{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Gaussian Process (GP) smoothing\n", "\n", "This example deals with the case when we want to **smooth** the observed data points $(x_i, y_i)$ of some 1-dimensional function $y=f(x)$, by finding the new values $(x_i, y'_i)$ such that the new data is more \"smooth\" (see more on the definition of smoothness through allocation of variance in the model description below) when moving along the $x$ axis. \n", "\n", "It is important to note that we are **not** dealing with the problem of interpolating the function $y=f(x)$ at the unknown values of $x$. Such problem would be called \"regression\" not \"smoothing\", and will be considered in other examples.\n", "\n", "If we assume the functional dependency between $x$ and $y$ is **linear** then, by making the independence and normality assumptions about the noise, we can infer a straight line that approximates the dependency between the variables, i.e. perform a linear regression. We can also fit more complex functional dependencies (like quadratic, cubic, etc), if we know the functional form of the dependency in advance.\n", "\n", "However, the **functional form** of $y=f(x)$ is **not always known in advance**, and it might be hard to choose which one to fit, given the data. For example, you wouldn't necessarily know which function to use, given the following observed data. Assume you haven't seen the formula that generated it:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline\n", "figsize(12, 6);" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import scipy.stats as stats\n", "\n", "x = np.linspace(0, 50, 100)\n", "y = np.exp(1.0 + np.power(x, 0.5) - np.exp(x / 15.0)) + np.random.normal(scale=1.0, size=x.shape)\n", "\n", "plot(x, y)\n", "xlabel(\"x\")\n", "ylabel(\"y\")\n", "title(\"Observed Data\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Let's try a linear regression first\n", "\n", "As humans, we see that there is a non-linear dependency with some noise, and we would like to capture that dependency. If we perform a linear regression, we see that the \"smoothed\" data is less than satisfactory:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot(x, y)\n", "xlabel(\"x\")\n", "ylabel(\"y\")\n", "\n", "lin = stats.linregress(x, y)\n", "plot(x, lin.intercept + lin.slope * x)\n", "title(\"Linear Smoothing\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Linear regression model recap\n", "\n", "The linear regression assumes there is a linear dependency between the input $x$ and output $y$, sprinkled with some noise around it so that for each observed data point we have:\n", "\n", "$$ y_i = a + b\\, x_i + \\epsilon_i $$\n", "\n", "where the observation errors at each data point satisfy:\n", "\n", "$$ \\epsilon_i \\sim N(0, \\sigma^2) $$\n", "\n", "with the same $\\sigma$, and the errors are independent:\n", "\n", "$$ cov(\\epsilon_i, \\epsilon_j) = 0 \\: \\text{ for } i \\neq j $$\n", "\n", "The parameters of this model are $a$, $b$, and $\\sigma$. It turns out that, under these assumptions, the maximum likelihood estimates of $a$ and $b$ don't depend on $\\sigma$. Then $\\sigma$ can be estimated separately, after finding the most likely values for $a$ and $b$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Gaussian Process smoothing model\n", "\n", "This model allows departure from the linear dependency by assuming that the dependency between $x$ and $y$ is a Brownian motion over the domain of $x$. This doesn't go as far as assuming a particular functional dependency between the variables. Instead, by **controlling the standard deviation of the unobserved Brownian motion** we can achieve different levels of smoothness of the recovered functional dependency at the original data points. \n", "\n", "The particular model we are going to discuss assumes that the observed data points are **evenly spaced** across the domain of $x$, and therefore can be indexed by $i=1,\\dots,N$ without the loss of generality. The model is described as follows:\n", "\n", "\\begin{equation}\n", "\\begin{aligned}\n", "z_i & \\sim \\mathcal{N}(z_{i-1} + \\mu, (1 - \\alpha)\\cdot\\sigma^2) \\: \\text{ for } i=2,\\dots,N \\\\\n", "z_1 & \\sim ImproperFlat(-\\infty,\\infty) \\\\\n", "y_i & \\sim \\mathcal{N}(z_i, \\alpha\\cdot\\sigma^2)\n", "\\end{aligned}\n", "\\end{equation}\n", "\n", "where $z$ is the hidden Brownian motion, $y$ is the observed data, and the total variance $\\sigma^2$ of each observation is split between the hidden Brownian motion and the noise in proportions of $1 - \\alpha$ and $\\alpha$ respectively, with parameter $0 < \\alpha < 1$ specifying the degree of smoothing.