{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# $C$$O_2$ Mauna Loa Gaussian Process Regression" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The goal of this notebook is to replicate the results from [chapter 5](http://www.gaussianprocess.org/gpml/chapters/RW5.pdf), p.118, of [Gaussian Processes for Machine Learning](http://www.gaussianprocess.org/gpml/chapters/)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I did not find a way on how to make [GPflow](https://github.com/GPflow/GPflow) perform this additive decomposition and therefore I decided to implement it by hand. In this set-up GPflow is used to find the correct parameters and the hand writte code is used to decompose the addtitive parts. \n", "\n", "There is currently work under-way to add this functionality to GPflow. For more details have a look at [Predicting component contributions #234](https://github.com/GPflow/GPflow/issues/234)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import warnings\n", "from IPython.display import display_html" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/user/cs/local/install/Anaconda3-5.1.0-Linux-x86_64/lib/python3.6/site-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n", " from ._conv import register_converters as _register_converters\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Christian Schuhegger \n", "last updated: 2018-05-05 \n", "\n", "CPython 3.6.4\n", "IPython 6.2.1\n", "\n", "numpy 1.14.2\n", "pandas 0.22.0\n", "matplotlib 2.2.2\n", "seaborn 0.8.1\n", "gpflow 1.1.0\n", "GPy 1.9.2\n", "bokeh 0.12.15\n", "statsmodels 0.8.0\n" ] } ], "source": [ "%load_ext watermark\n", "%watermark -a 'Christian Schuhegger' -u -d -v -p numpy,pandas,matplotlib,seaborn,gpflow,GPy,bokeh,statsmodels" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np, pandas as pd, matplotlib.pyplot as plt, seaborn as sns, gpflow" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's use the [bokeh](https://bokeh.pydata.org/en/latest/) library to make the chart interactive and so that you can zoom in. The hints on how to use bokeh on these examples came from [Looking at the Keeling Curve with GPs in PyMC3](https://bwengals.github.io/looking-at-the-keeling-curve-with-gps-in-pymc3.html)." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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\\n\"+\n \"\\n\"+\n \"\\n\"+\n \"from bokeh.resources import INLINE\\n\"+\n \"output_notebook(resources=INLINE)\\n\"+\n \"\\n\"+\n \"
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Please use the pandas.tseries module instead.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "+-----+-----------------+\n", "| co2 | R Documentation |\n", "+-----+-----------------+\n", "\n", "Mauna Loa Atmospheric CO2 Concentration\n", "---------------------------------------\n", "\n", "Description\n", "~~~~~~~~~~~\n", "\n", "Atmospheric concentrations of CO\\ *2* are expressed in parts per million\n", "(ppm) and reported in the preliminary 1997 SIO manometric mole fraction\n", "scale.\n", "\n", "Usage\n", "~~~~~\n", "\n", "::\n", "\n", " co2\n", "\n", "Format\n", "~~~~~~\n", "\n", "A time series of 468 observations; monthly from 1959 to 1997.\n", "\n", "Details\n", "~~~~~~~\n", "\n", "The values for February, March and April of 1964 were missing and have\n", "been obtained by interpolating linearly between the values for January\n", "and May of 1964.\n", "\n", "Source\n", "~~~~~~\n", "\n", "Keeling, C. D. and Whorf, T. P., Scripps Institution of Oceanography\n", "(SIO), University of California, La Jolla, California USA 92093-0220.\n", "\n", "ftp://cdiac.esd.ornl.gov/pub/maunaloa-co2/maunaloa.co2.\n", "\n", "References\n", "~~~~~~~~~~\n", "\n", "Cleveland, W. S. (1993) *Visualizing Data*. New Jersey: Summit Press.\n", "\n", "Examples\n", "~~~~~~~~\n", "\n", "::\n", "\n", " require(graphics)\n", " plot(co2, ylab = expression(\"Atmospheric concentration of CO\"[2]),\n", " las = 1)\n", " title(main = \"co2 data set\")\n", "\n" ] }, { "data": { "text/html": [ "
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console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\")\n", " clearInterval(timer);\n", " }\n", " }, 10, root)\n", " }\n", "})(window);" ], "application/vnd.bokehjs_exec.v0+json": "" }, "metadata": { "application/vnd.bokehjs_exec.v0+json": { "id": "52911efc-f359-4ff6-9a88-84aa0e4d737c" } }, "output_type": "display_data" } ], "source": [ "p = bokeh.plotting.figure(title=\"Fit to the Mauna Loa Data\", #x_axis_type='datetime', \n", " plot_width=900, plot_height=600)\n", "p.yaxis.axis_label = 'CO2 [ppm]'\n", "p.xaxis.axis_label = 'Date'\n", "\n", "# true value\n", "p.circle(x, y, color=\"black\", legend=\"Observed data\")\n", "p.legend.location = \"top_left\"\n", "bokeh.plotting.show(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Please use the GUI elements on the right top of the graph for moving and zooming into the graph." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As GPflow performs some optimization procedure to find the best fit parameters we will set-up the different aspects of the kernel functions with good starting points taken from [chapter 5](http://www.gaussianprocess.org/gpml/chapters/RW5.pdf) of [Gaussian Processes for Machine Learning](http://www.gaussianprocess.org/gpml/chapters/). In principle you could use arbitrary starting point values and it is the job of GPflow to find the best fit parameters." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As in [chapter 5](http://www.gaussianprocess.org/gpml/chapters/RW5.pdf) of [Gaussian Processes for Machine Learning](http://www.gaussianprocess.org/gpml/chapters/) we create the total fit as an additive composition of different aspects. \n", "\n", "* $k_1$ models a long term trend. \n", "* $k_2$ models the seasonal variation due to the vegetation changes due to the seasons in the northern hemisphere. \n", "* $k_3$ I will not include, as GPflow does not provide out of the box a rational quadratic kernel function. But we will see that this does not hurt us too much. \n", "* $k_4$ finally is the short term variations plus some \"white noise\". \n", "\n", "To be honest, I am not sure why $k_4$ includes the white noise at all, because in principle the gaussian process provides this white noise by default via the $\\sigma_n$ parameter (see [Gaussian Process Parameter Effects](https://github.com/cs224/dev-meetup-gaussian-processes) for details), which is called `m.likelihood.variance` in GPflow." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "k1_ = gpflow.kernels.RBF(1, variance=(66.0 ** 2), lengthscales=67.0)\n", "k2_exp_sine_squred_gamma= 2.0 / 1.3 ** 2.0\n", "k2_exp_sine_squred_period = 1.0\n", "k2_ = gpflow.kernels.RBF(1, variance=(2.4 ** 2.0), lengthscales=90.0) * gpflow.kernels.Periodic(1, period=k2_exp_sine_squred_period, variance=1.0, lengthscales=1.0/k2_exp_sine_squred_gamma)\n", "# k3 = how to do a rational quadratic term in GPflow?\n", "k4_ = gpflow.kernels.RBF(1, variance=(0.18 ** 2), lengthscales=1.6) + gpflow.kernels.White(1, variance=0.19)\n", "k1 = k1_\n", "k2 = k2_\n", "k4 = k4_\n", "kernel = k1 + k2 + k4\n", "k_ = kernel" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " /home/user/cs/local/install/Anaconda3-5.1.0-Linux-x86_64/lib/python3.6/site-packages/gpflow/densities.py:89: UserWarning:Shape of x must be 2D at computation.\n" ] }, { "data": { "text/html": [ "
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classpriortransformtrainableshapefixed_shapevalue
GPR/kern/rbf_1/varianceParameterNone+veTrue()True4356.0
GPR/kern/rbf_1/lengthscalesParameterNone+veTrue()True67.0
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GPR/kern/rbf_2/varianceParameterNone+veTrue()True0.0324
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GPR/kern/white/varianceParameterNone+veTrue()True0.19
GPR/likelihood/varianceParameterNone+veTrue()True0.01
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" ], "text/plain": [ " class prior transform trainable \\\n", "GPR/kern/rbf_1/variance Parameter None +ve True \n", "GPR/kern/rbf_1/lengthscales Parameter None +ve True \n", "GPR/kern/product/rbf/variance Parameter None +ve True \n", "GPR/kern/product/rbf/lengthscales Parameter None +ve True \n", "GPR/kern/product/periodic/variance Parameter None +ve True \n", "GPR/kern/product/periodic/lengthscales Parameter None +ve True \n", "GPR/kern/product/periodic/period Parameter None +ve True \n", "GPR/kern/rbf_2/variance Parameter None +ve True \n", "GPR/kern/rbf_2/lengthscales Parameter None +ve True \n", "GPR/kern/white/variance Parameter None +ve True \n", "GPR/likelihood/variance Parameter None +ve True \n", "\n", " shape fixed_shape value \n", "GPR/kern/rbf_1/variance () True 4356.0 \n", "GPR/kern/rbf_1/lengthscales () True 67.0 \n", "GPR/kern/product/rbf/variance () True 5.76 \n", "GPR/kern/product/rbf/lengthscales () True 90.0 \n", "GPR/kern/product/periodic/variance () True 1.0 \n", "GPR/kern/product/periodic/lengthscales () True 0.8450000000000001 \n", "GPR/kern/product/periodic/period () True 1.0 \n", "GPR/kern/rbf_2/variance () True 0.0324 \n", "GPR/kern/rbf_2/lengthscales () True 1.6 \n", "GPR/kern/white/variance () True 0.19 \n", "GPR/likelihood/variance () True 0.01 " ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m = gpflow.models.GPR(X, Y, kern=kernel)\n", "m.likelihood.variance = 0.01\n", "m.as_pandas_table()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "INFO:tensorflow:Optimization terminated with:\n", " Message: b'CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH'\n", " Objective function value: 129.032561\n", " Number of iterations: 91\n", " Number of functions evaluations: 133\n", "CPU times: user 3.69 s, sys: 447 ms, total: 4.14 s\n", "Wall time: 3.08 s\n" ] } ], "source": [ "%%time\n", "opt = gpflow.train.ScipyOptimizer()\n", "opt.minimize(m)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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classpriortransformtrainableshapefixed_shapevalue
GPR/kern/rbf_1/varianceParameterNone+veTrue()True4356.219071780713
GPR/kern/rbf_1/lengthscalesParameterNone+veTrue()True48.565715481551585
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GPR/kern/product/rbf/lengthscalesParameterNone+veTrue()True91.88714901784704
GPR/kern/product/periodic/varianceParameterNone+veTrue()True1.026393528093981
GPR/kern/product/periodic/lengthscalesParameterNone+veTrue()True0.6709642212683404
GPR/kern/product/periodic/periodParameterNone+veTrue()True0.9997023123140168
GPR/kern/rbf_2/varianceParameterNone+veTrue()True0.16043370929892875
GPR/kern/rbf_2/lengthscalesParameterNone+veTrue()True0.32753755974365617
GPR/kern/white/varianceParameterNone+veTrue()True0.03193821948646309
GPR/likelihood/varianceParameterNone+veTrue()True0.010237414042966209
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" ], "text/plain": [ " class prior transform trainable \\\n", "GPR/kern/rbf_1/variance Parameter None +ve True \n", "GPR/kern/rbf_1/lengthscales Parameter None +ve True \n", "GPR/kern/product/rbf/variance Parameter None +ve True \n", "GPR/kern/product/rbf/lengthscales Parameter None +ve True \n", "GPR/kern/product/periodic/variance Parameter None +ve True \n", "GPR/kern/product/periodic/lengthscales Parameter None +ve True \n", "GPR/kern/product/periodic/period Parameter None +ve True \n", "GPR/kern/rbf_2/variance Parameter None +ve True \n", "GPR/kern/rbf_2/lengthscales Parameter None +ve True \n", "GPR/kern/white/variance Parameter None +ve True \n", "GPR/likelihood/variance Parameter None +ve True \n", "\n", " shape fixed_shape \\\n", "GPR/kern/rbf_1/variance () True \n", "GPR/kern/rbf_1/lengthscales () True \n", "GPR/kern/product/rbf/variance () True \n", "GPR/kern/product/rbf/lengthscales () True \n", "GPR/kern/product/periodic/variance () True \n", "GPR/kern/product/periodic/lengthscales () True \n", "GPR/kern/product/periodic/period () True \n", "GPR/kern/rbf_2/variance () True \n", "GPR/kern/rbf_2/lengthscales () True \n", "GPR/kern/white/variance () True \n", "GPR/likelihood/variance () True \n", "\n", " value \n", "GPR/kern/rbf_1/variance 4356.219071780713 \n", "GPR/kern/rbf_1/lengthscales 48.565715481551585 \n", "GPR/kern/product/rbf/variance 5.64144286809577 \n", "GPR/kern/product/rbf/lengthscales 91.88714901784704 \n", "GPR/kern/product/periodic/variance 1.026393528093981 \n", "GPR/kern/product/periodic/lengthscales 0.6709642212683404 \n", "GPR/kern/product/periodic/period 0.9997023123140168 \n", "GPR/kern/rbf_2/variance 0.16043370929892875 \n", "GPR/kern/rbf_2/lengthscales 0.32753755974365617 \n", "GPR/kern/white/variance 0.03193821948646309 \n", "GPR/likelihood/variance 0.010237414042966209 " ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m.as_pandas_table()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's create a visualization of the fitted overall model. I will only plot the fit between 1990 and 2000, to on the one hand show how nicely the regression curve fits the existing data points and to show how gaussian processes can be used to predict the near term future behaviour together with some confidence interval." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "xx = np.linspace(1990, 2000, 1000).reshape(-1,1)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "def plot(m, with_data=True):\n", " if not isinstance(m, list):\n", " m = [m]\n", " predictions = [model.predict_y(xx) for model in m]\n", " \n", " p = bokeh.plotting.figure(title=\"Fit to the Mauna Loa Data\", #x_axis_type='datetime', \n", " plot_width=900, plot_height=600)\n", " p.yaxis.axis_label = 'CO2 [ppm]'\n", " p.xaxis.axis_label = 'Date'\n", " \n", " if with_data:\n", " # true value\n", " p.circle(x, y, color=\"black\", legend=\"Observed data\")\n", " for mean, var in predictions:\n", " xpts = xx[:,0]\n", " p.line(xpts, mean[:,0], line_width=1)\n", " lowerband = mean[:,0] - 2*np.sqrt(var[:,0])\n", " upperband = mean[:,0] + 2*np.sqrt(var[:,0])\n", " band_x = np.append(xpts, xpts[::-1])\n", " band_y = np.append(lowerband, upperband[::-1])\n", " p.patch(band_x, band_y, color='#7570B3', fill_alpha=0.2)\n", " p.legend.location = \"top_left\"\n", " bokeh.plotting.show(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see in the below figure the complete model matches nicely." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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hR+z8084n0AGhsMzWjifQIbs03NkOJ9AB1Pks244n0CIufTzeDifQAggBTSDOJ9AiYYVdI04n0AJ7SW0lzifQIpTNvShOJ9AC7pGNKw4n0CLIFd0tjifQAyHZ7TAOJ9Aje139Mo4n0ANVIg01TifQI66mHTfOJ9ADyGptOk4n0CPh7n08zifQBDuyTT+OJ9AkVTadAg5n0ARu+q0EjmfQJIh+/QcOZ9AEogLNSc5n0CT7ht1MTmfQBRVLLU7OZ9AlLs89UU5n0AVIk01UDmfQJaIXXVaOZ9AFu9ttWQ5n0CXVX71bjmfQBi8jjV5OZ9AmCKfdYM5n0AZia+1jTmfQJrvv/WXOZ9AGlbQNaI5n0CbvOB1rDmfQBsj8bW2OZ9AnIkB9sA5n0Ad8BE2yzmfQJ1WInbVOZ9AHr0ytt85n0CfI0P26TmfQB+KUzb0OZ9AoPBjdv45n0AhV3S2CDqfQKG9hPYSOp9AIiSVNh06n0CiiqV2JzqfQCPxtbYxOp9ApFfG9js6n0AkvtY2RjqfQKUk53ZQOp9AJov3tlo6n0Cm8Qf3ZDqfQCdYGDdvOp9AqL4od3k6n0AoJTm3gzqfQKmLSfeNOp9AKvJZN5g6n0CqWGp3ojqfQCu/eresOp9AqyWL97Y6n0AsjJs3wTqfQK3yq3fLOp9ALVm8t9U6n0Cuv8z33zqfQC8m3TfqOp9Ar4ztd/Q6n0Aw8/23/jqfQLFZDvgIO59AMcAeOBM7n0CyJi94HTufQDKNP7gnO59As/NP+DE7n0A0WmA4PDufQLTAcHhGO59ANSeBuFA7n0C2jZH4WjufQDb0oThlO59At1qyeG87n0A4wcK4eTufQLgn0/iDO59AOY7jOI47n0C69PN4mDufQDpbBLmiO59Au8EU+aw7n0A7KCU5tzufQLyONXnBO59APfVFucs7n0C9W1b51TufQD7CZjngO59Avyh3eeo7n0A/j4e59DufQMD1l/n+O59AQVyoOQk8n0DBwrh5EzyfQEIpybkdPJ9Awo/Z+Sc8n0BD9uk5MjyfQMRc+nk8PJ9ARMMKukY8n0DFKRv6UDyfQEaQKzpbPJ9AxvY7emU8n0BHXUy6bzyfQMjDXPp5PJ9ASCptOoQ8n0DJkH16jjyfQEr3jbqYPJ9Ayl2e+qI8n0BLxK46rTyfQMsqv3q3PJ9ATJHPusE8n0DN99/6yzyfQE1e8DrWPJ9AzsQAe+A8n0BPKxG76jyfQM+RIfv0PJ9AUPgxO/88n0DRXkJ7CT2fQFHFUrsTPZ9A0itj+x09n0BTknM7KD2fQNP4g3syPZ9AVF+Uuzw9n0DUxaT7Rj2fQFUstTtRPZ9A1pLFe1s9n0BW+dW7ZT2fQNdf5vtvPZ9AWMb2O3o9n0DYLAd8hD2fQFmTF7yOPZ9A2vkn/Jg9n0BaYDg8oz2fQNvGSHytPZ9AWy1ZvLc9n0Dck2n8wT2fQF36eTzMPZ9A3WCKfNY9n0Bex5q84D2fQN8tq/zqPZ9AX5S7PPU9n0Dg+st8/z2fQGFh3LwJPp9A4cfs/BM+n0BiLv08Hj6fQOOUDX0oPp9AY/sdvTI+n0DkYS79PD6fQGTIPj1HPp9A5S5PfVE+n0BmlV+9Wz6fQOb7b/1lPp9AZ2KAPXA+n0DoyJB9ej6fQGgvob2EPp9A6ZWx/Y4+n0Bq/ME9mT6fQOpi0n2jPp9Aa8niva0+n0DsL/P9tz6fQGyWAz7CPp9A7fwTfsw+n0BtYyS+1j6fQO7JNP7gPp9AbzBFPus+n0DvllV+9T6fQHD9Zb7/Pp9A8WN2/gk/n0BxyoY+FD+fQPIwl34eP59Ac5envig/n0Dz/bf+Mj+fQHRkyD49P59A9MrYfkc/n0B1Mem+UT+fQPaX+f5bP59Adv4JP2Y/n0D3ZBp/cD+fQHjLKr96P59A+DE7/4Q/n0B5mEs/jz+fQPr+W3+ZP59AemVsv6M/n0D7y3z/rT+fQHwyjT+4P59A/Jidf8I/n0B9/62/zD+fQP1lvv/WP59AfszOP+E/n0D/Mt9/6z+fQH+Z77/1P59AAAAAAABAn0A=\",\"dtype\":\"float64\",\"shape\":[1000]},\"y\":{\"__ndarray__\":\"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\",\"dtype\":\"float64\",\"shape\":[2000]},\"y\":{\"__ndarray__\":\"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{}, "source": [ "Now let's split the model into components and create model $m_1$ (blue) with only the long term trend and model $m_2$ (green) with only the product term of [p.120](http://www.gaussianprocess.org/gpml/chapters/RW5.pdf):\n", "$$\n", "\\begin{eqnarray}\n", "k_2(x,x')&=&\\theta_3^2\\cdot\\hbox{exp}\\left(-\\frac{(x-x')^2}{2\\theta_4^2}-\\frac{2\\sin^2(\\pi(x-x')/1.0)}{\\theta_5^2}\\right)\\\\\n", "&=&\\left(\\theta_3^2\\cdot\\hbox{exp}\\left(-\\frac{(x-x')^2}{2\\theta_4^2}\\right)\\right)\\cdot\\left(1.0\\cdot\\hbox{exp}\\left(-\\frac{2\\sin^2(\\pi(x-x')/1.0)}{\\theta_5^2}\\right)\\right)\n", "\\end{eqnarray}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Where $\\theta_3$ is the `variance` term in the `RBF` kernel and therefore the `variance` term in the `PeriodicKernel` kernel will be $1.0$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### How not to do it" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It turns out that the simplistic idea on how to decompose the additive components of the model by simply creating partial models is not correct. This would have looked like this:" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ " k1 = GPflow.kernels.RBF(1, variance=m.kern.rbf_1.variance.value, lengthscales=m.kern.rbf_1.lengthscales.value)\n", " m1 = GPflow.gpr.GPR(X, Y, kern=k1)\n", " m1.likelihood.variance = m.likelihood.variance.value\n", " m1.fixed = True\n", "\n", " k2 = GPflow.kernels.RBF(1, variance=m.kern.prod.rbf.variance.value, lengthscales=m.kern.prod.rbf.lengthscales.value) \\\n", " * \\\n", " GPflow.kernels.PeriodicKernel(1, period=m.kern.prod.periodickernel.period.value, \n", " variance=m.kern.prod.periodickernel.variance.value, \n", " lengthscales=m.kern.prod.periodickernel.lengthscales.value)\n", " m2 = GPflow.gpr.GPR(X, Y, kern=k2)\n", " m2.likelihood.variance = m.likelihood.variance.value\n", " m2.fixed = True\n", "\n", " k1 = GPflow.kernels.RBF(1, variance=m.kern.rbf_1.variance.value, lengthscales=m.kern.rbf_1.lengthscales.value)\n", " k2 = GPflow.kernels.RBF(1, variance=m.kern.prod.rbf.variance.value, lengthscales=m.kern.prod.rbf.lengthscales.value) \\\n", " * \\\n", " GPflow.kernels.PeriodicKernel(1, period=m.kern.prod.periodickernel.period.value, \n", " variance=m.kern.prod.periodickernel.variance.value, \n", " lengthscales=m.kern.prod.periodickernel.lengthscales.value)\n", " m3 = GPflow.gpr.GPR(X, Y, kern=(k1+k2))\n", " m3.likelihood.variance = m.likelihood.variance.value\n", " m3.fixed = True" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### How to do it" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Have a look at [The Kernel Cookbook](http://www.cs.toronto.edu/~duvenaud/cookbook/index.html) and scroll down to \"Additive decomposition\" or look at equation 1.17 at the [kernels](https://github.com/duvenaud/phd-thesis/blob/master/kernels.pdf) chapter of David Duvenaud's Phd [thesis](https://github.com/duvenaud/phd-thesis/).\n", "\n", "There it says (I leave out the $\\mu$ variables as we set the mean function to be 0):\n", "$$ f_1(X^*)|f_1(X) + f_2(X) \\sim \\mathcal{N}\\left({K_1^*}^T(K_1+K_2)^{-1}[f_1(X) + f_2(X)], ...\\right)$$\n", "but our simplistic approach from above would have calculated the following:\n", "$$ f_1(X^*)|f_1(X) + f_2(X) \\sim \\mathcal{N}\\left({K_1^*}^TK_1^{-1}[f_1(X) + f_2(X)], ...\\right)$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I did not find a way on how to make GPflow perform this additive decomposition and therefore I decided to implement it by hand. In this set-up GPflow is used to find the correct parameters and the hand writte code is used to decompose the addtitive parts." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "import functools\n", "\n", "# http://www.cs.toronto.edu/~duvenaud/cookbook/index.html\n", "\n", "class GPCovarianceFunctionWhiteNoise:\n", " def __init__(self, sigma):\n", " self.sigma = float(sigma)\n", "\n", " def covariance(self, x1, x2):\n", " lr = np.zeros(shape=(len(x1), len(x2)))\n", " np.fill_diagonal(lr, self.sigma ** 2)\n", " return lr\n", "\n", "class GPCovarianceFunctionSquaredExponential:\n", " def __init__(self, l, sigma):\n", " self.l = float(l)\n", " self.sigma = float(sigma)\n", "\n", " def covariance(self, x1, x2):\n", " return (self.sigma**2) * np.exp( -0.5 * (np.subtract.outer(x1, x2)**2) / (self.l ** 2))\n", "\n", "class GPCovarianceFunctionExpSine2Kernel:\n", " def __init__(self, l, period, sigma):\n", " self.l = float(l)\n", " self.period = float(period)\n", " self.sigma = float(sigma)\n", "\n", " def covariance(self, x1, x2):\n", " return (self.sigma**2) * np.exp( -2.0 * np.power(np.sin((np.pi / self.period) * np.abs(np.subtract.outer(x1, x2))),\n", " 2) / (self.l ** 2))\n", "\n", "class GPCovarianceFunctionSum:\n", " def __init__(self, k1, k2):\n", " self.k1 = k1\n", " self.k2 = k2\n", "\n", " def covariance(self, x1, x2):\n", " s1 = self.k1.covariance(x1, x2)\n", " s2 = self.k2.covariance(x1, x2)\n", " s = s1 + s2\n", " return s\n", "\n", "class GPCovarianceFunctionProduct:\n", " def __init__(self, k1, k2):\n", " self.k1 = k1\n", " self.k2 = k2\n", "\n", " def covariance(self, x1, x2):\n", " p1 = self.k1.covariance(x1, x2)\n", " p2 = self.k2.covariance(x1, x2)\n", " p = p1 * p2\n", " return p\n", "\n", "def conditional1(x_new, x, y, cov, sigma_n=0):\n", " if not isinstance(cov, list):\n", " cov = [cov]\n", "\n", " if len(cov) < 2:\n", " total_covariance_function = cov[0]\n", " else:\n", " total_covariance_function = functools.reduce(lambda a, x: GPCovarianceFunctionSum(a, x), cov)\n", "\n", " A = total_covariance_function.covariance(x_new, x_new)\n", " C = total_covariance_function.covariance(x_new, x)\n", " B = total_covariance_function.covariance(x, x) + np.power(sigma_n,2)*np.diag(np.ones(len(x)))\n", "\n", " mu = [np.linalg.inv(B).dot(C.T).T.dot(y).squeeze()]\n", " sigma = [(A - C.dot(np.linalg.inv(B).dot(C.T))).squeeze()]\n", "\n", " for i in range(0, len(cov)):\n", " partial_covariance_function = cov[i]\n", " C_ = partial_covariance_function.covariance(x_new, x)\n", " mu_ = np.linalg.inv(B).dot(C_.T).T.dot(y).squeeze()\n", " mu.append(mu_)\n", "\n", " return (mu, sigma)\n", "\n", "def predict1(x_new, x, y, cov, sigma_n=0):\n", " l_y_pred, l_sigmas = conditional1(x_new, x, y, cov=cov, sigma_n=sigma_n)\n", " if len(l_sigmas[0].shape) > 1:\n", " return l_y_pred, [np.diagonal(ls) for ls in l_sigmas]\n", " else:\n", " return l_y_pred, l_sigmas" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array(91.88714902)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "m.kern.product.rbf.lengthscales.value" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "xx = np.linspace(1990, 2000, 1000)\n", "k1 = GPCovarianceFunctionSquaredExponential(l=m.kern.rbf_1.lengthscales.value, \n", " sigma=np.sqrt(m.kern.rbf_1.variance.value))\n", "k2 = GPCovarianceFunctionProduct(\n", " GPCovarianceFunctionSquaredExponential(l=m.kern.product.rbf.lengthscales.value,\n", " sigma=np.sqrt(m.kern.product.rbf.variance.value)),\n", " GPCovarianceFunctionExpSine2Kernel(l=m.kern.product.periodic.lengthscales.value, \n", " period=m.kern.product.periodic.period.value, \n", " sigma=np.sqrt(m.kern.product.periodic.variance.value)))\n", "\n", "k4 = GPCovarianceFunctionSum(GPCovarianceFunctionSquaredExponential(l=m.kern.rbf_2.lengthscales.value, \n", " sigma=np.sqrt(m.kern.rbf_2.variance.value)),\n", " GPCovarianceFunctionWhiteNoise(sigma=np.sqrt(m.kern.white.variance.value)))\n", "\n", "k = GPCovarianceFunctionSum(k1, GPCovarianceFunctionSum(k2, k4))\n", "\n", "y_pred, sigmas = predict1(xx, x, y, cov=[k1, k2, k4], sigma_n=np.sqrt(m.likelihood.variance.value))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And if we then plot $m_1$ (blue) and $m_1 + m_2$ (green) and the combined/full model $m$ (red) in the same graph we get the picture below." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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bokeh.plotting.figure(title=\"Fit to the Mauna Loa Data\", #x_axis_type='datetime', \n", " plot_width=900, plot_height=600)\n", "p.yaxis.axis_label = 'CO2 [ppm]'\n", "p.xaxis.axis_label = 'Date'\n", "\n", "# total fit\n", "p.line(xx, y_pred[0], line_width=1, line_color=\"firebrick\", legend=\"Total fit\")\n", "\n", "# trend\n", "p.line(xx, y_pred[1], line_width=1, line_color=\"blue\", legend=\"Long term trend\")\n", "\n", "# trend + seasonal variation\n", "p.line(xx, y_pred[1] + y_pred[2], line_width=1, line_color=\"green\", legend=\"Long term trend + seasonal variation\")\n", "\n", "# true value\n", "p.circle(x, y, color=\"black\", legend=\"Observed data\")\n", "p.legend.location = \"top_left\"\n", "bokeh.plotting.show(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Please pay attention to the very wiggly red line, which is the full model fit. If you scroll up a bit and have a look at the fit of the full model produced by GPflow itself (in the plot function of this notebook via the GPflow `predict_y()` method) you will not see this wiggly pattern. Let's plot the $m_1+m_2$ (green), the $m$ from the hand created predictions (red) and the $m$ as generated by GPflow (blue) in one graph to see the differences." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/html": [ "\n", "
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\",\"dtype\":\"float64\",\"shape\":[1000]},\"y\":{\"__ndarray__\":\"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"gpflow_mean, _ = m.predict_y(xx.reshape(-1,1))\n", "\n", "p = bokeh.plotting.figure(title=\"Fit to the Mauna Loa Data\", #x_axis_type='datetime', \n", " plot_width=900, plot_height=600)\n", "p.yaxis.axis_label = 'CO2 [ppm]'\n", "p.xaxis.axis_label = 'Date'\n", "\n", "# total fit\n", "p.line(xx, y_pred[0], line_width=1, line_color=\"firebrick\", legend=\"Total fit by hand\")\n", "\n", "# total fit as produced by GPflow\n", "p.line(xx, gpflow_mean[:,0], line_width=1, line_color=\"blue\", legend=\"Total fit by GPflow\")\n", "\n", "# trend + seasonal variation\n", "p.line(xx, y_pred[1] + y_pred[2], line_width=1, line_color=\"green\", legend=\"Long term trend + seasonal variation\")\n", "\n", "p.legend.location = \"top_left\"\n", "bokeh.plotting.show(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see the difference is not big, but I am not entirely sure where this is coming from. Perhaps GPflow ignores white noise in its predictions (which actually makes sense)!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we then want to look at the seasonal variation (k2) and the short term variation (k4) we can do that as follows:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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\",\"dtype\":\"float64\",\"shape\":[1000]},\"y\":{\"__ndarray__\":\"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\",\"dtype\":\"float64\",\"shape\":[1000]}},\"selected\":null,\"selection_policy\":null},\"id\":\"5e38f396-850b-4136-9559-44cb807d079d\",\"type\":\"ColumnDataSource\"}],\"root_ids\":[\"4fab1e0e-cdcb-4a07-b8b2-38dab3dabc49\"]},\"title\":\"Bokeh 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bokeh.plotting.figure(title=\"Fit to the Mauna Loa Data\", #x_axis_type='datetime', \n", " plot_width=900, plot_height=600)\n", "p.yaxis.axis_label = 'CO2 [ppm]'\n", "p.xaxis.axis_label = 'Date'\n", "\n", "# total fit\n", "p.line(xx, y_pred[2], line_width=1, line_color=\"firebrick\", legend=\"Seasonal variation\")\n", "\n", "# trend\n", "p.line(xx, y_pred[3], line_width=1, line_color=\"blue\", legend=\"Short term variation\")\n", "\n", "# true value\n", "p.legend.location = \"top_left\"\n", "bokeh.plotting.show(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we want to see how the seasonal variation changed over the years we can do that as follows:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "# plot several years\n", "\n", "def dates_to_idx(timelist):\n", " reference_time = pd.to_datetime('1959-01-01')\n", " t = (timelist - reference_time) / pd.Timedelta(1, \"Y\")\n", " return np.asarray(t)+1959\n", "\n", "p = bokeh.plotting.figure(title=\"Several years of the seasonal component\",\n", " plot_width=900, plot_height=600)\n", "p.yaxis.axis_label = 'Δ CO2 [ppm]'\n", "p.xaxis.axis_label = 'Month'\n", "\n", "colors = bokeh.palettes.brewer['Paired'][5]\n", "years = [\"1960\", \"1970\", \"1980\", \"1990\", \"2000\"]\n" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Predicting year 1960\n", "Predicting year 1970\n", "Predicting year 1980\n", "Predicting year 1990\n", "Predicting year 2000\n" ] }, { "data": { "text/html": [ "\n", "
