diff --git a/docs/notebooks/point_clouds.ipynb b/docs/notebooks/point_clouds.ipynb index 530917f69..b5aec4c8d 100644 --- a/docs/notebooks/point_clouds.ipynb +++ b/docs/notebooks/point_clouds.ipynb @@ -8,28 +8,44 @@ "source": [ "# Point clouds\n", "\n", - "We cover in this tutorial the instantiation and use of a `PointCloud` geometry. \n", - "\n", - "A `PointCloud` geometry holds two arrays of vectors, endowed with a cost function. Such a geometry should cover most users' needs. \n", - "\n", - "We further show differentiation through optimal transport as an example of optimization that leverages first-order gradients." + "We cover in this tutorial how to solve OT problems between two pointclouds by instantiating a `PointCloud` geometry." ] }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], + "execution_count": 1, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "O2Qs8m9SN1ag", + "outputId": "ed53b82f-b649-4836-994a-453b16377772" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " Installing build dependencies ... \u001b[?25l\u001b[?25hdone\n", + " Getting requirements to build wheel ... \u001b[?25l\u001b[?25hdone\n", + " Installing backend dependencies ... \u001b[?25l\u001b[?25hdone\n", + " Preparing wheel metadata ... \u001b[?25l\u001b[?25hdone\n", + "\u001b[K |████████████████████████████████| 145 kB 14.7 MB/s \n", + "\u001b[K |████████████████████████████████| 185 kB 38.2 MB/s \n", + "\u001b[K |████████████████████████████████| 237 kB 58.4 MB/s \n", + "\u001b[K |████████████████████████████████| 85 kB 3.2 MB/s \n", + "\u001b[K |████████████████████████████████| 51 kB 5.6 MB/s \n", + "\u001b[?25h Building wheel for ott-jax (PEP 517) ... \u001b[?25l\u001b[?25hdone\n" + ] + } + ], "source": [ - "import sys\n", - "\n", - "if \"google.colab\" in sys.modules:\n", - " !pip install -q git+https://github.com/ott-jax/ott@main" + "%pip install -q git+https://github.com/ott-jax/ott@main" ] }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": { "id": "ITK9gegzfjJS" }, @@ -41,9 +57,9 @@ "import jax.numpy as jnp\n", "\n", "import ott\n", - "from ott.geometry import pointcloud\n", + "from ott.geometry import costs, pointcloud\n", "from ott.core import sinkhorn\n", - "from ott.tools import transport" + "from ott.core import linear_problems" ] }, { @@ -67,14 +83,13 @@ " rngs = jax.random.split(rng, 3)\n", " x = jax.random.normal(rngs[0], (n, d)) + 1\n", " y = jax.random.uniform(rngs[1], (m, d))\n", - " a = jnp.ones((n,)) / n\n", - " b = jnp.ones((m,)) / m\n", - " return x, y, a, b\n", + " return x, y\n", "\n", "\n", "rng = jax.random.PRNGKey(0)\n", - "n, m, d = 12, 14, 2\n", - "x, y, a, b = create_points(rng, n=n, m=m, d=d)" + "n, m, d = 11, 15, 2\n", + "x, y = create_points(rng, n=n, m=m, d=d)\n", + "geom = pointcloud.PointCloud(x, y)" ] }, { @@ -85,20 +100,62 @@ "source": [ "## Computes the regularized optimal transport\n", "\n", - "To compute the transport matrix between the two point clouds, one can define a `PointCloud` geometry (which by default uses `ott.geometry.costs.SqEuclidean` for cost function), then call the `sinkhorn` function, and build the transport matrix from the optimized potentials." + "To compute the transport matrix between the two point clouds, one defines first a `PointCloud` geometry \n", + "\n", + "A `PointCloud` geometry holds two arrays of vectors (supporting the two measures of interest), along with a cost function (a `CostFn` object, set by default to `costs.SqEuclidean`) and, possibly, an `epsilon` regularization parameter.\n", + "\n", + "This geometry object defines a `LinearProblem` object, which contains all the data needed to instantiate a linear OT problem (see Gromov-Wasserstein tutorials for *quadratic* OT problems).\n", + "\n", + "We can then call a `Sinkhorn` solver to solve that problem, and compute the OT between these points clouds. Note that all weights are assumed to be uniform in this notebook, but non-uniform weights can be passed as `a= .. ,b= ..` arguments when defining the `LinearProblem` below." ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 4, "metadata": { - "id": "EPZ1m4nwkIQO" + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "EPZ1m4nwkIQO", + "outputId": "eb7eaf8c-5b27-444b-b50e-3139e0e89192" }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " Sinkhorn has converged: True \n", + " Error upon last iteration: 0.00040601194 \n", + " Sinkhorn required 4 iterations to converge. \n", + " Entropy regularized OT cost: 2.5201843 \n", + " OT cost (without entropy): 2.3552217\n" + ] + } + ], "source": [ - "geom = pointcloud.PointCloud(x, y, epsilon=1e-2)\n", - "out = sinkhorn.sinkhorn(geom, a, b)\n", - "P = geom.transport_from_potentials(out.f, out.g)" + "# Define a linear problem with that cost structure.