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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Quasi-Bayesian Mixture Estimation"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Bayesian RLS (regression with a known variance)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Assume a row regressor $x_{t} \\in \\mathbb{R}^{n}$, determining via the column regression coefficients vector $\\beta \\in\\mathbb{R}^{k}$ the scalar regressand $y_{t}\\in\\mathbb{R}$."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Model**\n",
      "$$\n",
      "y_{t}|x_{t}, \\beta \\sim \\mathcal{N}(x_{t}\\beta, \\sigma^{2})\n",
      "$$\n",
      "\n",
      "with a pdf\n",
      "\n",
      "$$\n",
      "\\begin{align*}\n",
      "p(y_{t}|x_{t}, \\beta) &\\propto \\exp\\left\\{-\\frac{1}{2\\sigma^{2}} (y_{t} - x_{t}\\beta)^2\\right\\} \\\\\n",
      "&= \\exp\\left\\{ -\\frac{1}{2} \\left[ \\sigma^{-2}y_{t}^{\\intercal}y_{t} \n",
      "+ \\operatorname{Tr} \n",
      "\\left(\n",
      "\\begin{bmatrix}\n",
      "\\beta\\beta^{\\intercal}\\\\\n",
      "-2\\beta\n",
      "\\end{bmatrix}^{\\intercal}\n",
      "\\begin{bmatrix}\n",
      "x_{t}^{\\intercal} x_{t} \\sigma^{-2} \\\\\n",
      "x_{t}^{\\intercal} y_{t} \\sigma^{-2}\n",
      "\\end{bmatrix}\n",
      "\\right)\n",
      "\\right] \\right\\}\n",
      "\\end{align*}\n",
      "$$\n",
      "\n",
      "where $\\eta = \\begin{bmatrix}\n",
      "\\beta\\beta^{\\intercal}\\\\\n",
      "-2\\beta\n",
      "\\end{bmatrix}^{\\intercal}$ and\n",
      "$T = \\begin{bmatrix}\n",
      "x_{t}^{\\intercal} x_{t} \\sigma^{-2} \\\\\n",
      "x_{t}^{\\intercal} y_{t} \\sigma^{-2}\n",
      "\\end{bmatrix}$\n",
      "are the natural parameter and the sufficient statistic, respectively.\n",
      "\n",
      "**Prior**\n",
      "$$\n",
      "\\beta|V_{t-1} \\sim \\mathcal{N}(\\beta_{t-1}, V_{t-1})\n",
      "$$\n",
      "\n",
      "with a pdf\n",
      "\n",
      "$$\n",
      "\\begin{align*}\n",
      "\\pi(\\beta|V_{t-1}) &\\propto \\exp\\left\\{-\\frac{1}{2} (\\beta - \\beta_{t-1})^{\\intercal} V_{t-1}^{-1} (\\beta - \\beta_{t-1})\\right\\} \\\\\n",
      "&= \\exp\\left\\{ -\\frac{1}{2} \\left[ \\beta_{t-1}^{\\intercal}V_{t-1}^{-1}\\beta_{t-1}\n",
      "+ \\operatorname{Tr} \n",
      "\\left(\n",
      "\\begin{bmatrix}\n",
      "\\beta\\beta^{\\intercal}\\\\\n",
      "-2\\beta\n",
      "\\end{bmatrix}^{\\intercal}\n",
      "\\begin{bmatrix}\n",
      "V_{t-1}^{-1} \\\\\n",
      "V_{t-1}^{-1} \\beta_{t-1}\n",
      "\\end{bmatrix}\n",
      "\\right)\n",
      "\\right] \\right\\}\n",
      "\\end{align*}\n",
      "$$\n",
      "\n",
      "where $\\beta_{t-1}^{\\intercal}V_{t-1}^{-1}\\beta_{t-1}$ can be absorbed into the normalization constant.\n",
      "\n",
      "**Posterior**\n",
      "$$\n",
      "\\beta|V_{t} \\sim \\mathcal{N}(\\beta_{t}, V_{t}) \\qquad\\text{where}\\qquad\n",
      "V_{t}^{-1} = V_{t-1}^{-1} + x_{t}^{\\intercal} x_{t} \\sigma^{-2} \\qquad \\text{and}\\qquad\n",
      "\\beta_{t} = (x_{t}^{\\intercal} x_{t} \\sigma^{-2} + V_{t-1}^{-1})^{-1} (x_{t}^{\\intercal} y_{t} \\sigma^{-2} + V_{t-1}^{-1}\\beta_{t-1})\n",
      "$$\n",
      "\n",
      "**Note:** *a popular choice for a one-shot estimation is the prior $\\beta|\\sigma^{2} \\sim \\mathcal{N}(\\beta_{0}, \\sigma^{2}V_{0})$ with $V_{0} = (x_{0}^{\\intercal}x_{0})^{-1}$. Notice, that putting then the factors $\\sigma^{2}$ cancel in the posterior estimation of $\\beta$ and the well-known formulae $\\hat{\\beta}_{t} = (x_{t}^{\\intercal} x_{t} + V_{0}^{-1})^{-1} (x_{t}^{\\intercal} y_{t} + V_{0}^{-1}\\beta_{t-1})$ are recovered. However, we will need the 'weighting' factor $\\sigma^{2}$ for the diffusion. Note also the coincidence of these formulae with the measurement update of the Kalman filter: this is where this filter and the recursive least squares coincide.*\n",
      "\n",
      "\n",
      "**Predictive**\n",
      "$$\n",
      "y_{t+1}|X_{t}, Y_{t} \\sim \\mathcal{N}(x_{t}\\beta_{t}, \\sigma^{2})\n",
      "$$"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Quasi-Bayesian mixture estimation"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Consider a mixture of $K$ RLS models in the form\n",
      "$$\n",
      "p(y_{t}|x_{t}, \\phi, \\beta) = \\sum_{k=1}^{K} p_{k}(y_{t}|x_{t}, \\beta_{k})\n",
      "$$\n",