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xx = np.linspace(1990, 2000, 1000)\n", "# \n", "for i, year in enumerate(years):\n", " dates = pd.date_range(start=\"1/1/\"+year, end=\"12/31/\"+year, freq=\"10D\")\n", " tnew = dates_to_idx(dates)\n", "\n", " print(\"Predicting year\", year)\n", " y_pred_, sigmas_ = predict1(tnew, x, y, cov=[k1, k2, k4], sigma_n=np.sqrt(m.likelihood.variance.value))\n", "\n", " # plot mean\n", " t = np.asarray((dates - dates[0])/pd.Timedelta(1, \"M\")) + 1\n", " p.line(t, y_pred_[2], line_width=1, line_color=colors[i], legend=year)\n", "\n", "p.legend.location = \"bottom_left\"\n", "bokeh.plotting.show(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Alternative implementation 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here is an alternative implementation of the decomposition based on a comment in [Example that shows how to separate additive effects, e.g. time series decomposition of birthdays data](https://github.com/GPflow/GPflow/issues/491)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "XX = xx.reshape(-1, 1)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'0.0000003427'" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "_x_new = XX\n", "_x = X\n", "_y = Y\n", "_A = k_.compute_K_symm(_x_new)\n", "_C = k_.compute_K(_x_new, _x)\n", "_B = k_.compute_K_symm(_x) + m.likelihood.variance.value*np.diag(np.ones(len(_x)))\n", "\n", "_mu1 = np.linalg.inv(_B).dot(_C.T).T.dot(_y).squeeze()\n", "_tmp1 = np.linalg.inv(_B).dot(_C.T)\n", "_tmp2 = np.linalg.solve(_B, _C.T) \n", "'{:.10f}'.format(np.abs(_tmp1 - _tmp2).max())" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'0.0000001639'" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "_mu2 = np.linalg.solve(_B,_C.T).T.dot(_y).squeeze()\n", "'{:.10f}'.format(np.abs(_mu1 - _mu2).max())" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'0.0000001528'" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "_mu3 = _C.dot(np.linalg.inv(_B)).dot(_y).squeeze()\n", "'{:.10f}'.format(np.abs(_mu1 - _mu3).max())" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'0.0000001638'" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "_mu4 = _C.dot(np.linalg.solve(_B, _y)).squeeze()\n", "'{:.10f}'.format(np.abs(_mu1 - _mu4).max())" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "def conditional2(x_new, x, y, cov, sigma_n=0):\n", " if not isinstance(cov, list):\n", " cov = [cov]\n", "\n", " if len(cov) < 2:\n", " total_covariance_function = cov[0]\n", " else:\n", " # total_covariance_function = None\n", " total_covariance_function = functools.reduce(lambda a, x: a + x, cov)\n", "\n", " A = total_covariance_function.compute_K_symm(x_new)\n", " C = total_covariance_function.compute_K(x_new, x)\n", " B = total_covariance_function.compute_K_symm(x) + np.power(sigma_n,2)*np.diag(np.ones(len(x)))\n", "\n", " mu = [np.linalg.inv(B).dot(C.T).T.dot(y).squeeze()]\n", " sigma = [(A - C.dot(np.linalg.inv(B).dot(C.T))).squeeze()]\n", "\n", " for i in range(0, len(cov)):\n", " partial_covariance_function = cov[i]\n", " C_ = partial_covariance_function.compute_K(x_new, x)\n", " mu_ = np.linalg.inv(B).dot(C_.T).T.dot(y).squeeze()\n", " mu.append(mu_)\n", "\n", " return (mu, sigma)\n", "\n", "def predict2(x_new, x, y, cov, sigma_n=0):\n", " l_y_pred, l_sigmas = conditional2(x_new, x, y, cov=cov, sigma_n=sigma_n)\n", " if len(l_sigmas[0].shape) > 1:\n", " return l_y_pred, [np.diagonal(ls) for ls in l_sigmas]\n", " else:\n", " return l_y_pred, l_sigmas" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "y_pred2, sigmas2 = predict2(XX, X, Y, cov=[k1_, k2_, k4_], sigma_n=np.sqrt(m.likelihood.variance.value))" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1000" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(y_pred[0])" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.allclose(y_pred[0], y_pred2[0])" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "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", " \n", " 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nptfdelta%
0353.433528353.4914900.0579620.016400
1353.790253353.5933670.1968860.055650
2353.594593353.6911030.0965100.027294
3353.719705353.7849080.0652030.018434
4353.803838353.8751880.0713500.020166
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "df = pd.DataFrame(np.array([y_pred[0],y_pred2[0]]).T, columns=['np','tf'])\n", "df['delta'] = np.abs(df['np'] - df['tf'])\n", "df['%'] = df['delta'] / df['np'] * 100.0\n", "with pd.option_context('display.max_rows', None, 'display.max_columns', 3): \n", " display_html(df.head().to_html(),raw=True)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "delta 0.413584\n", "% 0.115987\n", "dtype: float64" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df[['delta','%']].max()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Alternative implementation 3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* [Detecting periodicities with Gaussian processes](https://www.researchgate.net/publication/301303918_Detecting_periodicities_with_Gaussian_processes)\n", " * [download](https://peerj.com/articles/cs-50/#supp-3) (see figure3.ipynb)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "import GPy" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " /home/user/cs/local/install/Anaconda3-5.1.0-Linux-x86_64/lib/python3.6/site-packages/paramz/transformations.py:111: RuntimeWarning:overflow encountered in expm1\n" ] }, { "data": { "text/html": [ "\n", "\n", "

\n", "Model: GP regression
\n", "Objective: 129.03256335476846
\n", "Number of Parameters: 11
\n", "Number of Optimization Parameters: 11
\n", "Updates: True
\n", "

\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
GP_regression. valueconstraintspriors
sum.rbf.variance 4356.219071780713 +ve
sum.rbf.lengthscale 48.565715481551585 +ve
sum.mul.rbf.variance 5.64144286809577 +ve
sum.mul.rbf.lengthscale 91.88714901784704 +ve
sum.mul.std_periodic.variance 1.026393528093981 +ve
sum.mul.std_periodic.period 0.9997023123140168 +ve
sum.mul.std_periodic.lengthscale 0.6709642212683404 +ve
sum.rbf_1.variance 0.16043370929892875 +ve
sum.rbf_1.lengthscale 0.32753755974365617 +ve
sum.white.variance 0.03193821948646309 +ve
Gaussian_noise.variance 0.010237414042966209 +ve