\n", "\n", "When we estimate the maximum likelihood values of the hidden process $z_i$ at each of the data points, $i=1,\\dots,N$, these values provide an approximation of the functional dependency $y=f(x)$ as $\\mathrm{E}\\,[f(x_i)] = z_i$ at the original data points $x_i$ only. Therefore, again, the method is called smoothing and not regression." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Let's describe the above GP-smoothing model in PyMC3" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "import pymc3 as pm\n", "\n", "from pymc3.distributions.timeseries import GaussianRandomWalk\n", "from scipy import optimize\n", "from theano import shared" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's create a model with a shared parameter for specifying different levels of smoothing. We use very wide priors for the \"mu\" and \"tau\" parameters of the hidden Brownian motion, which you can adjust according to your application." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "LARGE_NUMBER = 1e5\n", "\n", "model = pm.Model()\n", "with model:\n", " smoothing_param = shared(0.9)\n", " mu = pm.Normal(\"mu\", sigma=LARGE_NUMBER)\n", " tau = pm.Exponential(\"tau\", 1.0 / LARGE_NUMBER)\n", " z = GaussianRandomWalk(\"z\", mu=mu, tau=tau / (1.0 - smoothing_param), shape=y.shape)\n", " obs = pm.Normal(\"obs\", mu=z, tau=tau / smoothing_param, observed=y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's also make a helper function for inferring the most likely values of $z$:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "def infer_z(smoothing):\n", " with model:\n", " smoothing_param.set_value(smoothing)\n", " res = pm.find_MAP(vars=[z], method=\"L-BFGS-B\")\n", " return res[\"z\"]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Please note that in this example, we are only looking at the MAP estimate of the unobserved variables. We are not really interested in inferring the posterior distributions. Instead, we have a control parameter $\\alpha$ which lets us allocate the variance between the hidden Brownian motion and the noise. Other goals and/or different models may require sampling to obtain the posterior distributions, but for our goal a MAP estimate will suffice.\n", "\n", "### Exploring different levels of smoothing\n", "\n", "Let's try to allocate 50% variance to the noise, and see if the result matches our expectations." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/dependencies/pymc3/pymc3/tuning/starting.py:130: UserWarning: In future versions, set the optimization algorithm with a string. For example, use `method=\"L-BFGS-B\"` instead of `fmin=sp.optimize.fmin_l_bfgs_b\"`.\n", " \"In future versions, set the optimization algorithm with a string. \"\n" ] }, { "data": { "text/html": [ "\n", "
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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "smoothing = 0.5\n", "z_val = infer_z(smoothing)\n", "\n", "plot(x, y)\n", "plot(x, z_val)\n", "title(f\"Smoothing={smoothing}\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It appears that the variance is split evenly between the noise and the hidden process, as expected. \n", "\n", "Let's try gradually increasing the smoothness parameter to see if we can obtain smoother data:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/dependencies/pymc3/pymc3/tuning/starting.py:130: UserWarning: In future versions, set the optimization algorithm with a string. For example, use `method=\"L-BFGS-B\"` instead of `fmin=sp.optimize.fmin_l_bfgs_b\"`.\n", " \"In future versions, set the optimization algorithm with a string. \"\n" ] }, { "data": { "text/html": [ "\n", "
\n", " \n", " \n", " 0.80% [40/5000 00:00<00:00 logp = -5.1397e+06]\n", "
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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = subplots(2, 2)\n", "\n", "for ax, smoothing in zip(axes.ravel(), [0.95, 0.99, 0.999, 0.9999]):\n", "\n", " z_val = infer_z(smoothing)\n", "\n", " ax.plot(x, y)\n", " ax.plot(x, z_val)\n", " ax.set_title(f\"Smoothing={smoothing:05.4f}\")" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "pymc3 3.9.0\n", "re 2.2.1\n", "numpy 1.18.5\n", "matplotlib 3.2.1\n", "matplotlib.pylab 1.18.5\n", "logging 0.5.1.2\n", "last updated: Fri Jun 12 2020 \n", "\n", "CPython 3.7.7\n", "IPython 7.15.0\n", "watermark 2.0.2\n" ] } ], "source": [ "%load_ext watermark\n", "%watermark -n -u -v -iv -w" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This example originally contributed by: Andrey Kuzmenko, http://github.com/akuz" ] } ], "metadata": { "anaconda-cloud": {}, "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": "3.7.7" }, "latex_envs": { "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 0 } }, "nbformat": 4, "nbformat_minor": 4 }