{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Gaussian Process Regression\n", "\n", "The standard regression functionality approximates the functional relation between input variables and output variables by a linear or low-order polynomial. This can be an over-simplification at times.\n", "\n", "A more general approach is to approximate the functional relationship as the superposition of one-dimensional Gaussian processes. Gaussian processes are auto-correlated (and therefore smooth) along a spatial axis.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Background: The Principles of Gaussian Processes\n", "\n", "Let us first understand what Gaussian processes in halerium can be constructed and what it looks like." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Imports\n", "We will need numpy and halerium for constructing the Gaussian process and pylab for plotting." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import halerium.core as hal\n", "import pylab as pl" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now construct a Gaussian process" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "g = hal.Graph(\"g\")\n", "with g:\n", " hal.StaticVariable(\"uncorrelated_source\", shape=(100,),\n", " mean=0, variance=1)\n", " kernel = np.exp(-0.5*np.arange(-20, 21)**2 / 5**2) / 2\n", " hal.StaticVariable(\"gaussian_process\", shape=(100,),\n", " mean=hal.math.convolve(uncorrelated_source, kernel))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we have constructed an uncorrelated source field. On this field the correlation structure is imposed by convolving it with a kernel. Let's have a look at some examples." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[[],\n", " [],\n", " []]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# the evaluate function allows us to conveniently get a generative example\n", "gaussian_process_examples = [g.gaussian_process.evaluate() for i in range(3)]\n", "pl.figure(figsize=(12, 7))\n", "[pl.plot(gp_ex) for gp_ex in gaussian_process_examples]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see gaussian processes can be interpreted smooth functions.\n", "Due to the kernel the process has a preferred fluctuation scale and tends to go back to the origin at zero. We will see how this changes once we introduce data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using a Gaussian process as a function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To use a Gaussian process as a function we have to be able to evaluate it at arbitrary positions. We can do this using iterpolation." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "g = hal.Graph(\"g\")\n", "with g:\n", " hal.StaticVariable(\"uncorrelated_source\", shape=(100,),\n", " mean=0, variance=1)\n", " kernel = np.exp(-0.5*np.arange(-20, 21)**2 / 5**2)\n", " hal.StaticVariable(\"gaussian_process\", shape=(100,),\n", " mean=hal.math.convolve(uncorrelated_source, kernel))\n", " \n", " hal.Variable(\"x\", mean=0, variance=1)\n", " evaluated = hal.math.interpolate(\n", " evaluation_points=x, # where the interpolation is evaluated\n", " support_point_values=gaussian_process,\n", " support_point_base=-3, # we want the 100 points of the gaussian process\n", " support_point_spacing=6/100 # to cover the interval [-3, 3]\n", " )\n", " hal.Variable(\"y\", mean=evaluated, variance=0.01)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now the graph uses the gaussian process as a function that relates x and y as y=f(x)." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x_value_example = np.linspace(-5, 5, 1000)\n", "generative_model = hal.get_generative_model(g, data={g.x: x_value_example})\n", "y_value_example = generative_model.get_example(g.y)\n", "pl.figure(figsize=(12, 7))\n", "pl.plot(x_value_example, y_value_example)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see two things here:\n", "1. the function is noisy due to the variance of the variable y\n", "2. outside of the interpolation interval [-3, 3] the function becomes constant (apart from the noise)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Learning a Gaussian process from data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Create training data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us now create training data from which we hope to learn the Gaussian process." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "np.random.seed(151)\n", "x_data = np.random.randn(100)\n", "# we remove the interval [0.0, 1.0] for demonstration purposes\n", "x_data = x_data[(x_data < 0.) | (x_data > 1.0)]\n", "\n", "def real_function(x):\n", " return np.sin(4*np.tanh(x/1.5))\n", "\n", "y_data = real_function(x_data) + np.random.randn(*x_data.shape)*0.1" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pl.figure(figsize=(12, 7))\n", "pl.scatter(x_data, y_data, label=\"data\", color=\"b\", marker=\"x\")\n", "pl.plot(np.linspace(-4, 4, 1000),\n", " real_function(np.linspace(-4, 4, 1000)),\n", " label=\"real function\", color=\"k\")\n", "pl.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our training data are a noisy representation of the real function with a gap in the interval [0, 1]." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Train" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now use these data to infer the most likely Gaussian process representation." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "posterior_model = hal.get_posterior_model(g,\n", " data={g.x: x_data,\n", " g.y: y_data})\n", "trained_graph = posterior_model.get_posterior_graph()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we have a trained graph in which the posterior probability of the gaussian process is encoded. We can use this trained graph to make a prediction on a test set" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "x_test = np.linspace(-4, 4, 1000)\n", "prediction_model = hal.get_generative_model(trained_graph, data={g.x: x_test})\n", "y_pred_mean = prediction_model.get_means(g.y, n_samples=1000)\n", "y_pred_std = prediction_model.get_standard_deviations(g.y, n_samples=1000)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pl.figure(figsize=(12, 7))\n", "pl.plot(x_test, real_function(x_test), color=\"k\", label=\"real function\")\n", "pl.plot(x_test, y_pred_mean, color=\"r\", label=\"prediction\")\n", "pl.fill_between(x_test, y_pred_mean-y_pred_std, y_pred_mean+y_pred_std,\n", " color=\"r\", alpha=0.5, label=\"prediction uncertainty\")\n", "pl.scatter(x_data, y_data, label=\"data\", color=\"b\", marker=\"x\")\n", "pl.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see how the gaussian process attempts to interpolate between the observed data points. The training result is the most likely balance between the prior correlation structure of the gaussian process and the noise likelyhood of the observed data.\n", "\n", "In the regions without observations the difference between the prediction and the real function increases, as does the uncertainty.\n", "\n", "This is the way Gaussian process regression works." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gaussian process using convenience functions\n", "Halerium offers the user a convenience function that constructs an appropriate Gaussian process regression between variables with a single command." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "g2 = hal.Graph(\"g\")\n", "with g2:\n", " hal.Variable(\"x\", mean=0, variance=1)\n", " hal.Variable(\"y\")\n", " hal.regression.connect_via_gaussian_process(\n", " name_prefix=\"regression\",\n", " inputs=x,\n", " outputs=y,\n", " connect_outputs_scale_parameter=True, # this means we learn the variance as well\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `connect_via_gaussian_process` created all the necessary variables and operations for a gaussian process regression. Training and evaluation works the same way as above, but this time we use the `Trainer` and `Predictor` for convenience." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "trained_graph2 = hal.model.Trainer(g2, data={g2.x: x_data, g2.y: y_data}, method=\"MGVI\")()\n", "\n", "y_pred_mean2, y_pred_std2 = hal.Predictor(\n", " trained_graph2, data={g2.x: x_test}, measure=(\"mean\", \"std\"))(g2.y)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pl.figure(figsize=(12, 7))\n", "pl.plot(x_test, real_function(x_test), color=\"k\", label=\"real function\")\n", "pl.plot(x_test, y_pred_mean2, color=\"r\", label=\"prediction\")\n", "pl.fill_between(x_test, y_pred_mean2-y_pred_std2, y_pred_mean2+y_pred_std2,\n", " color=\"r\", alpha=0.5, label=\"prediction uncertainty\")\n", "pl.scatter(x_data, y_data, label=\"data\", color=\"b\", marker=\"x\")\n", "pl.