" ], "text/plain": [ "" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k1__ = GPy.kern.RBF (input_dim=1, variance=float(m.kern.rbf_1.variance.value) , lengthscale=float(m.kern.rbf_1.lengthscales.value))\n", "k2__1 = GPy.kern.RBF (input_dim=1, variance=float(m.kern.product.rbf.variance.value) , lengthscale=float(m.kern.product.rbf.lengthscales.value))\n", "k2__2 = GPy.kern.StdPeriodic(input_dim=1, variance=float(m.kern.product.periodic.variance.value), lengthscale=float(m.kern.product.periodic.lengthscales.value),period=float(m.kern.product.periodic.period.value))\n", "k2__ = k2__1 * k2__2\n", "k4__1 = GPy.kern.RBF (input_dim=1, variance=float(m.kern.rbf_2.variance.value) , lengthscale=float(m.kern.rbf_2.lengthscales.value))\n", "k4__2 = GPy.kern.White (input_dim=1, variance=float(m.kern.white.variance.value))\n", "k4__ = k4__1 + k4__2\n", "k__ = k1__ + k2__ + k4__\n", "m__ = GPy.models.GPRegression(X,Y,k__)\n", "m__.Gaussian_noise.variance[0] = float(m.likelihood.variance.value)\n", "m__" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "def conditional3(x_new, x, y, cov, sigma_n=0):\n", " if not isinstance(cov, list):\n", " cov = [cov]\n", "\n", " if len(cov) < 2:\n", " total_covariance_function = cov[0]\n", " else:\n", " # total_covariance_function = None\n", " total_covariance_function = functools.reduce(lambda a, x: a + x, cov)\n", "\n", " A = total_covariance_function.K(x_new) # total_covariance_function.K(x_new,x_new)\n", " C = total_covariance_function.K(x_new, x)\n", " B = total_covariance_function.K(x) + np.power(sigma_n,2)*np.diag(np.ones(len(x))) # total_covariance_function.K(x,x)\n", "\n", " mu = [np.linalg.inv(B).dot(C.T).T.dot(y).squeeze()]\n", " sigma = [(A - C.dot(np.linalg.inv(B).dot(C.T))).squeeze()]\n", "\n", " for i in range(0, len(cov)):\n", " partial_covariance_function = cov[i]\n", " C_ = partial_covariance_function.K(x_new, x)\n", " mu_ = np.linalg.inv(B).dot(C_.T).T.dot(y).squeeze()\n", " mu.append(mu_)\n", " \n", " # kxX = C_\n", " # K_1 = np.linalg.inv(B)\n", " # mean = C_.dot(np.linalg.inv(B)).dot(Y)\n", "\n", "\n", " return (mu, sigma)\n", "\n", "def predict3(x_new, x, y, cov, sigma_n=0):\n", " l_y_pred, l_sigmas = conditional3(x_new, x, y, cov=cov, sigma_n=sigma_n)\n", " if len(l_sigmas[0].shape) > 1:\n", " return l_y_pred, [np.diagonal(ls) for ls in l_sigmas]\n", " else:\n", " return l_y_pred, l_sigmas" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " /home/user/cs/local/install/Anaconda3-5.1.0-Linux-x86_64/lib/python3.6/site-packages/paramz/transformations.py:111: RuntimeWarning:overflow encountered in expm1\n" ] } ], "source": [ "y_pred3, sigmas3 = predict3(XX, X, Y, cov=[k1__, k2__, k4__], sigma_n=np.sqrt(m__.Gaussian_noise.variance[0]))" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.allclose(y_pred[0], y_pred3[0])" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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npgpflowgpydelta_gpflow%_gpflowdelta_gpy%_gpydelta_gpflow_gpy%_gpflow_gpy
0353.433528353.491490353.4914900.0579620.0164000.0579620.0164007.407044e-082.095395e-08
1353.790253353.593367353.5933670.1968860.0556500.1968860.0556502.133197e-086.032910e-09
2353.594593353.691103353.6911020.0965100.0272940.0965100.0272941.523574e-074.307639e-08
3353.719705353.784908353.7849080.0652030.0184340.0652030.0184343.971718e-081.122636e-08
4353.803838353.875188353.8751880.0713500.0201660.0713500.0201664.792372e-081.354255e-08
\n", "
" ], "text/plain": [ " np gpflow gpy delta_gpflow %_gpflow delta_gpy \\\n", "0 353.433528 353.491490 353.491490 0.057962 0.016400 0.057962 \n", "1 353.790253 353.593367 353.593367 0.196886 0.055650 0.196886 \n", "2 353.594593 353.691103 353.691102 0.096510 0.027294 0.096510 \n", "3 353.719705 353.784908 353.784908 0.065203 0.018434 0.065203 \n", "4 353.803838 353.875188 353.875188 0.071350 0.020166 0.071350 \n", "\n", " %_gpy delta_gpflow_gpy %_gpflow_gpy \n", "0 0.016400 7.407044e-08 2.095395e-08 \n", "1 0.055650 2.133197e-08 6.032910e-09 \n", "2 0.027294 1.523574e-07 4.307639e-08 \n", "3 0.018434 3.971718e-08 1.122636e-08 \n", "4 0.020166 4.792372e-08 1.354255e-08 " ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = pd.DataFrame(np.array([y_pred[0],y_pred2[0],y_pred3[0]]).T, columns=['np','gpflow','gpy'])\n", "df['delta_gpflow'] = np.abs(df['np'] - df['gpflow'])\n", "df['%_gpflow'] = df['delta_gpflow'] / df['np'] * 100.0\n", "df['delta_gpy'] = np.abs(df['np'] - df['gpy'])\n", "df['%_gpy'] = df['delta_gpy'] / df['np'] * 100.0\n", "df['delta_gpflow_gpy'] = np.abs(df['gpflow'] - df['gpy'])\n", "df['%_gpflow_gpy'] = df['delta_gpflow_gpy'] / df['gpflow'] * 100.0\n", "df.head()" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "delta_gpflow 4.135843e-01\n", "%_gpflow 1.159868e-01\n", "delta_gpy 4.135842e-01\n", "%_gpy 1.159867e-01\n", "delta_gpflow_gpy 2.924092e-07\n", "%_gpflow_gpy 8.092542e-08\n", "dtype: float64" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df[['delta_gpflow','%_gpflow','delta_gpy','%_gpy','delta_gpflow_gpy','%_gpflow_gpy']].max()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Using different GPy optimizers" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[GPy delivers \"wrong\" results compared to gpflow](https://github.com/SheffieldML/GPy/issues/614)" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " /home/user/cs/local/install/Anaconda3-5.1.0-Linux-x86_64/lib/python3.6/site-packages/paramz/transformations.py:111: RuntimeWarning:overflow encountered in expm1\n" ] }, { "data": { "text/html": [ "\n", "\n", "

\n", "Model: GP regression
\n", "Objective: 129.03256333921234
\n", "Number of Parameters: 11
\n", "Number of Optimization Parameters: 11
\n", "Updates: True
\n", "

\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
GP_regression. valueconstraintspriors
sum.rbf.variance 4356.219071782721 +ve
sum.rbf.lengthscale 48.5657154836552 +ve
sum.mul.rbf.variance 5.641442868106639 +ve
sum.mul.rbf.lengthscale 91.88714903815146 +ve
sum.mul.std_periodic.variance 1.0263935281187573 +ve
sum.mul.std_periodic.period 0.9997023902939737 +ve
sum.mul.std_periodic.lengthscale 0.6709642212192272 +ve
sum.rbf_1.variance 0.16043370928666736 +ve
