{ "metadata": { "name": "", "signature": "sha256:b309ee539740b642b20c71f55053c3e87a1fd4a2350b21d298b4e9ef3486f102" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Flexible Parametric Representations of Non Parametric Models\n", "\n", "### 18th March 2015 Neil D. Lawrence \n", "\n", "#### Inducing point description initially inspired by a notebook of James Hensman\n", "\n", "First import some relevant libraries and set a random seed." ] }, { "cell_type": "code", "collapsed": false, "input": [ "import GPy\n", "import pods\n", "from GPy.util.linalg import pdinv\n", "\n", "from matplotlib import pyplot as plt\n", "%matplotlib inline\n", "import numpy as np\n", "\n", "from IPython.display import display \n", "\n", "np.random.seed(123)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Flexible Parametric Approximation to Gaussian Process\n", "\n", "In this notebook we will try and demonstrate the principles underpinning a flexible parameteric approximation to a non-parameteric model. In particular, the argument goes along these lines. In general, we want to be non-parametric. What do we mean by non-parametric. Here we mean non-parametric in the sense that when we try and represent the relationship between training and test data, $p(\\mathbf{y}^\\ast|\\mathbf{y})$, through a posterior density over a vector of parameters, $\\mathbf{w}$, \n", "$$\n", "p(\\mathbf{y}^\\ast|\\mathbf{y}) = \\int p(\\mathbf{y}^\\ast|\\mathbf{w})p(\\mathbf{w}|\\mathbf{y}) \\text{d}\\mathbf{w},\n", "$$\n", "we find that the vector $\\mathbf{w}$ cannot be fixed dimensional.\n", "\n", "In a Gaussian process model, we normally relate the observations to a latent function through a likelihood that factorizes,\n", "$$\n", "p(\\mathbf{y}|\\mathbf{f}) = \\prod_{i=1}^n p(y_i|f_i), \n", "$$\n", "Variational inducing variables involve augmenting the prior over functions with a vector of variables, $\\mathbf{u}$, \n", "$$\n", "p(\\mathbf{f}) = \\int p(\\mathbf{f}|\\mathbf{u}) p(\\mathbf{u}) \\text{d}\\mathbf{u}\n", "$$\n", "and then lower bounding the conditional distribution,\n", "$$\n", "p(\\mathbf{y}|\\mathbf{u}) = \\int p(\\mathbf{y}|\\mathbf{f}) p(\\mathbf{f}|\\mathbf{u}) \\text{d}\\mathbf{u} \\geq \\prod_{i=1}^n c_i \\hat{p}(\\mathbf{y}|\\mathbf{u}) \n", "$$\n", "The lower bound is then used in a model that *looks* parametric, \n", "$$\n", "p(\\mathbf{y}^*|\\mathbf{y}) = \\int p(\\mathbf{y}^*|\\mathbf{u}) \\hat{p}(\\mathbf{u}|\\mathbf{y})\\text{d}\\mathbf{u},\n", "$$\n", "but with the important difference that the number of parameters can be changed at *run* time not just *design* time.\n", "\n", "## Example\n", "\n", "### Toy Data Set\n", "\n", "To show the model working in practice, we are first going to sample a function from a Gaussian process. We will use an exponentiated quadratic covariance function, \n", "Sample a data set with two different clusters on the inputs." ] }, { "cell_type": "code", "collapsed": false, "input": [ "N = 50\n", "noise_var = 0.01\n", "X = np.zeros((50, 1))\n", "X[:25, :] = np.linspace(0,3,25)[:,None] # First cluster of inputs/covariates\n", "X[25:, :] = np.linspace(7,10,25)[:,None] # Second cluster of inputs/covariates\n", "\n", "# Sample response variables from a Gaussian process with exponentiated quadratic covariance.