Julia REPL.
+
+## Instantiation
+
+First activate the documentation environment:
+```julia
+julia> ] activate .
+```
+Alternatively, you can start Julia with `julia --project=.`.
+
+Then install all packages:
+```julia
+julia> ] instantiate
+```
+By default, this will use the development version of KernelFunctions in the parent directory.
+
+## Build
+
+To build the documentation, run (after activating the documentation environment)
+```julia
+julia> include("make.jl")
+```
+You can speed up the process if you do not execute the examples and comment out the
+relevant sections in `docs/make.jl`.
+
+The output is in the `docs/build/` directory and best viewed in a browser.
+The documentation uses pretty URLs which can be a hindrance if you browse the documentation locally.
+The [Documenter documentation](https://juliadocs.github.io/Documenter.jl/stable/man/guide/#Building-an-Empty-Document) suggests that
+
+> You can run a local web server out of the `docs/build` directory. One way to accomplish
+> this is to install the [LiveServer](https://github.com/tlienart/LiveServer.jl) Julia
+> package. You can then start the server with `julia -e 'using LiveServer; serve(dir="docs/build")'`.
+> Alternatively, if you have Python installed, you can start one with
+> `python3 -m http.server --bind localhost` (or `python -m SimpleHTTPServer` with Python 2).
+
+If you make any changes, you can run
+```julia
+julia> include("make.jl")
+```
+again to rebuild the documentation.
+
+# How to contribute to the docs
+
+## To add additional docs dependencies
+
+To add additional dependencies, run (after activating the documentation environment)
+```julia
+julia> ] add NewDependency
+```
+or, as a shell one-liner:
+```shell
+julia --project=. -e 'using Pkg; Pkg.add("NewDependency")'
+```
+and commit the changes to Project.toml and Manifest.toml.
+
+
+## To add examples
+
+See [../examples](../examples/README.md)
diff --git a/docs/literate.jl b/docs/literate.jl
new file mode 100644
index 000000000..452d1cdf2
--- /dev/null
+++ b/docs/literate.jl
@@ -0,0 +1,53 @@
+# Retrieve name of example and output directory
+if length(ARGS) != 2
+    error("please specify the name of the example and the output directory")
+end
+const EXAMPLE = ARGS[1]
+const OUTDIR = ARGS[2]
+
+# Activate environment
+# Note that each example's Project.toml must include Literate as a dependency
+using Pkg: Pkg
+const EXAMPLEPATH = joinpath(@__DIR__, "..", "examples", EXAMPLE)
+Pkg.activate(EXAMPLEPATH)
+Pkg.instantiate()
+using Literate: Literate
+
+function preprocess(content)
+    # Add link to nbviewer below the first heading of level 1
+    sub = SubstitutionString(
+        """
+#md # ```@meta
+#md # EditURL = "@__REPO_ROOT_URL__/examples/@__NAME__/script.jl"
+#md # ```
+#md #
+\\0
+#
+#md # [![](https://img.shields.io/badge/show-nbviewer-579ACA.svg)](@__NBVIEWER_ROOT_URL__/examples/@__NAME__.ipynb)
+#md #
+# *You are seeing the
+#md # HTML output generated by [Documenter.jl](https://github.com/JuliaDocs/Documenter.jl) and
+#nb # notebook output generated by
+# [Literate.jl](https://github.com/fredrikekre/Literate.jl) from the
+# [Julia source file](@__REPO_ROOT_URL__/examples/@__NAME__/script.jl).
+#md # The corresponding notebook can be viewed in [nbviewer](@__NBVIEWER_ROOT_URL__/examples/@__NAME__.ipynb).*
+#nb # The rendered HTML can be viewed [in the docs](https://juliagaussianprocesses.github.io/KernelFunctions.jl/dev/examples/@__NAME__/).*
+#
+        """,
+    )
+    content = replace(content, r"^# # [^\n]*"m => sub; count=1)
+
+    # remove VSCode `##` block delimiter lines
+    content = replace(content, r"^##$."ms => "")
+
+    return content
+end
+
+# Convert to markdown and notebook
+const SCRIPTJL = joinpath(EXAMPLEPATH, "script.jl")
+Literate.markdown(
+    SCRIPTJL, OUTDIR; name=EXAMPLE, documenter=false, execute=true, preprocess=preprocess
+)
+Literate.notebook(
+    SCRIPTJL, OUTDIR; name=EXAMPLE, documenter=false, execute=true, preprocess=preprocess
+)
diff --git a/docs/make.jl b/docs/make.jl
index c2c14f8f9..8aca5486d 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -1,26 +1,59 @@
-using Documenter
+### Process examples
+# Always rerun examples
+const EXAMPLES_OUT = joinpath(@__DIR__, "src", "examples")
+ispath(EXAMPLES_OUT) && rm(EXAMPLES_OUT; recursive=true)
+mkpath(EXAMPLES_OUT)
 
-# Print `@debug` statements (https://github.com/JuliaDocs/Documenter.jl/issues/955)
-if haskey(ENV, "GITHUB_ACTIONS")
-    ENV["JULIA_DEBUG"] = "Documenter"
+# Install and precompile all packages
+# Workaround for https://github.com/JuliaLang/Pkg.jl/issues/2219
+examples = filter!(isdir, readdir(joinpath(@__DIR__, "..", "examples"); join=true))
+let script = "using Pkg; Pkg.activate(ARGS[1]); Pkg.instantiate()"
+    for example in examples
+        if !success(`$(Base.julia_cmd()) -e $script $example`)
+            error(
+                "project environment of example ",
+                basename(example),
+                " could not be instantiated",
+            )
+        end
+    end
+end
+# Run examples asynchronously
+processes = let literatejl = joinpath(@__DIR__, "literate.jl")
+    map(examples) do example
+        return run(
+            pipeline(
+                `$(Base.julia_cmd()) $literatejl $(basename(example)) $EXAMPLES_OUT`;
+                stdin=devnull,
+                stdout=devnull,
+                stderr=stderr,
+            );
+            wait=false,
+        )::Base.Process
+    end
 end
 
+# Check that all examples were run successfully
+isempty(processes) || success(processes) || error("some examples were not run successfully")
+
+### Build documentation
+using Documenter
+
 using KernelFunctions
+using PDMats, Kronecker  # we have to load all optional packages to generate the full API documentation
 
+# Doctest setup
 DocMeta.setdocmeta!(
     KernelFunctions,
     :DocTestSetup,
     quote
         using KernelFunctions
-        using LinearAlgebra
-        using Random
-        using PDMats: PDMats
-    end;
+    end;  # we have to load all packages used (implicitly) within jldoctest blocks in the API docstrings
     recursive=true,
 )
 
 makedocs(;
-    sitename="KernelFunctions",
+    sitename="KernelFunctions.jl",
     format=Documenter.HTML(),
     modules=[KernelFunctions],
     pages=[
@@ -29,11 +62,13 @@ makedocs(;
         "kernels.md",
         "transform.md",
         "metrics.md",
-        "theory.md",
         "create_kernel.md",
         "API" => "api.md",
-        "Examples" => "example.md",
         "Design" => "design.md",
+        "Examples" =>
+            map(filter!(filename -> endswith(filename, ".md"), readdir(EXAMPLES_OUT))) do x
+                return joinpath("examples", x)
+            end,
     ],
     strict=true,
     checkdocs=:exports,
diff --git a/docs/src/create_kernel.md b/docs/src/create_kernel.md
index d7a10c4db..c7234b41f 100644
--- a/docs/src/create_kernel.md
+++ b/docs/src/create_kernel.md
@@ -10,7 +10,7 @@ Here are a few ways depending on how complicated your kernel is:
 
 If your kernel function is of the form `k(x, y) = f(d(x, y))` where `d(x, y)` is a `PreMetric`,
 you can construct your custom kernel by defining `kappa` and `metric` for your kernel.
-Here is for example how one can define the `SqExponentialKernel` again :
+Here is for example how one can define the `SqExponentialKernel` again:
 
 ```julia
 struct MyKernel <: KernelFunctions.SimpleKernel end
diff --git a/docs/src/example.md b/docs/src/example.md
deleted file mode 100644
index 14601f1e8..000000000
--- a/docs/src/example.md
+++ /dev/null
@@ -1,21 +0,0 @@
-# Examples (WIP)
-
-Here are a few examples of known complex kernels and how to do them. Or how to use kernels in a certain context
-
-## Kernel Ridge Regression
-
-Make a simple example of kernel ridge regression
-
-## Gaussian Process Regression
-
-Make a simple example of gaussian process regression
-
-## Deep Kernel Learning
-
-Put a Flux neural net in front of the kernel
-cf. Wilson paper
-
-## Kernel Selection
-
-Create a large collection of kernels and optimize the weights
-cf AISTATS 2018 paper
diff --git a/docs/src/index.md b/docs/src/index.md
index 719e6bb79..697fb1577 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -1,17 +1,12 @@
 # KernelFunctions.jl
 
-Model-agnostic kernel functions compatible with automatic differentiation
-
-**KernelFunctions.jl** is a general purpose kernel package.
+**KernelFunctions.jl** is a general purpose [kernel](https://en.wikipedia.org/wiki/Positive-definite_kernel) package.
 It aims at providing a flexible framework for creating kernels and manipulating them.
-The main goals of this package compared to its predecessors/concurrents in [MLKernels.jl](https://github.com/trthatcher/MLKernels.jl), [Stheno.jl](https://github.com/willtebbutt/Stheno.jl), [GaussianProcesses.jl](https://github.com/STOR-i/GaussianProcesses.jl) and [AugmentedGaussianProcesses.jl](https://github.com/theogf/AugmentedGaussianProcesses.jl) are:
-- **Automatic Differentation** compatibility: all kernel functions should be differentiable via packages like [ForwardDiff.jl](https://github.com/JuliaDiff/ForwardDiff.jl) or [Zygote.jl](https://github.com/FluxML/Zygote.jl)
+The main goals of this package are:
 - **Flexibility**: operations between kernels should be fluid and easy without breaking.
 - **Plug-and-play**: including the kernels before/after other steps should be straightforward.