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The reconstruction is slightly different, because the `connect_via_gaussian_process` function uses a slightly different kernel. Additionally the variance of y is also learned, whereas in the example above it was known." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multiple or multivariate regression inputs and outputs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Gaussian process serves us as a representation of a 1-dimensional function, i.e. a function $f: \\mathbb{R} \\rightarrow \\mathbb{R}$. \n", "\n", "To represent functions $f: \\mathbb{R}^N \\rightarrow \\mathbb{R}^M$ the following simplification is applied:\n", "$$\n", " \\left(f(x)\\right)_i = \\sum_j h_{ij}(x_j).\n", "$$\n", "Here $h_{ij}$ is a 1-dimensional function $f: \\mathbb{R} \\rightarrow \\mathbb{R}$.\n", "This means the function is constructed separately for each output entry by summing independent 1-dimensional functions applied to each input entry.\n", "\n", "Let us see how this works in practice." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We construct a Graph with multiple multivariate variables and connect them." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "graph = hal.Graph(\"graph\")\n", "with graph:\n", " # a is a 4-dimensional vector with different means and standard deviations for its entries\n", " hal.Variable(\"a\", shape=(4,), mean=-np.arange(1, 5), variance=np.arange(1, 5))\n", " # b is a 2x3-dimensional matrix\n", " hal.Variable(\"b\", shape=(2, 3), mean=0, variance=0.001)\n", " \n", " # c is a 2x2-dimensional matrix\n", " hal.Variable(\"c\", shape=(2, 2), variance=0.1)\n", " # d is a scalar\n", " hal.Variable(\"d\", variance=0.1)\n", " \n", " hal.regression.connect_via_gaussian_process(\n", " name_prefix=\"regression\",\n", " inputs=[a, b],\n", " outputs=[c, d],\n", " # For the regression to work properly it needs to know\n", " # the locations and scales of the inputs and outputs.\n", " # Alternatively you can standardize your data.\n", " inputs_location=[-np.arange(1, 5), 0],\n", " inputs_scale=[np.sqrt(np.arange(1, 5)), np.sqrt(0.001)],\n", " # we just define these here, normally they would come from your data\n", " outputs_location=[5., 5.], \n", " outputs_scale=[10., 10.],\n", " # we do not want to fit the variances here\n", " connect_outputs_scale_parameter=False,\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we create an example with 200 data points" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "data_a, data_b, data_c, data_d = hal.get_generative_model(\n", " graph, data=hal.get_data_linker(n_data=200)).get_example(\n", " [graph.a, graph.b, graph.c, graph.d])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and split them into training and test data." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "train_data_a = data_a[:150]\n", "train_data_b = data_b[:150]\n", "train_data_c = data_c[:150]\n", "train_data_d = data_d[:150]\n", "\n", "test_data_a = data_a[150:]\n", "test_data_b = data_b[150:]\n", "test_data_c = data_c[150:]\n", "test_data_d = data_d[150:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we train the graph (this will take ~1 minute)..." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "41.167240858078\n" ] } ], "source": [ "train_data = {\n", " graph.a: train_data_a,\n", " graph.b: train_data_b,\n", " graph.c: train_data_c,\n", " graph.d: train_data_d\n", "}\n", "\n", "import time\n", "t_start = time.time()\n", "model = hal.get_posterior_model(graph, train_data)\n", "tr_graph = model.get_posterior_graph()\n", "print(time.time() - t_start)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "...and check whether we can predict the test set." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "test_data = {\n", " graph.a: test_data_a,\n", " graph.b: test_data_b\n", "}\n", "\n", "pr_model = hal.get_generative_model(tr_graph, test_data)\n", "pred_c_mean, pred_d_mean = pr_model.get_means([graph.c, graph.d])\n", "pred_c_std, pred_d_std = pr_model.get_standard_deviations([graph.c, graph.d])" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pl.figure(figsize=(5,5))\n", "pl.scatter(test_data_d, pred_d_mean)\n", "pl.xlabel(\"test data values\")\n", "pl.ylabel(\"predicted values\")\n", "pl.title(\"graph.d\")\n", "pl.plot([test_data_d.min(), test_data_d.max()],\n", " [test_data_d.min(), test_data_d.max()],\n", " color=\"k\", ls=\"--\", label=\"ideal line\")\n", "pl.legend()" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pl.figure(figsize=(10,10))\n", "for i, j in [[0,0], [0,1], [1,0], [1,1]]:\n", " ax = pl.subplot(2,2,2*i+j+1)\n", " ax.scatter(test_data_c[:, i, j], pred_c_mean[:, i, j])\n", " ax.set_xlabel(\"test data values\")\n", " ax.set_ylabel(\"predicted values\")\n", " ax.set_title(f\"graph.c[{i},{j}]\")\n", " ax.plot([test_data_c[:,i,j].min(), test_data_c[:,i,j].max()],\n", " [test_data_c[:,i,j].min(), test_data_c[:,i,j].max()],\n", " color=\"k\", ls=\"--\", label=\"ideal line\")\n", " ax.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that the trained graph yields accurate predictions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## More on `connect_via_gaussian_process`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's go through the arguments of `connect_via_gaussian_process`." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "gg = hal.Graph(\"gg\")\n", "with gg:\n", " hal.Variable(\"x\", mean=0, variance=1)\n", " hal.Variable(\"y\")\n", " hal.regression.connect_via_gaussian_process(\n", " name_prefix=\"regression\",\n", " inputs=x,\n", " outputs=y,\n", " connect_outputs_scale_parameter=True,\n", " inputs_location=0,\n", " inputs_scale=1,\n", " outputs_location=0,\n", " outputs_scale=1,\n", " interpolation_points=100,\n", " interpolation_range=4.,\n", " kernel_correlation_length=0.4,\n", " kernel_size=21\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first argument name_prefix is used to name the entities in the graph holding the regression parameters:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "gg\n", "├─regression_y\n", "│ ├─location\n", "│ │ ├─source_field\n", "│ │ └─field\n", "│ └─log_scale\n", "│ ├─source_field\n", "│ └─field\n", "├─inputs\n", "├─outputs\n", "├─x\n", "└─y\n" ] } ], "source": [ "from halerium.core.utilities.print import print_child_tree\n", "print_child_tree(gg)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Printing the graph's children reveals that besides regression parameters for the mean of `y` in `regression_y.location`, there are also regression parameters for the variance of `y` in `regression_y.log_scale`. Thus, the mean of `y` as well as the residual scatter of `y` is learned as a Gaussian process of `x`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The argument `inputs` specifies the input variables for the regression. This can be either a single variable or a list of variables.\n", "\n", "The argument `outputs` specifies the output variables of the regression, either as a single variable, or a list of variables.\n", "\n", "The argument `connect_outputs_scale_parameter` specifies whether to learn the variance(s) as field(s) as well. With `False` the printout of the graphs children would not have contained the `log_scale` entity.\n", "\n", "The arguments `inputs_location=0`, `inputs_scale=1`, `outputs_location=0`, and `outputs_scale=1` allow one to directly include scaling of the data for standardization in the regression. Standardization of the data would otherwise be a required step of data preparation. Here, one just needs to provide the empirical location and scale parameters of the data.\n", "\n", "The argument `interpolation_points` specifies the amount of points in each 1-D Gaussian random field. With more points finer functional details can be captured, but computation time is increased.\n", "\n", "The argument `interpolation_range` specifies the interpolation range in units of the `inputs_scale`. The interpolation range is `[inputs_location-interpolation_range*inputs_scale, inputs_location+interpolation_range*inputs_scale]`.\n", "\n", "The argument `kernel_correlation_length` defines the correlation length imposed by the kernel. It too is given w.r.t to the inputs scales.\n", "\n", "The argument `kernel_size` defines the kernels size. A larger kernel imposes the correlation structure more exactly, but requires more computational effort.\n", "\n", "More on these and a number of further arguments can be found in the documentation for `connect_via_gaussian_process`." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.7.9" } }, "nbformat": 4, "nbformat_minor": 4 }