sum.rbf_1.lengthscale 0.32753755952069186 +ve
sum.white.variance 0.03193821950509535 +ve
Gaussian_noise.variance 0.010237414044922417 +ve
" ], "text/plain": [ "" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k1__ = GPy.kern.RBF (input_dim=1, variance=float(m.kern.rbf_1.variance.value) , lengthscale=float(m.kern.rbf_1.lengthscales.value))\n", "k2__1 = GPy.kern.RBF (input_dim=1, variance=float(m.kern.product.rbf.variance.value) , lengthscale=float(m.kern.product.rbf.lengthscales.value))\n", "k2__2 = GPy.kern.StdPeriodic(input_dim=1, variance=float(m.kern.product.periodic.variance.value), lengthscale=float(m.kern.product.periodic.lengthscales.value),period=float(m.kern.product.periodic.period.value))\n", "k2__ = k2__1 * k2__2\n", "k4__1 = GPy.kern.RBF (input_dim=1, variance=float(m.kern.rbf_2.variance.value) , lengthscale=float(m.kern.rbf_2.lengthscales.value))\n", "k4__2 = GPy.kern.White (input_dim=1, variance=float(m.kern.white.variance.value))\n", "k4__ = k4__1 + k4__2\n", "k__ = k1__ + k2__ + k4__\n", "m__ = GPy.models.GPRegression(X,Y,k__)\n", "m__.Gaussian_noise.variance[0] = float(m.likelihood.variance.value)\n", "m__.optimize()\n", "m__" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " /home/user/cs/local/install/Anaconda3-5.1.0-Linux-x86_64/lib/python3.6/site-packages/paramz/transformations.py:111: RuntimeWarning:overflow encountered in expm1\n" ] }, { "data": { "text/html": [ "\n", "\n", "

\n", "Model: GP regression
\n", "Objective: 129.03256333607948
\n", "Number of Parameters: 11
\n", "Number of Optimization Parameters: 11
\n", "Updates: True
\n", "

\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "
GP_regression. valueconstraintspriors
sum.rbf.variance 4356.219071782721 +ve
sum.rbf.lengthscale 48.56571548365474 +ve
sum.mul.rbf.variance 5.641442868106637 +ve
sum.mul.rbf.lengthscale 91.88714903814706 +ve
sum.mul.std_periodic.variance 1.026393528118752 +ve
sum.mul.std_periodic.period 0.9997023902770954 +ve
sum.mul.std_periodic.lengthscale 0.6709642212192378 +ve
sum.rbf_1.variance 0.16043370928667006 +ve
sum.rbf_1.lengthscale 0.32753755952074015 +ve
sum.white.variance 0.03193821950509133 +ve
Gaussian_noise.variance 0.01023741404492199 +ve
" ], "text/plain": [ "" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k1__ = GPy.kern.RBF (input_dim=1, variance=float(m.kern.rbf_1.variance.value) , lengthscale=float(m.kern.rbf_1.lengthscales.value))\n", "k2__1 = GPy.kern.RBF (input_dim=1, variance=float(m.kern.product.rbf.variance.value) , lengthscale=float(m.kern.product.rbf.lengthscales.value))\n", "k2__2 = GPy.kern.StdPeriodic(input_dim=1, variance=float(m.kern.product.periodic.variance.value), lengthscale=float(m.kern.product.periodic.lengthscales.value),period=float(m.kern.product.periodic.period.value))\n", "k2__ = k2__1 * k2__2\n", "k4__1 = GPy.kern.RBF (input_dim=1, variance=float(m.kern.rbf_2.variance.value) , lengthscale=float(m.kern.rbf_2.lengthscales.value))\n", "k4__2 = GPy.kern.White (input_dim=1, variance=float(m.kern.white.variance.value))\n", "k4__ = k4__1 + k4__2\n", "k__ = k1__ + k2__ + k4__\n", "m__ = GPy.models.GPRegression(X,Y,k__)\n", "m__.Gaussian_noise.variance[0] = float(m.likelihood.variance.value)\n", "m__.optimize(optimizer='scg')\n", "m__" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [], "source": [ "def conditional(X_new, X, Y, cov, sigma_n=0, framework='gpy'):\n", " if not isinstance(cov, list):\n", " cov = [cov]\n", "\n", " if len(cov) < 2:\n", " total_covariance_function = cov[0]\n", " else:\n", " # total_covariance_function = None\n", " total_covariance_function = functools.reduce(lambda a, x: a + x, cov)\n", "\n", " if framework == 'gpflow':\n", " A = total_covariance_function.compute_K_symm(X_new)\n", " C = total_covariance_function.compute_K(X_new, X)\n", " B = total_covariance_function.compute_K_symm(X) + np.power(sigma_n,2)*np.diag(np.ones(len(X)))\n", " elif framework == 'gpy':\n", " A = total_covariance_function.K(X_new) # total_covariance_function.K(x_new,x_new)\n", " C = total_covariance_function.K(X_new, X)\n", " B = total_covariance_function.K(X) + np.power(sigma_n,2)*np.diag(np.ones(len(X))) # total_covariance_function.K(x,x)\n", " else:\n", " raise ValueError('Unknown framework parameter: {}'.format(framework))\n", "\n", " # mu = [np.linalg.inv(B).dot(C.T).T.dot(y).squeeze()]\n", " BY = np.linalg.solve(B, Y)\n", " mu = [C.dot(BY).squeeze()]\n", " sigma = [(A - C.dot(np.linalg.inv(B).dot(C.T))).squeeze()]\n", "\n", " for i in range(0, len(cov)):\n", " partial_covariance_function = cov[i]\n", " C_ = None\n", " if framework == 'gpflow':\n", " C_ = partial_covariance_function.compute_K(X_new, X)\n", " elif framework == 'gpy':\n", " C_ = partial_covariance_function.K(X_new, X)\n", " else:\n", " raise ValueError('Unknown framework parameter: {}'.format(framework))\n", " # mu_ = np.linalg.inv(B).dot(C_.T).T.dot(y).squeeze()\n", " mu_ = C_.dot(BY).squeeze()\n", " mu.append(mu_)\n", "\n", " return (mu, sigma)\n", "\n", "def predict(X_new, X, Y, cov, sigma_n=0, framework='gpy'):\n", " l_y_pred, l_sigmas = conditional(X_new, X, Y, cov=cov, sigma_n=sigma_n, framework=framework)\n", " if len(l_sigmas[0].shape) > 1:\n", " return l_y_pred, [np.diagonal(ls) for ls in l_sigmas]\n", " else:\n", " return l_y_pred, l_sigmas" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "with warnings.catch_warnings():\n", " warnings.filterwarnings(\"ignore\")\n", " y_pred2, sigmas2 = predict(XX, X, Y, cov=[k1_ , k2_ , k4_] , sigma_n=np.sqrt(m.likelihood.variance.value) , framework='gpflow')\n", " y_pred3, sigmas3 = predict(XX, X, Y, cov=[k1__, k2__, k4__], sigma_n=np.sqrt(m__.Gaussian_noise.variance[0]), framework='gpy')" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'0.0000001568'" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "'{:.10f}'.format(np.abs(y_pred2[0] - y_pred3[0]).max())" ] } ], "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": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 2 }