+- **Automatic Differentation** compatibility: all kernel functions which _ought_ to be differentiable using AD packages like [ForwardDiff.jl](https://github.com/JuliaDiff/ForwardDiff.jl) or [Zygote.jl](https://github.com/FluxML/Zygote.jl) _should_ be.
 
-The methodology of how kernels are computed is quite simple and is done in three phases :
-- A `Transform` object is applied sample-wise on every sample
-- The pairwise matrix is computed using [Distances.jl](https://github.com/JuliaStats/Distances.jl) by using a `Metric` proper to each kernel
-- The `Kernel` function is applied element-wise on the pairwise matrix
+This package builds on top of lots of excellent existing work in packages such as [MLKernels.jl](https://github.com/trthatcher/MLKernels.jl), [Stheno.jl](https://github.com/willtebbutt/Stheno.jl), [GaussianProcesses.jl](https://github.com/STOR-i/GaussianProcesses.jl), and [AugmentedGaussianProcesses.jl](https://github.com/theogf/AugmentedGaussianProcesses.jl).
 
-For a quick introduction on how to use it go to [User guide](@ref)
+See the [User guide](@ref) for a brief introduction.
diff --git a/docs/src/kernels.md b/docs/src/kernels.md
index ffc92f501..ae0f0843a 100644
--- a/docs/src/kernels.md
+++ b/docs/src/kernels.md
@@ -134,4 +134,5 @@ MOKernel
 IndependentMOKernel
 LatentFactorMOKernel
 IntrinsicCoregionMOKernel
+LinearMixingModelKernel
 ```
diff --git a/docs/src/theory.md b/docs/src/theory.md
deleted file mode 100644
index 71717e87e..000000000
--- a/docs/src/theory.md
+++ /dev/null
@@ -1,3 +0,0 @@
-# Theory
-
-See [Wikipedia article](https://en.wikipedia.org/wiki/Positive-definite_kernel)
diff --git a/docs/src/transform.md b/docs/src/transform.md
index 9ed878a84..1237642c7 100644
--- a/docs/src/transform.md
+++ b/docs/src/transform.md
@@ -36,3 +36,9 @@ SelectTransform
 ChainTransform
 PeriodicTransform
 ```
+
+## Convenience functions
+
+```@docs
+with_lengthscale
+```
diff --git a/docs/src/userguide.md b/docs/src/userguide.md
index b3539dc64..e3db6ffc3 100644
--- a/docs/src/userguide.md
+++ b/docs/src/userguide.md
@@ -15,6 +15,11 @@ For example, a squared exponential kernel is created by
       k = SqExponentialKernel() ∘ ScaleTransform(2.0)
       k = compose(SqExponentialKernel(), ScaleTransform(2.0))
     ```
+    Alternatively, you can use the convenience function [`with_lengthscale`](@ref):
+    ```julia
+    k = with_lengthscale(SqExponentialKernel(), 0.5)
+    ```
+    [`with_lengthscale`](@ref) also works with vector-valued lengthscales for ARD.
     Check the [Input Transforms](@ref input_transforms) page for more details.
 
 !!! tip "How do I set the kernel variance?"
@@ -73,18 +78,37 @@ kernelmatrix(k, ColVecs(X))  # returns a 5×5 matrix -- each column of X treated
 ```
 This is the mechanism used throughout KernelFunctions.jl to handle multi-dimensional inputs.
 
-You can also utilise the `obsdim` keyword argument if you prefer:
+You can utilise the `obsdim` keyword argument if you prefer:
 ```julia
 kernelmatrix(k, X; obsdim=1) # same as RowVecs(X)
 kernelmatrix(k, X; obsdim=2) # same as ColVecs(X)
 ```
 This is similar to the convention used in [Distances.jl](https://github.com/JuliaStats/Distances.jl).
 
-See [Input Types](@ref) for a more thorough discussion of these two approaches.
+### So what type should I use to represent a collection of inputs?
+The central assumption made by KernelFunctions.jl is that all collections of `N` inputs are represented by `AbstractVector`s of length `N`.
+Abstraction is then used to ensure that efficiency is retained, `ColVecs` and `RowVecs`
+being the most obvious examples of this.
+
+Concretely:
+1. For `Real`-valued inputs (scalars), a `Vector{<:Real}` is fine.
+1. For vector-valued inputs, consider a `ColVecs` or `RowVecs`.
+1. For a new input type, simply represent collections of inputs of this type as an `AbstractVector`.
+
+See [Input Types](@ref) and [Design](@ref) for a more thorough discussion of the
+considerations made when this design was adopted.
+
+The `obsdim` kwarg mentioned above is a special case for vector-valued inputs stored in a
+matrix.
+It is implemented as a lightweight wrapper that constructs either a `RowVecs` or `ColVecs`
+from your inputs, and passes this on.
+
 
 
+### Output Types
 
-We also support specific kernel matrix outputs:
+In addition to plain `Matrix`-like output, KernelFunctions.jl supports specific output
+types:
 - For a positive-definite matrix object of type `PDMat` from [`PDMats.jl`](https://github.com/JuliaStats/PDMats.jl), you can call the following:
 ```julia
 using PDMats
diff --git a/examples/README.md b/examples/README.md
new file mode 100644
index 000000000..de6ea3569
--- /dev/null
+++ b/examples/README.md
@@ -0,0 +1,52 @@
+# Example notebooks
+
+The examples in this directory are stored in [Literate.jl](https://github.com/fredrikekre/Literate.jl) format.
+
+To run them locally, navigate to the directory with the example that you want to run and
+start the Julia REPL and activate the project environment of the example:
+```julia
+julia> ] activate .
+```
+Alternatively, you can start Julia with `julia --project=.`. Then install all required
+packages with
+```julia
+julia> ] instantiate
+```
+Afterwards simply run
+```julia
+julia> include("script.jl")
+```
+In particular when editing an example, it can be convenient to (re-)run only some parts of
+an example.
+Many editors with Julia support such as VSCode, Juno, and Emacs support the evaluation of individual lines or code chunks.
+
+You can convert a notebook to markdown and Jupyter notebook formats, respectively, by executing
+```julia
+julia> using Literate
+julia> Literate.markdown("script.jl", "output_directory")
+julia> Literate.notebook("script.jl", "output_directory")
+```
+(see the [Literate.jl docs](https://fredrikekre.github.io/Literate.jl/v2/) for additional options) or run
+```shell
+julia docs/literate.jl myexample output_directory
+```
+which also executes the code and generates embedded plots etc. in the same way as in building the KernelFunctions documentation.
+
+## Add a new example
+
+Create a new subdirectory in here, and put your code in a file called `script.jl` so that it will get picked up by the automatic docs build.
+
+Every example uses a separate project environment. Therefore you should also create a new
+project environment in the directory of the example that contains all packages required by your script.
+Note that the dependencies of your example *must* include the `Literate` package.
+
+From a Julia REPL started in your example script's directory, you can run
+```julia
+julia> ] activate .
+julia> ] add Literate
+julia> ] add KernelFunctions
+julia> # add any other example-specific dependencies
+```
+to generate the project files.
+
+Make sure to commit both the `Project.toml` and the `Manifest.toml` file when you want to contribute your example in a pull request.