\n", "k = GPy.kern.RBF(1)\n", "y = np.random.multivariate_normal(np.zeros(N),k.K(X)+np.eye(N)*np.sqrt(noise_var))[:, None]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Full Gaussian Process\n", "Now we have the full data set we will construct a Gaussian process and optimize the parameters, showing the plot of the fit." ] }, { "cell_type": "code", "collapsed": false, "input": [ "m_full = GPy.models.GPRegression(X,y)\n", "m_full.optimize(messages=True) # Optimize parameters of covariance function\n", "_ = m_full.plot() # plot the regression\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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nfnC5maNzqazJqVdLQgg+33kGgK8tnjLiOxAhBJ5uGqsUryyYFs2l4it15/0F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\nW9rImGEbF8bxSJNWx+bDXTl0Z2Mkaha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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Inducing Variable Approximation\n", "\n", "In an inducing variable approximation, we introduce 'pseudo-observations' of the function, $\\mathbf{u}$, which 'induce' the approximation. We will start by introducing four 'pseudo-observations' at locations 2.5, 4, 7 and 8.5. We will then display the untrained model." ] }, { "cell_type": "code", "collapsed": false, "input": [ "kern = GPy.kern.RBF(1)\n", "Z = np.hstack(\n", " (np.linspace(2.5,4.,2),\n", " np.linspace(7,8.5,2)))[:,None]\n", "m = GPy.models.SparseGPRegression(X,y,kernel=kern,Z=Z)\n", "m.Gaussian_noise.variance = noise_var\n", "m.rbf.variance.constrain_fixed()\n", "m.rbf.lengthscale.constrain_fixed()\n", "m.Gaussian_noise.variance.constrain_fixed()\n", "m.plot()\n", "display(m)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "clang: warning: argument unused during compilation: '-fopenmp'\n", "In file included from /Users/neil/.cache/scipy/python27_compiled/sc_1790bf65208b11355ffcfd4b65a5f10913.cpp:11:\n", "In file included from /Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/weave/blitz/blitz/array.h:26:\n", "In file included from /Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/weave/blitz/blitz/array-impl.h:37:\n", "/Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/weave/blitz/blitz/range.h:120:34: warning: '&&' within '||' [-Wlogical-op-parentheses]\n", " return ((first_ < last_) && (stride_ == 1) || (first_ == last_));\n", " ~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~ ~~\n", "/Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/weave/blitz/blitz/range.h:120:34: note: place parentheses around the '&&' expression to silence this warning\n", " return ((first_ < last_) && (stride_ == 1) || (first_ == last_));\n", " ^\n", " ( )\n", "In file included from /Users/neil/.cache/scipy/python27_compiled/sc_1790bf65208b11355ffcfd4b65a5f10913.cpp:23:\n", "In