\n", + "ot_prob = linear_problems.LinearProblem(geom)\n", + "# Create a Sinkhorn solver\n", + "solver = sinkhorn.Sinkhorn()\n", + "# Solve OT problem\n", + "ot = solver(ot_prob)\n", + "# The out object contains many things, among which the regularized OT cost\n", + "print(\n", + " \" Sinkhorn has converged: \",\n", + " ot.converged,\n", + " \"\\n\",\n", + " \"Error upon last iteration: \",\n", + " ot.errors[(ot.errors > -1)][-1],\n", + " \"\\n\",\n", + " \"Sinkhorn required \",\n", + " jnp.sum(ot.errors > -1),\n", + " \" iterations to converge. \\n\",\n", + " \"Entropy regularized OT cost: \",\n", + " ot.reg_ot_cost,\n", + " \"\\n\",\n", + " \"OT cost (without entropy): \",\n", + " jnp.sum(ot.matrix * ot.geom.cost_matrix),\n", + ")" ] }, { @@ -107,54 +164,24 @@ "id": "fHsyN3gRkNu1" }, "source": [ - "A more concise syntax to compute the optimal transport matrix is to use the `transport.solve`. Note how weights are assumed to be uniform if no parameter `a` and `b` is passed to `transport.solve`. " - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": { - "id": "VCNc8Ptykdk6" - }, - "outputs": [], - "source": [ - "ot = transport.solve(x, y, a=a, b=b, epsilon=1e-2)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "tya0lB1rkq7U" - }, - "source": [ - "## Visualizes the transport" + "The `ot` output object contains several callables and properties, notably a simple way to instantiate, if needed, the OT matrix." ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 5, "metadata": { "colab": { - "height": 283 - }, - "executionInfo": { - "elapsed": 504, - "status": "ok", - "timestamp": 1637706746437, - "user": { - "displayName": "", - "photoUrl": "", - "userId": "" - }, - "user_tz": -60 + "base_uri": "https://localhost:8080/", + "height": 255 }, - "id": "U98QCImkkoJc", - "outputId": "fc3f5e39-d353-45b0-9ebf-a1c473ffa630" + "id": "VCNc8Ptykdk6", + "outputId": "4c315d26-b6f3-46f4-ec35-38dd519a6a26" }, "outputs": [ { "data": { - "image/png": "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\n", + "image/png": "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", "text/plain": [ "
" ] @@ -166,35 +193,36 @@ } ], "source": [ - "plt.imshow(ot.matrix, cmap=\"Purples\")\n", + "# you can instantiate the OT matrix\n", + "P = ot.matrix\n", + "plt.imshow(P, cmap=\"Purples\")\n", "plt.colorbar();" ] }, + { + "cell_type": "markdown", + "metadata": { + "id": "qCIBjOZMIlFZ" + }, + "source": [ + "You can also instantiate a `plott` object to help visualize the transport in 2D." + ] + }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 6, "metadata": { "colab": { + "base_uri": "https://localhost:8080/", "height": 265 }, - "executionInfo": { - "elapsed": 2787, - "status": "ok", - "timestamp": 1637695330954, - "user": { - "displayName": "", - "photoUrl": "", - "userId": "" - }, - "user_tz": -60 - }, "id": "LOHQHnzzSsqd", - "outputId": "f93bc42e-4bf1-4027-9ff7-029fa6e92c3e" + "outputId": "8d184866-171e-49b6-bb1b-78d529143e41" }, "outputs": [ { "data": { - "image/png": "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\n", + "image/png": "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", "text/plain": [ "
" ] @@ -216,15 +244,16 @@ "id": "KSTa0azglxNl" }, "source": [ - "## Differentiation through Optimal Transport\n", + "## OT Gradient Flows\n", + "\n", + "OTT returns quantities that are differentiable. In the following example, we leverage the gradients to move `N` points in a way that minimizes the overall regularized OT cost, given a ground cost function. \n", "\n", - "OTT returns quantities that are differentiable. In the following example, we leverage the gradients to move `N` points \n", - "in a way that minimizes the overall regularized OT cost, given a ground cost function, here the squared Euclidean distance." + "We start by defining a minimal optimization loop, that does fixed-length gradient descent, and records various `ot` objects along the way for plotting. By choosing various cost functions, we can then plot different types of gradient flows for the point cloud in `X`." ] }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 7, "metadata": { "id": "4OdxCfCLgAZX" }, @@ -233,60 +262,71 @@ "def