diff --git a/examples/deep-kernel-learning/Manifest.toml b/examples/deep-kernel-learning/Manifest.toml
new file mode 100644
index 000000000..c3a4f40f2
--- /dev/null
+++ b/examples/deep-kernel-learning/Manifest.toml
@@ -0,0 +1,1156 @@
+# This file is machine-generated - editing it directly is not advised
+
+[[AbstractFFTs]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "485ee0867925449198280d4af84bdb46a2a404d0"
+uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
+version = "1.0.1"
+
+[[AbstractTrees]]
+git-tree-sha1 = "03e0550477d86222521d254b741d470ba17ea0b5"
+uuid = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
+version = "0.3.4"
+
+[[Adapt]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "84918055d15b3114ede17ac6a7182f68870c16f7"
+uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
+version = "3.3.1"
+
+[[ArgTools]]
+uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
+
+[[Artifacts]]
+uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
+
+[[BFloat16s]]
+deps = ["LinearAlgebra", "Test"]
+git-tree-sha1 = "4af69e205efc343068dc8722b8dfec1ade89254a"
+uuid = "ab4f0b2a-ad5b-11e8-123f-65d77653426b"
+version = "0.1.0"
+
+[[Base64]]
+uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
+
+[[Bzip2_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "c3598e525718abcc440f69cc6d5f60dda0a1b61e"
+uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
+version = "1.0.6+5"
+
+[[CEnum]]
+git-tree-sha1 = "215a9aa4a1f23fbd05b92769fdd62559488d70e9"
+uuid = "fa961155-64e5-5f13-b03f-caf6b980ea82"
+version = "0.4.1"
+
+[[CUDA]]
+deps = ["AbstractFFTs", "Adapt", "BFloat16s", "CEnum", "CompilerSupportLibraries_jll", "DataStructures", "ExprTools", "GPUArrays", "GPUCompiler", "LLVM", "LazyArtifacts", "Libdl", "LinearAlgebra", "Logging", "Memoization", "Printf", "Random", "Random123", "RandomNumbers", "Reexport", "Requires", "SparseArrays", "SpecialFunctions", "TimerOutputs"]
+git-tree-sha1 = "f6f6d2fc7a80b7710b2db4ecb1f59a1b2c2a715a"
+uuid = "052768ef-5323-5732-b1bb-66c8b64840ba"
+version = "3.3.0"
+
+[[Cairo_jll]]
+deps = ["Artifacts", "Bzip2_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
+git-tree-sha1 = "e2f47f6d8337369411569fd45ae5753ca10394c6"
+uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
+version = "1.16.0+6"
+
+[[ChainRules]]
+deps = ["ChainRulesCore", "Compat", "LinearAlgebra", "Random", "Statistics"]
+git-tree-sha1 = "a41f9e72cffd789d5e19e75f1626b2786d640151"
+uuid = "082447d4-558c-5d27-93f4-14fc19e9eca2"
+version = "0.8.11"
+
+[[ChainRulesCore]]
+deps = ["Compat", "LinearAlgebra", "SparseArrays"]
+git-tree-sha1 = "dbc9aae1227cfddaa9d2552f3ecba5b641f6cce9"
+uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+version = "0.10.5"
+
+[[CodecZlib]]
+deps = ["TranscodingStreams", "Zlib_jll"]
+git-tree-sha1 = "ded953804d019afa9a3f98981d99b33e3db7b6da"
+uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
+version = "0.7.0"
+
+[[ColorSchemes]]
+deps = ["ColorTypes", "Colors", "FixedPointNumbers", "Random", "StaticArrays"]
+git-tree-sha1 = "c8fd01e4b736013bc61b704871d20503b33ea402"
+uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
+version = "3.12.1"
+
+[[ColorTypes]]
+deps = ["FixedPointNumbers", "Random"]
+git-tree-sha1 = "024fe24d83e4a5bf5fc80501a314ce0d1aa35597"
+uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
+version = "0.11.0"
+
+[[Colors]]
+deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
+git-tree-sha1 = "417b0ed7b8b838aa6ca0a87aadf1bb9eb111ce40"
+uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
+version = "0.12.8"
+
+[[CommonSubexpressions]]
+deps = ["MacroTools", "Test"]
+git-tree-sha1 = "7b8a93dba8af7e3b42fecabf646260105ac373f7"
+uuid = "bbf7d656-a473-5ed7-a52c-81e309532950"
+version = "0.3.0"
+
+[[Compat]]
+deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
+git-tree-sha1 = "e4e2b39db08f967cc1360951f01e8a75ec441cab"
+uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
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+[[Xorg_libX11_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
+git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
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+[[Xorg_libXcursor_jll]]
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+
+[[Xorg_libXdmcp_jll]]
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+
+[[Xorg_libXext_jll]]
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+git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
+uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
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+
+[[Xorg_libXfixes_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
+git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
+uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
+version = "5.0.3+4"
+
+[[Xorg_libXi_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
+git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
+uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
+version = "1.7.10+4"
+
+[[Xorg_libXinerama_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
+git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
+uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
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+
+[[Xorg_libXrandr_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
+git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
+uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
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+
+[[Xorg_libXrender_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
+git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
+uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
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+
+[[Xorg_libpthread_stubs_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
+uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
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+
+[[Xorg_libxcb_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
+git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
+uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
+version = "1.13.0+3"
+
+[[Xorg_libxkbfile_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
+git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
+uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
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+
+[[Xorg_xcb_util_image_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
+uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
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+
+[[Xorg_xcb_util_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
+git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
+uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
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+
+[[Xorg_xcb_util_keysyms_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
+uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
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+
+[[Xorg_xcb_util_renderutil_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
+uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
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+
+[[Xorg_xcb_util_wm_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
+uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
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+
+[[Xorg_xkbcomp_jll]]
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+git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
+uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
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+
+[[Xorg_xkeyboard_config_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
+git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
+uuid = "33bec58e-1273-512f-9401-5d533626f822"
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+
+[[Xorg_xtrans_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
+uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
+version = "1.4.0+3"
+
+[[ZipFile]]
+deps = ["Libdl", "Printf", "Zlib_jll"]
+git-tree-sha1 = "c3a5637e27e914a7a445b8d0ad063d701931e9f7"
+uuid = "a5390f91-8eb1-5f08-bee0-b1d1ffed6cea"
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+
+[[Zlib_jll]]
+deps = ["Libdl"]
+uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
+
+[[Zstd_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "cc4bf3fdde8b7e3e9fa0351bdeedba1cf3b7f6e6"
+uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
+version = "1.5.0+0"
+
+[[Zygote]]
+deps = ["AbstractFFTs", "ChainRules", "ChainRulesCore", "DiffRules", "Distributed", "FillArrays", "ForwardDiff", "IRTools", "InteractiveUtils", "LinearAlgebra", "MacroTools", "NaNMath", "Random", "Requires", "SpecialFunctions", "Statistics", "ZygoteRules"]
+git-tree-sha1 = "b1d95edd4e693066c38c13a10aab0a8f6a6e2f65"
+uuid = "e88e6eb3-aa80-5325-afca-941959d7151f"
+version = "0.6.12"
+
+[[ZygoteRules]]
+deps = ["MacroTools"]
+git-tree-sha1 = "9e7a1e8ca60b742e508a315c17eef5211e7fbfd7"
+uuid = "700de1a5-db45-46bc-99cf-38207098b444"
+version = "0.2.1"
+
+[[libass_jll]]
+deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "acc685bcf777b2202a904cdcb49ad34c2fa1880c"
+uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
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+
+[[libfdk_aac_jll]]
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+git-tree-sha1 = "7a5780a0d9c6864184b3a2eeeb833a0c871f00ab"
+uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
+version = "0.1.6+4"
+
+[[libpng_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
+uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
+version = "1.6.38+0"
+
+[[libvorbis_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
+git-tree-sha1 = "c45f4e40e7aafe9d086379e5578947ec8b95a8fb"
+uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
+version = "1.3.7+0"
+
+[[nghttp2_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
+
+[[p7zip_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
+
+[[x264_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "d713c1ce4deac133e3334ee12f4adff07f81778f"
+uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
+version = "2020.7.14+2"
+
+[[x265_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "487da2f8f2f0c8ee0e83f39d13037d6bbf0a45ab"
+uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
+version = "3.0.0+3"
+
+[[xkbcommon_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
+git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
+uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
+version = "0.9.1+5"
diff --git a/examples/deep-kernel-learning/Project.toml b/examples/deep-kernel-learning/Project.toml
new file mode 100644
index 000000000..f3b3a5b77
--- /dev/null
+++ b/examples/deep-kernel-learning/Project.toml
@@ -0,0 +1,19 @@
+[deps]
+Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
+Flux = "587475ba-b771-5e3f-ad9e-33799f191a9c"
+KernelFunctions = "ec8451be-7e33-11e9-00cf-bbf324bd1392"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+Literate = "98b081ad-f1c9-55d3-8b20-4c87d4299306"
+MLDataUtils = "cc2ba9b6-d476-5e6d-8eaf-a92d5412d41d"
+Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
+
+[compat]
+Distributions = "0.25"
+Flux = "0.12"
+KernelFunctions = "0.10"
+Literate = "2"
+MLDataUtils = "0.5"
+Plots = "1"
+Zygote = "0.6"
+julia = "1.3"
diff --git a/examples/deepkernellearning.jl b/examples/deep-kernel-learning/script.jl
similarity index 54%
rename from examples/deepkernellearning.jl
rename to examples/deep-kernel-learning/script.jl
index 94346eea2..14c1560c3 100644
--- a/examples/deepkernellearning.jl
+++ b/examples/deep-kernel-learning/script.jl
@@ -1,3 +1,10 @@
+# # Deep Kernel Learning
+#
+# !!! warning
+#     This example is under construction
+
+# Setup
+
 using KernelFunctions
 using MLDataUtils
 using Zygote
@@ -10,31 +17,52 @@ Flux.@functor KernelSum
 Flux.@functor Matern32Kernel
 Flux.@functor FunctionTransform
 
+# set up a kernel with a neural network feature extractor:
+
 neuralnet = Chain(Dense(1, 3), Dense(3, 2))
-k = SqExponentialKernel(FunctionTransform(neuralnet))