file included from /Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/numpy/core/include/numpy/arrayobject.h:4:\n", "In file included from /Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/numpy/core/include/numpy/ndarrayobject.h:17:\n", "In file included from /Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/numpy/core/include/numpy/ndarraytypes.h:1761:\n", "/Users/neil/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/numpy/core/include/numpy/npy_1_7_deprecated_api.h:15:2: warning: \"Using deprecated NumPy API, disable it by \" \"#defining NPY_NO_DEPRECATED_API NPY_1_7_API_VERSION\" [-W#warnings]\n", "#warning \"Using deprecated NumPy API, disable it by \" \\\n", " ^\n", "/Users/neil/.cache/scipy/python27_compiled/sc_1790bf65208b11355ffcfd4b65a5f10913.cpp:24:10: fatal error: 'omp.h' file not found\n", "#include \n", " ^\n", "2 warnings and 1 error generated.\n", "\n", " Weave compilation failed. Falling back to (slower) numpy implementation\n", "\n", "WARNING: reconstraining parameters sparse_gp_mpi.rbf.variance\n", "WARNING: reconstraining parameters sparse_gp_mpi.rbf.lengthscale\n", "WARNING: reconstraining parameters sparse_gp_mpi.Gaussian_noise.variance\n" ] }, { "html": [ "\n", "\n", "

\n", "Model: sparse gp mpi
\n", "Log-likelihood: -1822.27351085
\n", "Number of Parameters: 7
\n", "

\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "
sparse_gp_mpi.ValueConstraintPriorTied to
inducing inputs (4, 1)
rbf.variance 1.0 fixed
rbf.lengthscale 1.0 fixed
Gaussian_noise.variance 0.01 fixed
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27do+YO300YIUczf0ZSEDLovhwJ4dLmH/3at/ZdP/vOZTen5XAV+wZIXrHP/6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\nPZw8eZL169ezaMlyvvmfP+b537/JomW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OQpKQQIq5xC+0GhU6D1wtQgge+9QiVCrB+3vO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\nAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "When the prior over $\\mathbf{u}$ is integrated over the effective likelihood, $\\hat{p}(\\mathbf{y}|\\mathbf{u})$, it's possible to show that the resulting marginal likelihood, $\\hat{p}(\\mathbf{y})$, which forms the core of the lower bound on the likelihood, is a Gaussian process with a low rank form for the covariance,\n", "$$\n", "\\hat{p}(\\mathbf{y}) \\sim \\mathcal{N}(\\mathbf{0}, \\hat{\\mathbf{K}})\n", "$$\n", "where\n", "$$\n", "\\hat{\\mathbf{K}} = \\mathbf{K}_{fu}\\mathbf{K}_{uu}^{-1} \\mathbf{K}_{uf} + \\sigma^2 \\mathbf{I},\n", "$$\n", "where $\\mathbf{K}_{fu}$ gives the cross covariance between the variables of our function $f()$ and those of the inducing functions $u()$. \n", "\n", "Let's have a look at the form of this approximation for the un-optimized inducing variables." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Visualise full covariance and approximation.\n", "Kff = m_full.kern.K(m.X,m.X)\n", "Kfu = m.kern.K(m.X, m.Z)\n", "Kuu = m.kern.K(m.Z, m.Z)\n", "Kuf = Kfu.T\n", "noise = m['.