optimize(\n", " x: jnp.ndarray,\n", " y: jnp.ndarray,\n", - " a: jnp.ndarray,\n", - " b: jnp.ndarray,\n", - " cost_fn=ott.geometry.costs.SqEuclidean(),\n", - " num_iter: int = 101,\n", - " dump_every: int = 10,\n", + " num_iter: int = 300,\n", + " dump_every: int = 5,\n", " learning_rate: float = 0.2,\n", + " **kwargs, # passed to the pointcloud.PointCloud geometry\n", "):\n", - " reg_ot_cost_vg = jax.value_and_grad(\n", - " jax.jit(\n", - " (\n", - " lambda geom, a, b: ott.core.sinkhorn.sinkhorn(\n", - " geom, a, b\n", - " ).reg_ot_cost\n", - " )\n", - " ),\n", - " argnums=0,\n", - " )\n", + " # Wrapper function that returns OT cost and OT output given a geometry.\n", + " def reg_ot_cost(geom):\n", + " out = ott.core.sinkhorn.Sinkhorn()(linear_problems.LinearProblem(geom))\n", + " return out.reg_ot_cost, out\n", "\n", - " ot = transport.solve(\n", - " x, y, a=a, b=b, cost_fn=cost_fn, epsilon=1e-2, jit=True\n", - " )\n", - " result = [ot]\n", - " for i in range(1, num_iter + 1):\n", - " reg_ot_cost, geom_g = reg_ot_cost_vg(ot.geom, ot.a, ot.b)\n", + " # The jax.value_and_grad operator. Note that we make explicit that\n", + " # we only wish to differentiate the first output using the has_aux flag.\n", + " reg_ot_cost_vg = jax.jit(jax.value_and_grad(reg_ot_cost, has_aux=True))\n", + "\n", + " # Naive gradient descent\n", + " ots = []\n", + " for i in range(0, num_iter + 1):\n", + " geom = pointcloud.PointCloud(x, y, **kwargs)\n", + " (reg_ot_cost, ot), geom_g = reg_ot_cost_vg(geom)\n", + " assert ot.converged\n", " x = x - geom_g.x * learning_rate\n", - " ot = transport.solve(\n", - " x, y, a=a, b=b, cost_fn=cost_fn, epsilon=1e-2, jit=True\n", - " )\n", " if i % dump_every == 0:\n", - " result.append(ot)\n", + " ots.append(ot)\n", + " return ots" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "id": "iF8IIUDeoWc-" + }, + "outputs": [], + "source": [ + "from IPython import display\n", "\n", - " return result" + "# Helper function to plot successively the optimal transports\n", + "def plot_ots(ots):\n", + " fig = plt.figure(figsize=(8, 5))\n", + " plott = ott.tools.plot.Plot(fig=fig)\n", + " anim = plott.animate(ots, frame_rate=4)\n", + " html = display.HTML(anim.to_jshtml())\n", + " display.display(html)\n", + " plt.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ZlbYdocFxEtK" + }, + "source": [ + "$W_2^2$ Gradient Flow\n" ] }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 9, "metadata": { "colab": { + "base_uri": "https://localhost:8080/", "height": 458 }, - "executionInfo": { - "elapsed": 18181, - "status": "ok", - "timestamp": 1637761565776, - "user": { - "displayName": "", - "photoUrl": "", - "userId": "" - }, - "user_tz": -60 - }, - "id": "iF8IIUDeoWc-", - "outputId": "22794b00-a4ea-4dbc-c943-ff01e8d85df3" + "id": "IZXah5jZqjj8", + "outputId": "c4d029ed-7bc5-403b-e96f-31fa9adac2ea" }, "outputs": [ { @@ -294,7 +334,8 @@ "text/html": [ "\n", "\n", + "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/\n", + "css/font-awesome.min.css\">\n", "\n", + "\n", + "\n", + "\n", + "
\n", + " \n", + "
\n", + " \n", + "
\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
\n", + "
\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
\n", + "
\n", + "
\n", + "\n", + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_ots(\n", + " optimize(\n", + " x, y, num_iter=400, epsilon=1e-2, power=0.5, cost_fn=costs.Euclidean()\n", + " )\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "dWLXiHimLlcf" + }, + "source": [ + "$W_{\\text{cosine}}$ Gradient Flow" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 458 + }, + "id": "uqDk-W7BK7X_", + "outputId": "3c6bc9db-b2f3-45b7-f512-cf88cebdbbee" + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
\n", + " \n", + "
\n", + " \n", + "
\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
\n", + "
\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
\n", + "
\n", + "
\n", + "\n", + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_ots(optimize(x, y, num_iter=300, epsilon=1e-2, cost_fn=costs.Cosine()))" + ] + } + ], + "metadata": { + "accelerator": "GPU", + "colab": { + "collapsed_sections": [], + "machine_shape": "hm", + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3.9.15 64-bit", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.15" + }, + "vscode": { + "interpreter": { + "hash": "a665b5d41d17b532ea9890333293a1b812fa0b73c9c25c950b3cedf1bebd0438" + } } }, "nbformat": 4, - "nbformat_minor": 4 + "nbformat_minor": 0 }