+k = SqExponentialKernel() ∘ FunctionTransform(neuralnet)
+
+# Generate date
+
 xmin = -3;
 xmax = 3;
 x = range(xmin, xmax; length=100)
 x_test = rand(Uniform(xmin, xmax), 200)
 x, y = noisy_function(sinc, x; noise=0.1)
-X = reshape(x, :, 1)
+X = RowVecs(reshape(x, :, 1))
+X_test = RowVecs(reshape(x_test, :, 1))
 λ = [0.1]
-function f(x, k, λ)
-    return kernelmatrix(k, X, x; obsdim=1) *
-           inv(kernelmatrix(k, X; obsdim=1) + exp(λ[1]) * I) *
-           y
-end
+#md nothing #hide
+
+#
+
+f(x, k, λ) = kernelmatrix(k, x, X) / (kernelmatrix(k, X) + exp(λ[1]) * I) * y
 f(X, k, 1.0)
-loss(k, λ) = ŷ -> sum(y - ŷ) / length(y) + exp(λ[1]) * norm(ŷ)(f(X, k, λ))
+
+#
+
+loss(k, λ) = (ŷ -> sum(y - ŷ) / length(y) + exp(λ[1]) * norm(ŷ))(f(X, k, λ))
 loss(k, λ)
+
+#
+
 ps = Flux.params(k)
 # push!(ps,λ)
 opt = Flux.Momentum(1.0)
-##
+#md nothing #hide
+
+#
+
+plots = []
 for i in 1:10
     grads = Zygote.gradient(() -> loss(k, λ), ps)
     Flux.Optimise.update!(opt, ps, grads)
     p = Plots.scatter(x, y; lab="data", title="Loss = $(loss(k,λ))")
     Plots.plot!(x, f(X, k, λ); lab="Prediction", lw=3.0)
-    display(p)
+    push!(plots, p)
 end
+
+#
+
+l = @layout grid(10, 1)
+plot(plots...; layout=l, size=(300, 1500))
diff --git a/examples/gaussian-process-priors/Manifest.toml b/examples/gaussian-process-priors/Manifest.toml
new file mode 100644
index 000000000..1b421a0ce
--- /dev/null
+++ b/examples/gaussian-process-priors/Manifest.toml
@@ -0,0 +1,921 @@
+# This file is machine-generated - editing it directly is not advised
+
+[[Adapt]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "84918055d15b3114ede17ac6a7182f68870c16f7"
+uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
+version = "3.3.1"
+
+[[ArgTools]]
+uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
+
+[[Artifacts]]
+uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
+
+[[Base64]]
+uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
+
+[[Bzip2_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "c3598e525718abcc440f69cc6d5f60dda0a1b61e"
+uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
+version = "1.0.6+5"
+
+[[Cairo_jll]]
+deps = ["Artifacts", "Bzip2_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
+git-tree-sha1 = "e2f47f6d8337369411569fd45ae5753ca10394c6"
+uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
+version = "1.16.0+6"
+
+[[ChainRulesCore]]
+deps = ["Compat", "LinearAlgebra", "SparseArrays"]
+git-tree-sha1 = "be770c08881f7bb928dfd86d1ba83798f76cf62a"
+uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+version = "0.10.9"
+
+[[ColorSchemes]]
+deps = ["ColorTypes", "Colors", "FixedPointNumbers", "Random", "StaticArrays"]
+git-tree-sha1 = "c8fd01e4b736013bc61b704871d20503b33ea402"
+uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
+version = "3.12.1"
+
+[[ColorTypes]]
+deps = ["FixedPointNumbers", "Random"]
+git-tree-sha1 = "024fe24d83e4a5bf5fc80501a314ce0d1aa35597"
+uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
+version = "0.11.0"
+
+[[Colors]]
+deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
+git-tree-sha1 = "417b0ed7b8b838aa6ca0a87aadf1bb9eb111ce40"
+uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
+version = "0.12.8"
+
+[[Compat]]
+deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
+git-tree-sha1 = "dc7dedc2c2aa9faf59a55c622760a25cbefbe941"
+uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
+version = "3.31.0"
+
+[[CompilerSupportLibraries_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
+
+[[CompositionsBase]]
+git-tree-sha1 = "f3955eb38944e5dd0fabf8ca1e267d94941d34a5"
+uuid = "a33af91c-f02d-484b-be07-31d278c5ca2b"
+version = "0.1.0"
+
+[[Contour]]
+deps = ["StaticArrays"]
+git-tree-sha1 = "9f02045d934dc030edad45944ea80dbd1f0ebea7"
+uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
+version = "0.5.7"
+
+[[DataAPI]]
+git-tree-sha1 = "ee400abb2298bd13bfc3df1c412ed228061a2385"
+uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
+version = "1.7.0"
+
+[[DataStructures]]
+deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
+git-tree-sha1 = "4437b64df1e0adccc3e5d1adbc3ac741095e4677"
+uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
+version = "0.18.9"
+
+[[DataValueInterfaces]]
+git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
+uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464"
+version = "1.0.0"
+
+[[Dates]]
+deps = ["Printf"]
+uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
+
+[[DelimitedFiles]]
+deps = ["Mmap"]
+uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
+
+[[Distances]]
+deps = ["LinearAlgebra", "Statistics", "StatsAPI"]
+git-tree-sha1 = "abe4ad222b26af3337262b8afb28fab8d215e9f8"
+uuid = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
+version = "0.10.3"
+
+[[Distributed]]
+deps = ["Random", "Serialization", "Sockets"]
+uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
+
+[[Distributions]]
+deps = ["FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns"]
+git-tree-sha1 = "2733323e5c02a9d7f48e7a3c4bc98d764fb704da"
+uuid = "31c24e10-a181-5473-b8eb-7969acd0382f"
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+git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
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diff --git a/examples/gaussian-process-priors/Project.toml b/examples/gaussian-process-priors/Project.toml
new file mode 100644
index 000000000..44e7d9f0d
--- /dev/null
+++ b/examples/gaussian-process-priors/Project.toml
@@ -0,0 +1,13 @@
+[deps]
+Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
+KernelFunctions = "ec8451be-7e33-11e9-00cf-bbf324bd1392"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+Literate = "98b081ad-f1c9-55d3-8b20-4c87d4299306"
+Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+
+[compat]
+Distributions = "0.25"
+KernelFunctions = "0.10"
+Literate = "2"
+Plots = "1"
diff --git a/examples/gaussian-process-priors/script.jl b/examples/gaussian-process-priors/script.jl
new file mode 100644
index 000000000..b1ba3dcee
--- /dev/null
+++ b/examples/gaussian-process-priors/script.jl
@@ -0,0 +1,128 @@
+# # Gaussian process prior samples
+#
+# The kernels defined in this package can also be used to specify the
+# covariance of a Gaussian process prior.
+# A Gaussian process (GP) is defined by its mean function $m(\cdot)$ and its covariance function or kernel $k(\cdot, \cdot')$:
+# ```math
+#   f \sim \mathcal{GP}\big(m(\cdot), k(\cdot, \cdot')\big)
+# ```
+# In this notebook we show how the choice of kernel affects the samples from a GP (with zero mean).
+
+## Load required packages
+using KernelFunctions, LinearAlgebra
+using Plots, Plots.PlotMeasures
+default(; lw=1.0, legendfontsize=8.0)
+using Random: seed!
+seed!(42); # reproducibility
+
+##
+# ## Evaluation at finite set of points
+#
+# The function values $\mathbf{f} = \{f(x_n)\}_{n=1}^N$ of the GP at a finite number $N$ of points $X = \{x_n\}_{n=1}^N$ follow a multivariate normal distribution $\mathbf{f} \sim \mathcal{MVN}(\mathbf{m}, \mathrm{K})$ with mean vector $\mathbf{m}$ and covariance matrix $\mathrm{K}$, where
+# ```math
+# \begin{aligned}
+#   \mathbf{m}_i &= m(x_i) \\
+#   \mathrm{K}_{i,j} &= k(x_i, x_j)
+# \end{aligned}
+# ```
+# with $1 \le i, j \le N$.
+#
+# We can visualize the infinite-dimensional GP by evaluating it on a fine grid to approximate the dense real line:
+num_inputs = 101
+xlim = (-5, 5)
+X = range(xlim...; length=num_inputs);
+
+# Given a kernel `k`, we can compute the kernel matrix as `K = kernelmatrix(k, X)`.
+
+##
+# ## Random samples
+#
+# To sample from the multivariate normal distribution $p(\mathbf{f}) = \mathcal{MVN}(0, \mathrm{K})$, we could make use of Distributions.jl and call `rand(MvNormal(K))`.
+# Alternatively, we could use the [AbstractGPs.jl](https://github.com/JuliaGaussianProcesses/AbstractGPs.jl) package and construct a `GP` object which we evaluate at the points of interest and from which we can then sample: `rand(GP(k)(X))`.
+
+# Here, we will explicitly construct samples using the Cholesky factorization $\mathrm{L} = \operatorname{cholesky}(\mathrm{K})$,
+# with $\mathbf{f} = \mathrm{L} \mathbf{v}$, where $\mathbf{v} \sim \mathcal{N}(0, \mathbf{I})$ is a vector of standard-normal random variables.
+
+# We will use the same randomness $\mathbf{v}$ to generate comparable samples across different kernels.
+num_samples = 7
+v = randn(num_inputs, num_samples);
+
+# Mathematically, a kernel matrix is by definition positive semi-definite, but due to finite-precision inaccuracies, the computed kernel matrix might not be exactly positive definite. To avoid Cholesky errors, we add a small "nugget" term on the diagonal:
+function mvn_sample(K)
+    L = cholesky(K + 1e-6 * I)
+    f = L.L * v
+    return f
+end;
+
+##
+# ## Visualization
+# We now define a function that visualizes a kernel for us.
+
+function visualize(k::Kernel)
+    K = kernelmatrix(k, X)
+    f = mvn_sample(K)
+
+    p_kernel_2d = heatmap(
+        X,
+        X,
+        K;
+        yflip=true,
+        colorbar=false,
+        ylabel=string(nameof(typeof(k))),
+        ylim=xlim,
+        yticks=([xlim[1], 0, xlim[end]], ["\u22125", raw"$x'$", "5"]),
+        vlim=(0, 1),
+        title=raw"$k(x, x')$",
+        aspect_ratio=:equal,
+        left_margin=5mm,
+    )
+
+    p_kernel_cut = plot(
+        X,
+        k.(X, 0.0);
+        title=string(raw"$k(x, x_\mathrm{ref})$"),
+        label=raw"$x_\mathrm{ref}=0.0$",
+        legend=:topleft,
+        foreground_color_legend=nothing,
+    )
+    plot!(X, k.(X, 1.5); label=raw"$x_\mathrm{ref}=1.5$")
+
+    p_samples = plot(X, f; c="blue", title=raw"$f(x)$", ylim=(-3, 3), label=nothing)
+
+    return plot(
+        p_kernel_2d,
+        p_kernel_cut,
+        p_samples;
+        layout=(1, 3),
+        xlabel=raw"$x$",
+        xlim=xlim,
+        xticks=collect(xlim),
+    )
+end;
+
+##
+# We can now visualize a kernel and show samples from
+# a Gaussian process with a given kernel:
+
+plot(visualize(SqExponentialKernel()); size=(800, 210), bottommargin=5mm, topmargin=5mm)
+
+##
+# ## Kernel comparison
+# This also allows us to compare different kernels:
+
+kernels = [
+    Matern12Kernel(),
+    Matern32Kernel(),
+    Matern52Kernel(),
+    SqExponentialKernel(),
+    WhiteKernel(),
+    ConstantKernel(),
+    LinearKernel(),
+    compose(PeriodicKernel(), ScaleTransform(0.2)),
+    NeuralNetworkKernel(),
+]
+plot(
+    [visualize(k) for k in kernels]...;
+    layout=(length(kernels), 1),
+    size=(800, 220 * length(kernels) + 100),
+)
diff --git a/examples/kernel-ridge-regression/Manifest.toml b/examples/kernel-ridge-regression/Manifest.toml
new file mode 100644
index 000000000..8b8a2d648
--- /dev/null
+++ b/examples/kernel-ridge-regression/Manifest.toml
@@ -0,0 +1,921 @@
+# This file is machine-generated - editing it directly is not advised
+
+[[Adapt]]
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diff --git a/examples/kernel-ridge-regression/Project.toml b/examples/kernel-ridge-regression/Project.toml
new file mode 100644
index 000000000..13219d95c
--- /dev/null
+++ b/examples/kernel-ridge-regression/Project.toml
@@ -0,0 +1,13 @@
+[deps]
+Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
+KernelFunctions = "ec8451be-7e33-11e9-00cf-bbf324bd1392"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+Literate = "98b081ad-f1c9-55d3-8b20-4c87d4299306"
+Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+
+[compat]
+Distributions = "0.25"
+KernelFunctions = "0.10"
+Literate = "2"
+Plots = "1"
+julia = "1.3"
diff --git a/examples/kernel-ridge-regression/script.jl b/examples/kernel-ridge-regression/script.jl
new file mode 100644
index 000000000..62afc5944
--- /dev/null
+++ b/examples/kernel-ridge-regression/script.jl
@@ -0,0 +1,162 @@
+# # Kernel Ridge Regression
+#
+# Building on linear regression, we can fit non-linear data sets by introducing a feature space. In a higher-dimensional feature space, we can overfit the data; ridge regression introduces regularization to avoid this. In this notebook we show how we can use KernelFunctions.jl for *kernel* ridge regression.
