Add an initial cookbook page for quadratic time mmd

shogun-toolbox · Jul 4, 2016 · 919a51e · 919a51e
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diff --git a/doc/cookbook/source/examples/statistical_testing/quadratic_time_mmd.rst b/doc/cookbook/source/examples/statistical_testing/quadratic_time_mmd.rst
@@ -0,0 +1,38 @@
+==================
+Quadratic Time MMD
+==================
+
+The unbiased statistic is given by
+
+.. math::
+
+  \frac{1}{n(n-1)}\sum_{i=1}^n\sum_{j=1}^n k(x_i,x_i) + k(x_j, x_j) - 2k(x_i,x_j).
+  
+
+See :cite:`gretton2012kernel` for a detailed introduction.
+
+-------
+Example
+-------
+
+Imagine we have samples from :math:`p` and :math:`p`. We create CDenseFeatures (here 64 bit floats aka RealFeatures)as
+
+.. sgexample:: quadratic_time_mmd.sg:create_features
+
+We create an instance of :sgclass:`CQuadraticTimeMMD`, passing it data and the kernel to use, a :sgclass:`CGaussianKernel` here.
+
+.. sgexample:: quadratic_time_mmd.sg:create_instance
+
+Computing the statistic is done as
+
+.. sgexample:: quadratic_time_mmd.sg:estimate_mmd
+
+We can perform the hypothesis test as
+
+.. sgexample:: quadratic_time_mmd.sg:perform_test
+
+----------
+References
+----------
+.. bibliography:: ../../references.bib
+    :filter: docname in docnames
diff --git a/doc/cookbook/source/index.rst b/doc/cookbook/source/index.rst
@@ -32,6 +32,15 @@ Regression
 
    examples/regression/**
 
+Statistical Testing
+-------------------
+
+.. toctree::
+   :maxdepth: 1
+   :glob:
+
+   examples/statistical_testing/**
+
 Kernels
 -------
 

diff --git a/doc/cookbook/source/references.bib b/doc/cookbook/source/references.bib
@@ -16,13 +16,26 @@ @article{fan2008liblinear
   journal={The Journal of Machine Learning Research},
   volume={9},
   pages={1871--1874},
+<<<<<<< bcd4d7fdaeb804f05bc0d0f0c1f66ae81e7e2ba3
   year={2008}
 }
 @book{Rasmussen2005GPM,
   author = {Rasmussen, C. E. and Williams, C. K. I.},
   title = {Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)},
   year = {2005},
   publisher = {The MIT Press}
+=======
+  year={2008},
+
+@article{gretton2012kernel,
+  title={A kernel two-sample test},
+  author={Gretton, A. and Borgwardt, K.M. and Rasch, M.J. and Sch{\"o}lkopf, B. and Smola, A.},
+  journal={The Journal of Machine Learning Research},
+  volume={13},
+  number={1},
+  pages={723--773},
+  year={2012},
+>>>>>>> Add an initial cookbook page for quadratic time mmd
 }
 @article{ueda2000smem,
   title={SMEM Algorithm for Mixture Models},

diff --git a/examples/meta/src/statistical_testing/quadratic_time_mmd.sg b/examples/meta/src/statistical_testing/quadratic_time_mmd.sg
@@ -1,18 +1,27 @@
 CSVFile f_features_p("../../data/two_sample_test_gaussian.dat")
 CSVFile f_features_q("../../data/two_sample_test_laplace.dat")
 
+#![create_features]
 RealFeatures features_p(f_features_p)
 RealFeatures features_q(f_features_q)
+#![create_features]
 
-GaussianKernel kernel()
-
+#![create_instance]
 QuadraticTimeMMD mmd()
+GaussianKernel kernel()
 mmd.set_kernel(kernel)
 mmd.set_p(features_p)
 mmd.set_q(features_q)
+#![create_instance]
 
+#![estimate_mmd]
 Real statistic = mmd.compute_statistic()
+#![estimate_mmd]
+
+#![perform_test]
 Real alpha = 0.05
 Real threshold = mmd.compute_threshold(alpha)
 Real p_value = mmd.compute_p_value(alpha)
 Real h0_rejected = mmd.perform_test(alpha)
+#![perform_test]
+