*noise'][0]\n", "fig, ax = plt.subplots(1, 2, figsize=(12, 8))\n", "ax[0].matshow(np.dot(np.dot(Kfu,pdinv(Kuu)[0]),Kuf) + np.eye(m.X.shape[0])*m['.*noise'])\n", "ax[0].set_title('Low Rank Approximation')\n", "ax[1].matshow(Kff + np.eye(m.X.shape[0])*m['.*noise'])\n", "ax[1].set_title('Full Covariance')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 7, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Variational Compression\n", "\n", "The variational compression bound minmizes the additional information obtained about $\\mathbf{f}$ by knowing $\\mathbf{y}$ with respect to that which is known by observing $\\mathbf{u}$ alone. Maximizing the lower bound (whilst keeping model parameters fixed) compresses the information from $\\mathbf{y}$ into $q(\\mathbf{u})$. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "m.optimize(messages=True)\n", "m.plot()\n", "display(m)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n", "

\n", "Model: sparse gp mpi
\n", "Log-likelihood: -832.753958521
\n", "Number of Parameters: 7
\n", "

\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "
sparse_gp_mpi.ValueConstraintPriorTied to
inducing inputs (4, 1)
rbf.variance 1.0 fixed
rbf.lengthscale 1.0 fixed
Gaussian_noise.variance 0.01 fixed
" ], "metadata": {}, "output_type": "display_data", "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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Sa3F06Bxyu5hbgbur87CY4JgDk8VcFMUDgiBEmT4U+6K3XF6VSs2OHTs6NaXo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\nwUZVbROuDgJT4obubNCeyC+p5VxuNVGhQ3NiMZC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"text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "m.randomize()\n", "m.Z.unconstrain()\n", "m.optimize('bfgs', messages=True)\n", "_ = m.plot()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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9eewHK9j+xRmef30P+49n88NfvcZ3bp3H0jljXH7utLf1Vsmfu0+D9DVJ5nbY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\n3Dh/4OyI057woItz0gaD4sA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"text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Joint Optimization\n", "\n", "In practice we actually optimize the model parameters alongside the variational parameters. This means we either find better solutions, or solutions where it's easier to compress the information from $\\mathbf{y}$ into $\\mathbf{u}$. The former case occurs because for certain choices of prior over $\\mathbf{f}$ the values of $\\mathbf{y}$ do not provide a lot of information." ] }, { "cell_type": "code", "collapsed": false, "input": [ "M = 8\n", "Z = np.random.rand(M,1)*12\n", "m = GPy.models.SparseGPRegression(X,y,kernel=kern,Z=Z)\n", "m.likelihood.variance = noise_var\n", "\n", "fig, ax = plt.subplots(1, 2, figsize=(16, 8))\n", "m.optimize(messages=True)\n", "m.plot(ax=ax[0])\n", "m_full.plot(ax=ax[1])\n", "print M, \"inducing variables\"\n", "print \"Full model log likelihood: \", m_full.log_likelihood()\n", "print \"Lower bound from variational method: \", m.log_likelihood()\n", "print \"Information gain (in nats) associated with y \", m_full.log_likelihood() - m.log_likelihood()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "8 inducing variables\n", "Full model log likelihood: -36.4462976038\n", "Lower bound from variational method: [[-39.99802542]]\n", "Information gain (in nats) associated with y [[ 3.55172782]]\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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AzoJeLynBiAfvKVu+x5GGgK5lijOiZ5jFEIiCQa1WoTQ/DRXFFjiFCu8cbcGZ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VAAAg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\n/wFEGkIFAEw+vwAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 10 }, { "cell_type": "code", "collapsed": false, "input": [ "Kff = m_full.kern.K(m.X,m.X)\n", "Kfu = m.kern.K(m.X, m.Z)\n", "Kuu = m.kern.K(m.Z, m.Z)\n", "Kuf = Kfu.T\n", "sigma2 = m.likelihood.variance\n", "KfuKuuIKuf = np.dot(np.dot(Kfu,pdinv(Kuu)[0]),Kuf)\n", "fig, ax = plt.subplots(1, 2, figsize=(12, 6))\n", "ax[0].matshow(KfuKuuIKuf + np.eye(m.X.shape[0])*sigma2)\n", "ax[0].set_title('Low Rank Approximation')\n", "ax[1].matshow(Kff + np.eye(m.X.shape[0])*sigma2)\n", "_ = ax[1].set_title('Full Covariance')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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9LVqSXpAOb1CPRpL12XouWT+oZ0eyfurSO5P1mVHighSnMUT1INkhSl24Mkhp\neNcvt2k8jwd1APuZ+Jz9zKSNdVwqTmogpWHs9YFuN54zu7sk/aG7L5G0StJbzewkSZdLutndT5D0\njfJ7AEBnMWcDQJ0xm1133+buG8vHT0naLOkoSedJuqZc7RpJ51c1SADA+DBnA8C+mrpm18x6Ja2Q\ntE7SIncfKhcNSao+FRwAMG7M2QDQxCeomdnBkr4g6e3u/qTZ3uti3d3NzNPPvLbu8VJJJ7c0UACo\n1mD5lYfW5+x/q3t8nKQXVThKAGjVoMY7Z4+r2TWzmSomzTXufkNZHjKzI9x9m5kdqfDDYS8c10AA\noLN6y6+atZ0ZRhtMbM7+lckZJABMSK/GO2ePeRmDFacDrpZ0j7t/uG7RjZIuKR9fIumG0c8FAEwu\n5mwA2Nd4zuyeLukNkn5gZhvK2jslfUDSdWb2FpUxNumnp6LHngh2lVpXinPBgvUfOzpYX9Kmmc3t\nIqoHr9yWGelIstlL0nles4Kcr4OUjh47ZH46tm3JSVvSA5LiSK8ohi0SnAeKIsY+dVO6/qbfanK/\n6dQ2AGkVzNlTUKaRZFL1sWT9UZ1IMmRqzGbX3W9TfAb4Fe0dDgBgIpizAWBffIIaAAAAskWzCwAA\ngGzR7AIAACBbNLsAAADI1rg/VKJ1qTiDJtMVwvWfabIuaWeQ1LBpXvyclOiVC+qbD05/mMaBxwSp\nC0qnLhwc1A9cnN6OJP3C09vSC5pNY5gb1IO0hyh14d8/ka6f+uF0PdwvgApE822X6PaUBilMaiCl\nAWgNZ3YBAACQLZpdAAAAZItmFwAAANmi2QUAAEC2aHYBAACQrUlIY0iJUheiepSuMLPJ9RssG+5N\n1zcdmq5Hr9ycoL4gPdZ7Frwkvfr8x9J1petReoMkHXRi+piP0OPpJ0TH8KOgHqQxRMLUhb8N6v/S\n3PYBtFuXJzRIpDRMQH9UJ6UBXYIzuwAAAMgWzS4AAACyRbMLAACAbNHsAgAAIFs0uwAAAMhWh9IY\nojt7ozSGaP1o+I3SGKJ9RLsOEh/unZeuHxxsZ0G6vHPBwmT9rnNOSdaj1IWDGhzzbD2XXnDiXcny\nEbODlIb0UBWFOmgkqM8N6lHqwj8EdQAVSM2RUfINKQ1jIaUB6DzO7AIAACBbNLsAAADIFs0uAAAA\nskWzCwAAgGzR7AIAACBb5u7VbdzMpfdUtn1Mb+/RFeGy/tODBfOD+uKgflJQX54uP70q/f/H9bP7\nkvV1Oi15gSSaAAAMBUlEQVRZvz24VXu90tuRpK13Bnd9fy94wsagvimo3xvUH4pGFN0JPhTUtwf1\nJ6IdNFgWpZM0kwRzudzdGuw8O8zZqFLDOfvYYMELgvrxQT2aIs9Kl+9fenSyPqDVyfotOjNZv1Vn\nJOtb1wXzcrGTtGbn7MFoB9FcG83N0Rz8cFBPp0O1lojVbLJLajtXhHM2Z3YBAACQLZpdAAAAZItm\nFwAAANmi2QUAAEC2aHYBAACQrRmdHgDQqjBxQVL/t5t8Tk9Qj/6FBPW5M3Yn6ytWbWhuv4EejcTL\nlqWXbdGS5nbSrDClIX2Xc2c1uksYQJXCxAVJ/T8M6pWMZK/jo2SCpQPt2UE6