+
+## Loading and setup of required packages
+using KernelFunctions
+using LinearAlgebra
+using Distributions
+
+## Plotting
+using Plots;
+default(; lw=2.0, legendfontsize=11.0, ylims=(-150, 500));
+
+using Random: seed!
+seed!(42);
+
+##
+# ## Toy data
+# Here we use a one-dimensional toy problem. We generate data using the fourth-order polynomial $f(x) = (x+4)(x+1)(x-1)(x-3)$:
+
+f_truth(x) = (x + 4) * (x + 1) * (x - 1) * (x - 3)
+
+x_train = -5:0.5:5
+x_test = -7:0.1:7
+
+noise = rand(Uniform(-20, 20), length(x_train))
+y_train = f_truth.(x_train) + noise
+y_test = f_truth.(x_test)
+
+plot(x_test, y_test; label=raw"$f(x)$")
+scatter!(x_train, y_train; seriescolor=1, label="observations")
+
+##
+# ## Linear regression
+# For training inputs $\mathrm{X}=(\mathbf{x}_n)_{n=1}^N$ and observations $\mathbf{y}=(y_n)_{n=1}^N$, the linear regression weights $\mathbf{w}$ using the least-squares estimator are given by
+# ```math
+# \mathbf{w} = (\mathrm{X}^\top \mathrm{X})^{-1} \mathrm{X}^\top \mathbf{y}
+# ```
+# We predict at test inputs $\mathbf{x}_*$ using
+# ```math
+# \hat{y}_* = \mathbf{x}_*^\top \mathbf{w}
+# ```
+# This is implemented by `linear_regression`:
+
+function linear_regression(X, y, Xstar)
+    weights = (X' * X) \ (X' * y)
+    return Xstar * weights
+end;
+
+# A linear regression fit to the above data set:
+
+y_pred = linear_regression(x_train, y_train, x_test)
+scatter(x_train, y_train; label="observations")
+plot!(x_test, y_pred; label="linear fit")
+
+##
+# ## Featurization
+# We can improve the fit by including additional features, i.e. generalizing to $\tilde{\mathrm{X}} = (\phi(x_n))_{n=1}^N$, where $\phi(x)$ constructs a feature vector for each input $x$. Here we include powers of the input, $\phi(x) = (1, x, x^2, \dots, x^d)$:
+
+function featurize_poly(x; degree=1)
+    return repeat(x, 1, degree + 1) .^ (0:degree)'
+end
+
+function featurized_fit_and_plot(degree)
+    X = featurize_poly(x_train; degree=degree)
+    Xstar = featurize_poly(x_test; degree=degree)
+    y_pred = linear_regression(X, y_train, Xstar)
+    scatter(x_train, y_train; legend=false, title="fit of order $degree")
+    return plot!(x_test, y_pred)
+end
+
+plot((featurized_fit_and_plot(degree) for degree in 1:4)...)
+
+##
+# Note that the fit becomes perfect when we include exactly as many orders in the features as we have in the underlying polynomial (4).
+#
+# However, when increasing the number of features, we can quickly overfit to noise in the data set:
+
+featurized_fit_and_plot(20)
+
+##
+# ## Ridge regression
+# To counteract this unwanted behaviour, we can introduce regularization. This leads to *ridge regression* with $L_2$ regularization of the weights ([Tikhonov regularization](https://en.wikipedia.org/wiki/Tikhonov_regularization)).
+# Instead of the weights in linear regression,
+# ```math
+# \mathbf{w} = (\mathrm{X}^\top \mathrm{X})^{-1} \mathrm{X}^\top \mathbf{y}
+# ```
+# we introduce the ridge parameter $\lambda$:
+# ```math
+# \mathbf{w} = (\mathrm{X}^\top \mathrm{X} + \lambda \mathbb{1})^{-1} \mathrm{X}^\top \mathbf{y}
+# ```
+# As before, we predict at test inputs $\mathbf{x}_*$ using
+# ```math
+# \hat{y}_* = \mathbf{x}_*^\top \mathbf{w}
+# ```
+# This is implemented by `ridge_regression`:
+
+function ridge_regression(X, y, Xstar, lambda)
+    weights = (X' * X + lambda * I) \ (X' * y)
+    return Xstar * weights
+end
+
+function regularized_fit_and_plot(degree, lambda)
+    X = featurize_poly(x_train; degree=degree)
+    Xstar = featurize_poly(x_test; degree=degree)
+    y_pred = ridge_regression(X, y_train, Xstar, lambda)
+    scatter(x_train, y_train; legend=false, title="\$\\lambda=$lambda\$")
+    return plot!(x_test, y_pred)
+end
+
+plot((regularized_fit_and_plot(20, lambda) for lambda in (1e-3, 1e-2, 1e-1, 1))...)
+
+##
+# ## Kernel ridge regression
+# Instead of constructing the feature matrix explicitly, we can use *kernels* to replace inner products of feature vectors with a kernel evaluation: $\langle \phi(x), \phi(x') \rangle = k(x, x')$ or $\tilde{\mathrm{X}} \tilde{\mathrm{X}}^\top = \mathrm{K}$, where $\mathrm{K}_{ij} = k(x_i, x_j)$.
+#
+# To apply this "kernel trick" to ridge regression, we can rewrite the ridge estimate for the weights
+# ```math
+# \mathbf{w} = (\mathrm{X}^\top \mathrm{X} + \lambda \mathbb{1})^{-1} \mathrm{X}^\top \mathbf{y}
+# ```
+# using the [matrix inversion lemma](https://tlienart.github.io/pub/csml/mtheory/matinvlem.html#basic_lemmas)
+# as
+# ```math
+# \mathbf{w} = \mathrm{X}^\top (\mathrm{X} \mathrm{X}^\top + \lambda \mathbb{1})^{-1} \mathbf{y}
+# ```
+# where we can now replace the inner product with the kernel matrix,
+# ```math
+# \mathbf{w} = \mathrm{X}^\top (\mathrm{K} + \lambda \mathbb{1})^{-1} \mathbf{y}
+# ```
+# And the prediction yields another inner product,
+# ```math
+# \hat{y}_* = \mathbf{x}_*^\top \mathbf{w} = \langle \mathbf{x}_*, \mathbf{w} \rangle = \mathbf{k}_* (\mathrm{K} + \lambda \mathbb{1})^{-1} \mathbf{y}
+# ```
+# where $(\mathbf{k}_*)_n = k(x_*, x_n)$.
+#
+# This is implemented by `kernel_ridge_regression`:
+
+function kernel_ridge_regression(k, X, y, Xstar, lambda)
+    K = kernelmatrix(k, X)
+    kstar = kernelmatrix(k, Xstar, X)
+    return kstar * ((K + lambda * I) \ y)
+end;
+
+# Now, instead of explicitly constructing features, we can simply pass in a `PolynomialKernel` object:
+
+function kernelized_fit_and_plot(kernel, lambda=1e-4)
+    y_pred = kernel_ridge_regression(kernel, x_train, y_train, x_test, lambda)
+    if kernel isa PolynomialKernel
+        title = string("order ", kernel.degree)
+    else
+        title = string(nameof(typeof(kernel)))
+    end
+    scatter(x_train, y_train; label=nothing)
+    return plot!(x_test, y_pred; label=nothing, title=title)
+end
+
+plot((kernelized_fit_and_plot(PolynomialKernel(; degree=degree, c=1)) for degree in 1:4)...)