      "where the unknown parameters $\\phi = [\\phi_{1},\\ldots,\\phi_{K}]$ are the component weights and $\\beta = [\\beta_{1},\\ldots,\\beta_{K}]$ are the regression coefficients. Their estimation exploits the principles described in the paper, Section II. In particular, the estimation of $\\beta$ employs the prior, posterior and predictive pdfs given above."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Diffusion quasi-Bayesian mixture estimation"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The diffusion quasi-Bayesian estimation presented in the paper is applied to the mixture of two RLS models with unknown regression coefficients.\n",
      "\n",
      "* Adaptation phase - the node $i$ incorporates the measurements $x_{t}^{[j]}$ and $x_{t}^{[j]}$ of its neighborhood $j\\in\\mathcal{N}_{i}$. It exploits their noise variances $(\\sigma^{2})^{[j]}$ for evaluation of the posterior pdf, see the theory above.\n",
      "* Combination phase - the node $i$ forms a convex combination of the posterior sufficient statistics - c.f. the theory above."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Python code"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Below we give the python code producing the results in the paper. First, some initializations:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np                                  # numerical package\n",
      "from scipy.stats import norm                        # normal distribution from scientific package\n",
      "from copy import deepcopy                           # deepcopy of python data types\n",
      "import networkx as nx                               # graph package\n",
      "from prettytable import PrettyTable                 # pretty printing of tables\n",
      "\n",
      "np.set_printoptions(precision=4, suppress=True)     # printing: n-digits precision, no scientific format\n",
      "seed = 1234                                         # seed for reproducible results"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Setting the diffusion network:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nnodes = 25                           # number of network nodes\n",
      "mode = 'ATC'                          # Diff. mode: 'ATC' - adapt-then-combine, 'null' for no coop.\n",
      "edge_prob = .2                        # probability of an edge\n",
      "\n",
      "if mode == 'ATC':\n",
      "    # We generate a network of nnodes, interconnected with probability 0.2\n",
      "    G = nx.binomial_graph(nnodes, edge_prob, seed=seed)\n",
      "    adjacency_matrix = nx.adjacency_matrix(G)\n",
      "    np.fill_diagonal(adjacency_matrix, 1)                     # The nodes are self-adjacent\n",
      "elif mode == 'null':\n",
      "    adjacency_matrix = np.eye(nnodes) \n",
      "    G = nx.from_numpy_matrix(adjacency_matrix)\n",
      "\n",
      "# Plot the network (first node is 1, not 0)\n",
      "G = nx.convert_node_labels_to_integers(G, first_label=1)\n",
      "nx.draw(G, node_color='yellow')\n",
      "    \n",
      "# Adapt weights\n",
      "if mode == 'ATC':                              \n",
      "    # Measurements are shared \n",
      "    adapt_weights = adjacency_matrix.copy()\n",
      "elif mode == 'null':        \n",
      "    # Measurements are not shared\n",
      "    adapt_weights = np.eye(nnodes)\n",
      "\n",
      "# Combine weights are always uniform\n",
      "combine_weights = adjacency_matrix.copy() \n",
      "np.fill_diagonal(combine_weights, 1)\n",
      "normsum = combine_weights.sum(axis=1)\n",
      "combine_weights = combine_weights / normsum\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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OwM3NDbt378bx48exaNEitf08Fi1aBG1tbQwYMCDLx+jrGyIhIW20/fwtMTIC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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xb61710c>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Simulation of data"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note: `beta0` and `beta1` below correspond to $\\beta_2$ and $\\beta_1$ in the paper. That is, indexing in the code runs from 0 and the components are swapped wrt the paper."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ndat = 600                            # number of simulated data\n",
      "beta0 = np.array([.3, 1.3, -.9])      # coeffs. of the 1st component\n",
      "beta1 = np.array([.3, 0., .9])        # coeffs. of the 2nd component\n",
      "np.random.seed(seed)\n",