WEeStFUNkhraYXBR\ntdufFFFKw8ymtsKZXQAAAGSLZhcAAADZotkFAABAtmh2AQAAkC2aXQAAAGSLNAZ0r/nxoih1oemU\nhjaZF3weeF/f+vQTZrdx58vS5TxSGto1hZHSAFTuBfGi/qiea0qDFCY1kNIwHlFKQxpndgEAAJAt\nml0AAABki2YXAAAA2aLZBQAAQLZodgEAAJAt0hjQvRY3WNaTLk+1lIa52p2sk9IAIDvHN/+U/qhO\nSkP7ZZHSkMaZXQAAAGSLZhcAAADZotkFAABAtmh2AQAAkC2aXQAAAGSLNAZ0r5MaLGvyb3bXpzRI\n7UtqIKUBQBX62rep/qhOSkP7ZZDSwJldAAAAZItmFwAAANmi2QUAAEC2aHYBAACQLZpdAAAAZKth\ns2tmc8xsnZltNLN7zOz9ZX2hmd1sZveZ2U1mtmByhgsAaIR5GwD21TCgyd13mtnL3X2Hmc2QdJuZ\n/ZKk8yTd7O4fNLPLJF1efgGTZ3mDZW0K1euWSDKpQSxZrpFkUhtjyYbbtJ3OY97GlHVW9bvoj+pT\nLZJMal8sGZFkYxrzMgZ331E+nCWpR9KjKibNa8r6NZLOr2R0AICmMW8DwF5jNrtmdoCZbZQ0JOlb\n7n63pEXuPlSuMiSpe9p7AMgc8zYA7DXmm73uvlvScjObL+nfzOzlo5a7mXm8hYG6x73lFwBMNT8o\nv7rfxObtgbrHvWLOBjA13Vd+jW3cVza6++Nm9hVJp0oaMrMj3H2bmR0paXv8zNXj3QUAdNAp5VfN\nZzo1kLZpbd5ePXkDBICWnVB+1Xw1XHOsNIbDanfsmtmBkl4paYOkGyVdUq52iaQbJjBaAECbMG8D\nwL7GOrN7pKRrzOwAFY3xGnf/hpltkHSdmb1F0qCkC6odJrC/p1fF/1ebOyNOLWiHqZbSIMVJDdmm\nNEhxUkPbUhq6EvM2pqT7l8b/LhumFrRBf1TvUEqD1OCYSWlou7Gix+6S9NJE/RFJr6hqUACA1jBv\nA8C++AQ1AAAAZItmFwAAANmi2QUAAEC2aHYBAACQrXHn7AJTzfrZfeGyFas2JOvztKuq4UgipWEf\npDQAqDPQKMM5SCAgpaFOt6c0SB1LauDMLgAAALJFswsAAIBs0ewCAAAgWzS7AAAAyBbNLgAAALJF\nGgO61jqdFi/sSZejBIIosaBdSGmoQ0oDMC3dojObfxIpDXuQ0tA6zuwCAAAgWzS7AAAAyBbNLgAA\nALJFswsAAIBs0ewCAAAgW6QxoGvdHt062kiQKEBKw16kNJQeqn63wHRyq85o38ZIadiDlIaxcWYX\nAAAA2aLZBQAAQLZodgEAAJAtml0AAABki2YXAAAA2SKNAV1rvfrCZT0aaW5jXZ7S0Og57TLVUhqk\nipMabqtu08B0tHVdg7v3WwjXSeqSlIZGz2kXUhr24swuAAAAskWzCwAAgGzR7AIAACBbNLsAAADI\nFs0uAAAAskUaA7rW1jvjOz57ljWZxhDpkpQGKU5qyDalQQqTGtqS0kAaA9BeA/Gi8A7+TFMapDip\nodFz2qFTKQ1SxUkNg/EizuwCAAAgWzS7AAAAyBbNLgAAALJFswsAAIBs0ewCAAAgW6QxoHt9L14U\n3o0f3L3ftCmW0iDFqQtTLaVhxaoN6Sf0tHHnVaY0AGhNgzk7kmtKgxSnLmSb0iCFP7e2pDQMxos4\nswsAAIBs0ewCAAAgWzS7AAAAyBbNLgAAALJFswsAAIBs0ewCAAAgW0SPoXttbP4pRJLV1TsUSTZP\nu5L16DWKXtOWEEkGdE4Lc3aESLKx12+XrokkuyFexJldAAAAZItmFwAAANmi2QUAAEC2aHYBAACQ\nLZpdAAAAZIs0BnSvTe3bFCkNdfUOpTRExxymNEhtS2oYWdazX21rezYNoGaw+l2Q0jD2+u3SNSkN\n4swuAAAAMkazCwAAgGzR7AIAACBbNLsAAADI1riaXTPrMbMNZvbl8vuFZnazmd1nZjeZ2YJqhwkA\nGC/mbADYa7xpDG+XdI+kQ8rvL5d0s7t/0MwuK7+/vILxAbF7q98FKQ119SmW0iA1SGpoMqVhRNml\nMTBnYwoaihcNLqp0z6Q0jL1+uzQ85nYlNSR+bo3m7DHP7JrZ0ZLOlfQJSVaWz5N0Tfn4GknnNzNG\nAEA1mLMBYF/juYzhQ5L+RNrn9Moid6/9F21IUrX/JQMAjBdzNgDUaXgZg5m9RtJ2d99gZqtT67i7\nm5nHWxmoe9xbfgHA1PLgwGY9OLC508OYEOZsANPFzoHbtXPg9nGtO9Y1uy+TdJ6ZnStpjqR5ZrZG\n0pCZHeHu28zsSEnb402sHtdAAKCTnr/6JD1/9Ul7vt98xRc7OJqWMWcDmBbmrD5Nc1aftuf7x6/4\n+3DdhpcxuPufuftidz9W0uslfdPd3yjpRkmXlKtdIumGiQ4aADAxzNkAsL/xpjHU1N76+oCk68zs\nLSo+7fqCdg4KGJeHGiyrOKlhqqU0SNUnNUy1lAYpPuZ2pDR8oYXxTEHM2ZhCWkgmyDSlQao+qaE/\nqncopUFqcMxtSGlolMYw7mbX3ddKWls+fkTSKyY4LgBARZizAaDAJ6gBAAAgWzS7AAAAyBbNLgAA\nALJFswsAAIBsNZvGAEwhDe5kfejodD3TlAYpTiAgpWGvFas2JOsjPT1VDgeApIbxzs3q9pQGKUwg\nIKWhThMpDf/cYBlndgEAAJAtml0AAABki2YXAAAA2aLZBQAAQLZodgEAAJAt0hjQxYaaf0quKQ1S\nmNQQJRDM06427nx/UzGlITrmlX3rqt85MO09XP0uSGloWX9U7/KUBokzuwAAAMgYzS4AAACyRbML\nAACAbNHsAgAAIFs0uwAAAMgWaQzoYm38nPWcUxp60uW+vvXJ+lztbuPO9zcVUxqqPmYAkvRk53ZN\nSkPL+qP6VExpCHBmFwAAANmi2QUAAEC2aHYBAACQLZpdAAAAZItmFwAAANkijQFd7Inqd5FzSsPs\ndLlbUhoaPadpw23aDoAGnun0APbXqZQGqX1JDV2S0tDoOVXjzC4AAACyRbMLAACAbNHsAgAAIFs0\nuwAAAMgWzS4AAACyRbMLAACAbBE9hi7WSvRYm/7KT7VIMql9sWRdEkkmxbFkbYskA9BGuzo9gPGr\nOJJMahBLlmkkmRTHkjV6TjtwZhcAAADZotkFAABAtmh2AQAAkC2aXQAAAGSLZhcAAADZIo0BXeyZ\nTg9gfx1KaZAaJDVkmtIgxakLTac0jLRlOAAaGu70ACaOlIYJ6Y/qFac0cGYXAAAA2aLZBQAAQLZo\ndgEAAJAtml0AAABki2YXAAAA2SKNAV2s0Z29UyypYRqmNKxYtSFZn6ddbdpxrG0pDQAmSZcnNZDS\nMCH9Ub1NKQ2c2QUAAEC2aHYBAACQLZpdAAAAZItmFwAAANmi2QUAAEC2SGNAF2vlrv52pTS06c7h\nKZjSMLKsJ11Xuh4Z6Umvv7JvXbI+V7vTG2rlpR5Jl5tNaQDQTo3m7JlBnZSGsZDSMDbO7AIAACBb\nk9jsDk7erqaMwU4PoAMGOz2ASfaDTg9g0j04sLnTQ8CkGOz0ADpgsNMD6IDBTg+gA+7r9AAm3c6B\n2zs9hI6i2a3UYKcH0AGDnR7AJKPZRa4GOz2ADhjs9AA6YLDTA+gAmt3phssYAAAAkC2aXQAAAGTL\n3L26jZtVt3EAqJi7W6fHMJmYswF0s2jOrrTZBQAAADqJyxgAAACQLZpdAAAAZItmFwAAANmi2QUA\nAEC2aHYBAACQrf8Po6OZBrnzyOcAAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ceres Data\n", "\n", "Now we will look at some real data. This is data as published by Franz von Zach's volume, Monatliche Correspondenz by Giuseppe Piazzi for observations of the (dwarf) planet Ceres, as shown in the Google book below. }" ] }, { "cell_type": "code", "collapsed": false, "input": [ "pods.notebook.display_google_book('JBw4AAAAMAAJ', 'PA280')" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "" ], "metadata": {}, "output_type": "display_data", "text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We've made the data available in the pods library. The data is famous because Gauss fitted the orbit of Ceres, and made a made a prediction about the location of the planet a year after its discovery, allowing the planet to be recovered (it had been lost behind the sun). This established Gauss at the age of 23 as a leading European mathematician. Gauss later claimed that he used the Gaussian error model when making his predictions. The data is in the form of a pandas data frame, which can be loaded and summarized as follows." ] }, { "cell_type": "code", "collapsed": false, "input": [ "import pods\n", "data = pods.datasets.ceres()['data']\n", "data.describe()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
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Mittlere SonnenzeitGerade Aufstig in ZeitGerade Aufstiegung in GradenNordlich AbweichGeocentrische LaengerGeocentrische BreiteOrt der Sonne + 20\" AberrationLogar. d. Distanz
count 21.000000 21.000000 21.000000 20.000000 19.000000 19.000000 19.000000 19.000000
mean 7.460553 3.474579 52.117897 17.052194 1.867660 1.802494 10.089094 9.993320
std 0.784663 0.055710 0.836052 0.985692 0.036103 0.815463 0.444599 0.000609
min 6.199500 3.424925 51.374056 15.628750 1.832791 0.600806 9.396909 9.992616
25% 6.807333 3.435597 51.533972 16.329201 1.839015 1.153542 9.780756 9.992807
50% 7.400750 3.448292 51.724389 17.015889 1.851418 1.707806 10.084920 9.993189
75% 8.038194 3.504792 52.571889 17.827847 1.889333 2.383375 10.431290 9.993735
max 8.721611 3.618483 54.277250 18.799667 1.952000 3.111694 10.813114 9.994582
\n", "