+
+##
+# However, we can now also use kernels that would have an infinite-dimensional feature expansion, such as the squared exponential kernel:
+
+kernelized_fit_and_plot(SqExponentialKernel())
diff --git a/examples/kernelridgeregression.jl b/examples/kernelridgeregression.jl
deleted file mode 100644
index 0bc02f25a..000000000
--- a/examples/kernelridgeregression.jl
+++ /dev/null
@@ -1,40 +0,0 @@
-using KernelFunctions
-using MLDataUtils
-using Zygote
-using Flux
-using Distributions, LinearAlgebra
-using Plots
-
-Flux.@functor SqExponentialKernel
-Flux.@functor ScaleTransform
-Flux.@functor KernelSum
-Flux.@functor Matern32Kernel
-
-xmin = -3;
-xmax = 3;
-x = range(xmin, xmax; length=100)
-x_test = range(xmin, xmax; length=300)
-x, y = noisy_function(sinc, x; noise=0.1)
-X = reshape(x, :, 1)
-X_test = reshape(x_test, :, 1)
-k = SqExponentialKernel(1.0)#+Matern32Kernel(2.0)
-λ = [-1.0]
-function f(x, k, λ)
-    return kernelmatrix(k, x, X; obsdim=1) *
-           inv(kernelmatrix(k, X; obsdim=1) + exp(λ[1]) * I) *
-           y
-end
-f(X, k, 1.0)
-loss(k, λ) = ŷ -> sum(y - ŷ) / length(y) + exp(λ[1]) * norm(ŷ)(f(X, k, λ))
-loss(k, λ)
-ps = Flux.params(k)
-push!(ps, λ)
-opt = Flux.Momentum(0.1)
-##
-for i in 1:10
-    grads = Zygote.gradient(() -> loss(k, λ), ps)
-    Flux.Optimise.update!(opt, ps, grads)
-    p = Plots.scatter(x, y; lab="data", title="Loss = $(loss(k,λ))")
-    Plots.plot!(x_test, f(X_test, k, λ); lab="Prediction", lw=3.0)
-    display(p)
-end
diff --git a/examples/support-vector-machine/Manifest.toml b/examples/support-vector-machine/Manifest.toml
new file mode 100644
index 000000000..8b8a2d648
--- /dev/null
+++ b/examples/support-vector-machine/Manifest.toml
@@ -0,0 +1,921 @@
+# This file is machine-generated - editing it directly is not advised
+
+[[Adapt]]
+deps = ["LinearAlgebra"]
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+git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
+uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
+version = "0.4.0+1"
+
+[[Xorg_xcb_util_renderutil_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
+uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
+version = "0.3.9+1"
+
+[[Xorg_xcb_util_wm_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
+git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
+uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
+version = "0.4.1+1"
+
+[[Xorg_xkbcomp_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
+git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
+uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
+version = "1.4.2+4"
+
+[[Xorg_xkeyboard_config_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
+git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
+uuid = "33bec58e-1273-512f-9401-5d533626f822"
+version = "2.27.0+4"
+
+[[Xorg_xtrans_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
+uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
+version = "1.4.0+3"
+
+[[Zlib_jll]]
+deps = ["Libdl"]
+uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
+
+[[Zstd_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "cc4bf3fdde8b7e3e9fa0351bdeedba1cf3b7f6e6"
+uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
+version = "1.5.0+0"
+
+[[ZygoteRules]]
+deps = ["MacroTools"]
+git-tree-sha1 = "9e7a1e8ca60b742e508a315c17eef5211e7fbfd7"
+uuid = "700de1a5-db45-46bc-99cf-38207098b444"
+version = "0.2.1"
+
+[[libass_jll]]
+deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "acc685bcf777b2202a904cdcb49ad34c2fa1880c"
+uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
+version = "0.14.0+4"
+
+[[libfdk_aac_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "7a5780a0d9c6864184b3a2eeeb833a0c871f00ab"
+uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
+version = "0.1.6+4"
+
+[[libpng_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
+git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
+uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
+version = "1.6.38+0"
+
+[[libvorbis_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
+git-tree-sha1 = "c45f4e40e7aafe9d086379e5578947ec8b95a8fb"
+uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
+version = "1.3.7+0"
+
+[[nghttp2_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
+
+[[p7zip_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
+
+[[x264_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "d713c1ce4deac133e3334ee12f4adff07f81778f"
+uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
+version = "2020.7.14+2"
+
+[[x265_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "487da2f8f2f0c8ee0e83f39d13037d6bbf0a45ab"
+uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
+version = "3.0.0+3"
+
+[[xkbcommon_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
+git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
+uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
+version = "0.9.1+5"
diff --git a/examples/support-vector-machine/Project.toml b/examples/support-vector-machine/Project.toml
new file mode 100644
index 000000000..13219d95c
--- /dev/null
+++ b/examples/support-vector-machine/Project.toml
@@ -0,0 +1,13 @@
+[deps]
+Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
+KernelFunctions = "ec8451be-7e33-11e9-00cf-bbf324bd1392"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+Literate = "98b081ad-f1c9-55d3-8b20-4c87d4299306"
+Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+
+[compat]
+Distributions = "0.25"
+KernelFunctions = "0.10"
+Literate = "2"
+Plots = "1"
+julia = "1.3"
diff --git a/examples/support-vector-machine/script.jl b/examples/support-vector-machine/script.jl
new file mode 100644
index 000000000..7cf80cac4
--- /dev/null
+++ b/examples/support-vector-machine/script.jl
@@ -0,0 +1,42 @@
+# # Support Vector Machine
+#
+# !!! warning
+#     This example is under construction
+
+using KernelFunctions
+using Distributions
+using Plots
+
+using LinearAlgebra
+using Random
+
+## Set plotting theme
+theme(:wong)
+
+## Set seed
+Random.seed!(1234);
+
+# Number of samples:
+N = 100;
+
+# Select randomly between two classes:
+y = rand([-1, 1], N);
+
+# Random attributes for both classes:
+X = Matrix{Float64}(undef, 2, N)
+rand!(MvNormal(randn(2), I), view(X, :, y .== 1))
+rand!(MvNormal(randn(2), I), view(X, :, y .== -1));
+
+# Create a 2D grid:
+xgrid = range(floor(Int, minimum(X)), ceil(Int, maximum(X)); length=100)
+Xgrid = ColVecs(mapreduce(collect, hcat, Iterators.product(xgrid, xgrid)));
+
+# Create kernel function:
+k = SqExponentialKernel() ∘ ScaleTransform(2.0)
+
+# Optimal prediction:
+f(x, X, k, λ) = kernelmatrix(k, x, X) / (kernelmatrix(k, X) + exp(λ) * I) * y
+
+# Compute prediction on a grid:
+contourf(xgrid, xgrid, f(Xgrid, ColVecs(X), k, 0.1))
+scatter!(X[1, :], X[2, :]; color=y, lab="data", widen=false)
diff --git a/examples/svm.jl b/examples/svm.jl
deleted file mode 100644
index 34f7ec632..000000000
--- a/examples/svm.jl
+++ /dev/null
@@ -1,26 +0,0 @@
-using KernelFunctions
-using MLDataUtils
-using Zygote
-using Flux
-using Distributions, LinearAlgebra
-using Plots
-
-N = 100 #Number of samples
-μ = randn(2, 2) # Random Centers
-xgrid = range(-3, 3; length=100) # Create a grid
-Xgrid = hcat(collect.(Iterators.product(xgrid, xgrid))...)' #Combine into a 2D grid
-y = rand([-1, 1], N) # Select randomly between the two classes
-X = zeros(N, 2)
-X[y .== 1, :] = rand(MvNormal(μ[:, 1], I), count(y .== 1))' #Attribute samples from class 1
-X[y .== -1, :] = rand(MvNormal(μ[:, 2], I), count(y .== -1))' # Attribute samples from class 2
-
-k = SqExponentialKernel(2.0) # Create kernel function
-function f(x, k, λ)
-    return kernelmatrix(k, x, X; obsdim=1) *
-           inv(kernelmatrix(k, X; obsdim=1) + exp(λ[1]) * I) *
-           y
-end # Optimal prediction f
-svmloss(y, ŷ) = ŷ -> sum(maximum.(0.0, 1 - y * ŷ)) - λ * norm(ŷ)(f(X, k, λ)) # Total svm loss with regularisation
-pred = f(Xgrid, k, λ) #Compute prediction on a grid
-contourf(xgrid, xgrid, pred)
-scatter!(eachcol(X)...; color=y, lab="data")
diff --git a/src/KernelFunctions.jl b/src/KernelFunctions.jl
index 670c1c8f6..248993573 100644
--- a/src/KernelFunctions.jl
+++ b/src/KernelFunctions.jl
@@ -27,6 +27,7 @@ export Transform,
     IdentityTransform,
     FunctionTransform,
     PeriodicTransform
+export with_lengthscale
 
 export NystromFact, nystrom
 
@@ -36,7 +37,8 @@ export spectral_mixture_kernel, spectral_mixture_product_kernel
 export ColVecs, RowVecs
 
 export MOInput
-export IndependentMOKernel, LatentFactorMOKernel, IntrinsicCoregionMOKernel
+export IndependentMOKernel,
+    LatentFactorMOKernel, IntrinsicCoregionMOKernel, LinearMixingModelKernel
 
 # Reexports
 export tensor, ⊗, compose
@@ -74,6 +76,7 @@ include(joinpath("transform", "selecttransform.jl"))
 include(joinpath("transform", "chaintransform.jl"))
 include(joinpath("transform", "periodic_transform.jl"))
 include(joinpath("kernels", "transformedkernel.jl"))
+include(joinpath("transform", "with_lengthscale.jl"))
 
 include(joinpath("basekernels", "constant.jl"))
 include(joinpath("basekernels", "cosine.jl"))
@@ -106,6 +109,7 @@ include(joinpath("mokernels", "moinput.jl"))
 include(joinpath("mokernels", "independent.jl"))
 include(joinpath("mokernels", "slfm.jl"))
 include(joinpath("mokernels", "intrinsiccoregion.jl"))
+include(joinpath("mokernels", "lmm.jl"))
 
 include("chainrules.jl")
 include("zygoterules.jl")
diff --git a/src/matrix/kernelmatrix.jl b/src/matrix/kernelmatrix.jl
index da42bec37..888026a23 100644
--- a/src/matrix/kernelmatrix.jl
+++ b/src/matrix/kernelmatrix.jl
@@ -24,9 +24,16 @@ kernelmatrix!
 
 """
     kernelmatrix(κ::Kernel, x::AbstractVector)
+
+Compute the kernel `κ` for each pair of inputs in `x`.
+Returns a matrix of size `(length(x), length(x))` satisfying
+`kernelmatrix(κ, x)[p, q] == κ(x[p], x[q])`.
+
     kernelmatrix(κ::Kernel, x::AbstractVector, y::AbstractVector)
 
-Calculate the kernel matrix of `x` (and `y`) with respect to kernel `κ`.
+Compute the kernel `κ` for each pair of inputs in `x` and `y`.
+Returns a matrix of size `(length(x), length(y))` satisfying
+`kernelmatrix(κ, x, y)[p, q] == κ(x[p], y[q])`.
 
     kernelmatrix(κ::Kernel, X::AbstractMatrix; obsdim::Int=2)
     kernelmatrix(κ::Kernel, X::AbstractMatrix, Y::AbstractMatrix; obsdim::Int=2)
@@ -65,11 +72,11 @@ kernelmatrix_diag!
 """
     kernelmatrix_diag(κ::Kernel, x::AbstractVector)
 
-Calculate the diagonal matrix of `x` with respect to kernel `κ`.
+Compute the diagonal of `kernelmatrix(κ, x)` efficiently.
 
     kernelmatrix_diag(κ::Kernel, x::AbstractVector, y::AbstractVector)
 
-Calculate the diagonal of `kernelmatrix(κ, x, y)` efficiently.
+Compute the diagonal of `kernelmatrix(κ, x, y)` efficiently.
 Requires that `x` and `y` are the same length.
 
     kernelmatrix_diag(κ::Kernel, X::AbstractMatrix; obsdim::Int=2)
diff --git a/src/matrix/kernelpdmat.jl b/src/matrix/kernelpdmat.jl
index 8348d454a..e0146c863 100644
--- a/src/matrix/kernelpdmat.jl
+++ b/src/matrix/kernelpdmat.jl
@@ -6,10 +6,10 @@ export kernelpdmat
     kernelpdmat(k::Kernel, X::AbstractMatrix; obsdim::Int=2)
     kernelpdmat(k::Kernel, X::AbstractVector)
 
-Compute a positive-definite matrix in the form of a `PDMat` matrix see [PDMats.jl](https://github.com/JuliaStats/PDMats.jl)
-with the cholesky decomposition precomputed.
-The algorithm recursively tries to add recursively a diagonal nugget until positive
-definiteness is achieved or until the noise is too big.
+Compute a positive-definite matrix in the form of a `PDMat` matrix (see [PDMats.jl](https://github.com/JuliaStats/PDMats.jl)),
+with the Cholesky decomposition precomputed.
+The algorithm adds a diagonal "nugget" term to the kernel matrix which is increased until positive
+definiteness is achieved. The algorithm gives up with an error if the nugget becomes larger than 1% of the largest value in the kernel matrix.
 """
 function kernelpdmat(κ::Kernel, X::AbstractMatrix; obsdim::Int=defaultobs)
     return kernelpdmat(κ, vec_of_vecs(X; obsdim=obsdim))
diff --git a/src/mokernels/intrinsiccoregion.jl b/src/mokernels/intrinsiccoregion.jl
index 9e38ba09b..cf8e6879c 100644
--- a/src/mokernels/intrinsiccoregion.jl
+++ b/src/mokernels/intrinsiccoregion.jl
@@ -1,5 +1,5 @@
 @doc raw"""
-    IntrinsicIntrinsicCoregionMOKernel(; kernel::Kernel, B::AbstractMatrix)
+    IntrinsicCoregionMOKernel(; kernel::Kernel, B::AbstractMatrix)
 
 Kernel associated with the intrinsic coregionalization model.
 
diff --git a/src/mokernels/lmm.jl b/src/mokernels/lmm.jl
new file mode 100644
index 000000000..1427d2a1c
--- /dev/null
+++ b/src/mokernels/lmm.jl
@@ -0,0 +1,45 @@
+@doc raw"""
+    LinearMixingModelKernel(g, e::MOKernel, A::AbstractMatrix)
+
+Kernel associated with the linear mixing model.
+
+# Definition
+
+For inputs ``x, x'`` and output dimensions ``p_x, p_{x'}'``, the kernel is defined as[^BPTHST]
+```math
+k\big((x, p_x), (x, p_{x'})\big) = H_{:,p_{x}}K(x, x')H_{:,p_{x'}}
+```
+where ``K(x, x') = Diag(k_1(x, x'), ..., k_m(x, x'))`` with zero off-diagonal entries.
+``H_{:,p_{x}}`` is the ``p_x``-th column (`p_x`-th output) of ``H \in \mathbb{R}^{m \times p}``
+representing ``m`` basis vectors for the ``p`` dimensional output space of ``f``.
+``k_1, \ldots, k_m`` are ``m`` kernels, one for each latent process, ``H`` is a
+mixing matrix of ``m`` basis vectors spanning the output space.
+
+[^BPTHST]: Wessel P. Bruinsma, Eric Perim, Will Tebbutt, J. Scott Hosking, Arno Solin, Richard E. Turner (2020). [Scalable Exact Inference in Multi-Output Gaussian Processes](https://arxiv.org/pdf/1911.06287.pdf).
+"""
+struct LinearMixingModelKernel{Tk<:AbstractVector{<:Kernel},Th<:AbstractMatrix} <: MOKernel
+    K::Tk
+    H::Th
+end
+
+function LinearMixingModelKernel(k::Kernel, H::AbstractMatrix)
+    return LinearMixingModelKernel(Fill(k, size(H, 1)), H)
+end
+
+function (κ::LinearMixingModelKernel)((x, px)::Tuple{Any,Int}, (y, py)::Tuple{Any,Int})
+    (px > size(κ.H, 2) || py > size(κ.H, 2) || px < 1 || py < 1) &&
+        error("`px` and `py` must be within the range of the number of outputs")
+    return sum(κ.H[i, px] * κ.K[i](x, y) * κ.H[i, py] for i in 1:length(κ.K))
+end
+
+function Base.show(io::IO, k::LinearMixingModelKernel)
+    return print(io, "Linear Mixing Model Multi-Output Kernel")
+end
+
+function Base.show(io::IO, mime::MIME"text/plain", k::LinearMixingModelKernel)
+    print(io, "Linear Mixing Model Multi-Output Kernel. Kernels:")
+    for k in k.K
+        print(io, "\n\t")
+        show(io, mime, k)
+    end
+end
diff --git a/src/transform/with_lengthscale.jl b/src/transform/with_lengthscale.jl
new file mode 100644
index 000000000..72360dba8
--- /dev/null
+++ b/src/transform/with_lengthscale.jl
@@ -0,0 +1,43 @@
+"""
+    with_lengthscale(kernel::Kernel, lengthscale::Real)
+
+Construct a transformed kernel with `lengthscale`.
+
+# Examples
+
+```jldoctest
+julia> kernel = with_lengthscale(SqExponentialKernel(), 2.5);
+
+julia> x = rand(2);
+
+julia> y = rand(2);
+
+julia> kernel(x, y) ≈ (SqExponentialKernel() ∘ ScaleTransform(0.4))(x, y)
+true
+```
+"""
+function with_lengthscale(kernel::Kernel, lengthscale::Real)
+    return kernel ∘ ScaleTransform(inv(lengthscale))
+end
+
+"""
+    with_lengthscale(kernel::Kernel, lengthscales::AbstractVector{<:Real})
+
+Construct a transformed "ARD" kernel with different `lengthscales` for each dimension.
+
+# Examples
+
+```jldoctest
+julia> kernel = with_lengthscale(SqExponentialKernel(), [0.5, 2.5]);
+
+julia> x = rand(2);
+
+julia> y = rand(2);
+
+julia> kernel(x, y) ≈ (SqExponentialKernel() ∘ ARDTransform([2, 0.4]))(x, y)
+true
+```
+"""
+function with_lengthscale(kernel::Kernel, lengthscales::AbstractVector{<:Real})
+    return kernel ∘ ARDTransform(map(inv, lengthscales))
+end
diff --git a/test/mokernels/lmm.jl b/test/mokernels/lmm.jl
new file mode 100644
index 000000000..645304c76
--- /dev/null
+++ b/test/mokernels/lmm.jl
@@ -0,0 +1,48 @@
+@testset "lmm" begin
+    rng = MersenneTwister(123)
+    FDM = FiniteDifferences.central_fdm(5, 1)
+    N = 10
+    in_dim = 3
+    out_dim = 6
+    x1 = MOInput([rand(rng, in_dim) for _ in 1:N], out_dim)
+    x2 = MOInput([rand(rng, in_dim) for _ in 1:N], out_dim)
+    H = rand(4, 6)
+
+    k = LinearMixingModelKernel(
+        [Matern32Kernel(), SqExponentialKernel(), FBMKernel(), Matern32Kernel()], H
+    )
+    @test k isa LinearMixingModelKernel
+    @test k isa MOKernel
+    @test k isa Kernel
+    @test k(x1[1], x2[1]) isa Real
+
+    @test string(k) == "Linear Mixing Model Multi-Output Kernel"
+    @test repr("text/plain", k) == (
+        "Linear Mixing Model Multi-Output Kernel. Kernels:\n" *
+        "\tMatern 3/2 Kernel (metric = Euclidean(0.0))\n" *
+        "\tSquared Exponential Kernel (metric = Euclidean(0.0))\n" *
+        "\tFractional Brownian Motion Kernel (h = 0.5)\n" *
+        "\tMatern 3/2 Kernel (metric = Euclidean(0.0))"
+    )
+
+    k = LinearMixingModelKernel(SEKernel(), H)
+
+    @test k isa LinearMixingModelKernel
+    @test k isa MOKernel
+    @test k isa Kernel
+    @test length(k.K) == 4
+    for kernel in k.K
+        @test isa(kernel, SEKernel)
+    end
+
+    @test string(k) == "Linear Mixing Model Multi-Output Kernel"
+    @test repr("text/plain", k) == (
+        "Linear Mixing Model Multi-Output Kernel. Kernels:\n" *
+        "\tSquared Exponential Kernel (metric = Euclidean(0.0))\n" *
+        "\tSquared Exponential Kernel (metric = Euclidean(0.0))\n" *
+        "\tSquared Exponential Kernel (metric = Euclidean(0.0))\n" *
+        "\tSquared Exponential Kernel (metric = Euclidean(0.0))"
+    )
+
+    test_ADs(k)
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index e878d8158..2f74221a8 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -19,6 +19,10 @@ using KernelFunctions: SimpleKernel, metric, kappa, ColVecs, RowVecs, TestUtils
 
 using KernelFunctions.TestUtils: test_interface
 
+# The GROUP is used to run different sets of tests in parallel on the GitHub Actions CI.
+# If you want to introduce a new group, ensure you also add it to .github/workflows/ci.yml
+const GROUP = get(ENV, "GROUP", "")
+
 # Writing tests:
 # 1. The file structure of the test should match precisely the file structure of src.
 #   Amongst other things, this means that there should be exactly 1 test file per src file.
@@ -54,122 +58,135 @@ using KernelFunctions.TestUtils: test_interface
 include("test_utils.jl")
 
 @testset "KernelFunctions" begin
-    include("utils.jl")
-
-    @testset "distances" begin
-        include(joinpath("distances", "pairwise.jl"))
-        include(joinpath("distances", "dotproduct.jl"))
-        include(joinpath("distances", "delta.jl"))
-        include(joinpath("distances", "sinus.jl"))
+    if GROUP == "" || GROUP == "Transform"
+        @testset "transform" begin
+            include(joinpath("transform", "transform.jl"))
+            print(" ")
+            include(joinpath("transform", "scaletransform.jl"))
+            print(" ")
+            include(joinpath("transform", "ardtransform.jl"))
+            print(" ")
+            include(joinpath("transform", "lineartransform.jl"))
+            print(" ")
+            include(joinpath("transform", "functiontransform.jl"))
+            print(" ")
+            include(joinpath("transform", "selecttransform.jl"))
+            print(" ")
+            include(joinpath("transform", "chaintransform.jl"))
+            print(" ")
+            include(joinpath("transform", "periodic_transform.jl"))
+            print(" ")
+            include(joinpath("transform", "with_lengthscale.jl"))
+            print(" ")
+        end
+        @info "Ran tests on Transform"
     end
-    @info "Ran tests on Distances"
 
-    @testset "transform" begin
-        include(joinpath("transform", "transform.jl"))
-        print(" ")
-        include(joinpath("transform", "scaletransform.jl"))
-        print(" ")
-        include(joinpath("transform", "ardtransform.jl"))
-        print(" ")
-        include(joinpath("transform", "lineartransform.jl"))
-        print(" ")
-        include(joinpath("transform", "functiontransform.jl"))
-        print(" ")
-        include(joinpath("transform", "selecttransform.jl"))
-        print(" ")
-        include(joinpath("transform", "chaintransform.jl"))
-        print(" ")
-        include(joinpath("transform", "periodic_transform.jl"))
-        print(" ")
+    if GROUP == "" || GROUP == "BaseKernels"
+        @testset "basekernels" begin
+            include(joinpath("basekernels", "constant.jl"))
+            print(" ")
+            include(joinpath("basekernels", "cosine.jl"))
+            print(" ")
+            include(joinpath("basekernels", "exponential.jl"))
+            print(" ")
+            include(joinpath("basekernels", "exponentiated.jl"))
+            print(" ")
+            include(joinpath("basekernels", "fbm.jl"))
+            print(" ")
+            include(joinpath("basekernels", "gabor.jl"))
+            print(" ")
+            include(joinpath("basekernels", "matern.jl"))
+            print(" ")
+            include(joinpath("basekernels", "nn.jl"))
+            print(" ")
+            include(joinpath("basekernels", "periodic.jl"))
+            print(" ")
+            include(joinpath("basekernels", "piecewisepolynomial.jl"))
+            print(" ")
+            include(joinpath("basekernels", "polynomial.jl"))
+            print(" ")
+            include(joinpath("basekernels", "rational.jl"))
+            print(" ")
+            include(joinpath("basekernels", "sm.jl"))
+            print(" ")
+            include(joinpath("basekernels", "wiener.jl"))
+            print(" ")
+        end
+        @info "Ran tests on BaseKernel"
     end
-    @info "Ran tests on Transform"
 
-    @testset "basekernels" begin
-        include(joinpath("basekernels", "constant.jl"))
-        print(" ")
-        include(joinpath("basekernels", "cosine.jl"))
-        print(" ")
-        include(joinpath("basekernels", "exponential.jl"))
-        print(" ")
-        include(joinpath("basekernels", "exponentiated.jl"))
-        print(" ")
-        include(joinpath("basekernels", "fbm.jl"))
-        print(" ")
-        include(joinpath("basekernels", "gabor.jl"))
-        print(" ")
-        include(joinpath("basekernels", "matern.jl"))
-        print(" ")
-        include(joinpath("basekernels", "nn.jl"))
-        print(" ")
-        include(joinpath("basekernels", "periodic.jl"))
-        print(" ")
-        include(joinpath("basekernels", "piecewisepolynomial.jl"))
-        print(" ")
-        include(joinpath("basekernels", "polynomial.jl"))
-        print(" ")
-        include(joinpath("basekernels", "rational.jl"))
-        print(" ")
-        include(joinpath("basekernels", "sm.jl"))
-        print(" ")
-        include(joinpath("basekernels", "wiener.jl"))
-        print(" ")
+    if GROUP == "" || GROUP == "Kernels"
+        @testset "kernels" begin
+            include(joinpath("kernels", "kernelproduct.jl"))
+            include(joinpath("kernels", "kernelsum.jl"))
+            include(joinpath("kernels", "kerneltensorproduct.jl"))
+            include(joinpath("kernels", "overloads.jl"))
+            include(joinpath("kernels", "scaledkernel.jl"))
+            include(joinpath("kernels", "transformedkernel.jl"))
+            include(joinpath("kernels", "normalizedkernel.jl"))
+            include(joinpath("kernels", "neuralkernelnetwork.jl"))
+        end
+        @info "Ran tests on Kernel"
     end
-    @info "Ran tests on BaseKernel"
 
-    @testset "kernels" begin
-        include(joinpath("kernels", "kernelproduct.jl"))
-        include(joinpath("kernels", "kernelsum.jl"))
-        include(joinpath("kernels", "kerneltensorproduct.jl"))
-        include(joinpath("kernels", "overloads.jl"))
-        include(joinpath("kernels", "scaledkernel.jl"))
-        include(joinpath("kernels", "transformedkernel.jl"))
-        include(joinpath("kernels", "normalizedkernel.jl"))
-        include(joinpath("kernels", "neuralkernelnetwork.jl"))
+    if GROUP == "" || GROUP == "MultiOutput"
+        @testset "multi_output" begin
+            include(joinpath("mokernels", "moinput.jl"))
+            include(joinpath("mokernels", "independent.jl"))
+            include(joinpath("mokernels", "slfm.jl"))
+            include(joinpath("mokernels", "intrinsiccoregion.jl"))
+            include(joinpath("mokernels", "lmm.jl"))
+        end
+        @info "Ran tests on Multi-Output Kernels"
     end
-    @info "Ran tests on Kernel"
 
-    @testset "matrix" begin
-        include(joinpath("matrix", "kernelmatrix.jl"))
-        include(joinpath("matrix", "kernelkroneckermat.jl"))
-        include(joinpath("matrix", "kernelpdmat.jl"))
-    end
-    @info "Ran tests on matrix"
+    if GROUP == "" || GROUP == "Others"
+        include("utils.jl")
 
-    @testset "multi_output" begin
-        include(joinpath("mokernels", "moinput.jl"))
-        include(joinpath("mokernels", "independent.jl"))
-        include(joinpath("mokernels", "slfm.jl"))
-        include(joinpath("mokernels", "intrinsiccoregion.jl"))
-    end
-    @info "Ran tests on Multi-Output Kernels"
+        @testset "distances" begin
+            include(joinpath("distances", "pairwise.jl"))
+            include(joinpath("distances", "dotproduct.jl"))
+            include(joinpath("distances", "delta.jl"))
+            include(joinpath("distances", "sinus.jl"))
+        end
+        @info "Ran tests on Distances"
 
-    @testset "approximations" begin
-        include(joinpath("approximations", "nystrom.jl"))
-    end
+        @testset "matrix" begin
+            include(joinpath("matrix", "kernelmatrix.jl"))
+            include(joinpath("matrix", "kernelkroneckermat.jl"))
+            include(joinpath("matrix", "kernelpdmat.jl"))
+        end
+        @info "Ran tests on matrix"
+
+        @testset "approximations" begin
+            include(joinpath("approximations", "nystrom.jl"))
+        end
 
-    include("generic.jl")
-    include("chainrules.jl")
-    include("zygoterules.jl")
+        include("generic.jl")
+        include("chainrules.jl")
+        include("zygoterules.jl")
 
-    @testset "doctests" begin
-        DocMeta.setdocmeta!(
-            KernelFunctions,
-            :DocTestSetup,
-            quote
-                using KernelFunctions
-                using LinearAlgebra
-                using Random
-                using PDMats: PDMats
-            end;
-            recursive=true,
-        )
-        doctest(
-            KernelFunctions;
-            doctestfilters=[
-                r"{([a-zA-Z0-9]+,\s?)+[a-zA-Z0-9]+}",
-                r"(Array{[a-zA-Z0-9]+,\s?1}|Vector{[a-zA-Z0-9]+})",
-                r"(Array{[a-zA-Z0-9]+,\s?2}|Matrix{[a-zA-Z0-9]+})",
-            ],
-        )
+        @testset "doctests" begin
+            DocMeta.setdocmeta!(
+                KernelFunctions,
+                :DocTestSetup,
+                quote
+                    using KernelFunctions
+                    using LinearAlgebra
+                    using Random
+                    using PDMats: PDMats
+                end;
+                recursive=true,
+            )
+            doctest(
+                KernelFunctions;
+                doctestfilters=[
+                    r"{([a-zA-Z0-9]+,\s?)+[a-zA-Z0-9]+}",
+                    r"(Array{[a-zA-Z0-9]+,\s?1}|Vector{[a-zA-Z0-9]+})",
+                    r"(Array{[a-zA-Z0-9]+,\s?2}|Matrix{[a-zA-Z0-9]+})",
+                ],
+            )
+        end
     end
 end
diff --git a/test/transform/with_lengthscale.jl b/test/transform/with_lengthscale.jl
new file mode 100644
index 000000000..60d401e82
--- /dev/null
+++ b/test/transform/with_lengthscale.jl
@@ -0,0 +1,17 @@
+@testset "with_lengthscale" begin
+    @testset "ScaleTransform" begin
+        l = exp(rand())
+        kernel = @inferred(with_lengthscale(SqExponentialKernel(), l))
+
+        @test kernel isa TransformedKernel{<:SqExponentialKernel,<:ScaleTransform}
+        @test kernel.transform.s[1] ≈ inv(l)
+    end
+
+    @testset "ARDTransform" begin
+        l = map(exp, rand(5))
+        kernel = @inferred(with_lengthscale(SqExponentialKernel(), l))
+
+        @test kernel isa TransformedKernel{<:SqExponentialKernel,<:ARDTransform}
+        @test kernel.transform.v ≈ map(inv, l)
+    end
+end