      "X = np.random.normal(size=(ndat, 3))  # regressors"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Y1 = np.dot(X, beta0)                 # simulated data with 1st component\n",
      "Y2 = np.dot(X, beta1)                 # simulated data with 2nd component\n",
      "Y = Y2                                # final data consist of 2nd component, later 1st component will replace some points\n",
      "\n",
      "# time indices where the 1st component will occur\n",
      "beta0_set = set(range(50, 70)) \\\n",
      "            | set(range(120, 130)) \\\n",
      "            | set(range(170, 190)) \\\n",
      "            | set(range(210, 220)) \\\n",
      "            | set(range(240, 250)) \\\n",
      "            | set(range(300, 315)) \\\n",
      "            | set(range(400, 420)) \\\n",
      "            | set(range(510, 530))\n",
      "beta0_tuple = list(beta0_set)\n",
      "Y[np.array(beta0_tuple)] = Y1[np.array(beta0_tuple)]    # here we do the replacement\n",
      "\n",
      "# Measurements of nodes\n",
      "YY = Y[:,newaxis] * np.ones((ndat, nnodes))\n",
      "noise_std_array = np.zeros(nnodes)\n",
      "for i in range(nnodes):\n",
      "    noise_std = .05 * (i+1)\n",
      "    np.random.seed(seed)\n",
      "    YY[:,i] += np.random.normal(scale=noise_std, size=(ndat))\n",
      "    noise_std_array[i] = noise_std"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Objects for RLS modelling"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The components will be represented by the `QB_RLS_component` class. It's documented in the code..."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class QB_RLS_component():\n",
      "    def __init__(self, prior_invV, prior_beta, noise_std, kappa):\n",
      "        \"\"\"Constructor\"\"\"\n",
      "        self.prior_invV = prior_invV                               # sufficient statistic 1\n",
      "        self.beta = prior_beta                                     # prior/posterior mean\n",
      "        self.prior_invV_beta = self.prior_invV.dot(self.beta)      # sufficient statistic 2\n",
      "        self.noise_std = noise_std                                 # known noise st.dev.\n",
      "        self.kappa = kappa                                         # component's Dirichlet hyperparameter       \n",
      "        self.log_beta = []                                         # list for logging the beta estimates\n",
      "    \n",
      "    def predictive_loglikelihood(self, xt, yt, noise_std):         \n",
      "        \"\"\"Predictive loglikelihood\"\"\"\n",
      "        mean = np.dot(xt, self.beta)\n",
      "        return norm.logpdf(yt, loc=mean, scale=noise_std)\n",
      "    \n",
      "    def update(self, xt, yt, w, noise_std=None):\n",
      "        \"\"\"Update of component's hyperparameters\"\"\"\n",
      "        if noise_std is None:                                       # Use own noise st. dev. if unset\n",
      "            noise_std = self.noise_std\n",
      "        xTx = np.outer(xt, xt)\n",
      "        xTy = xt * yt\n",
      "        self.prior_invV += w * xTx / noise_std**2                             # update of suff. stat. 1\n",
      "        self.prior_invV_beta += w * xTy / noise_std**2                        # update of suff. stat. 2\n",
      "        self.beta = np.linalg.inv(self.prior_invV).dot(self.prior_invV_beta)  # calculate posterior mean (beta)\n",
      "        self.kappa += w                                                       # update Dirichlet hyperparameter\n",
      "        \n",
      "    def savelog(self):\n",
      "        \"\"\"Logging of the beta estimate\"\"\"\n",
      "        self.log_beta.append(self.beta.copy())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next is the class `QB_RLS`, for quasi-Bayesian estimation of a mixture of RLS models."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class QB_RLS():\n",
      "    def __init__(self, components):\n",
      "        \"\"\"Constructor\"\"\"\n",
      "        self.components = components                                # list of 'QB_RLS_component' components\n",
      "        self.ncomponents = len(components)                          # number of components\n",
      "        self.log_w = []                                             # list for logging components' weights\n",
      "        \n",
      "    def update(self, xt, yt, weight=1., noise_std=None):\n",
      "        \"\"\"Mixture update\"\"\"\n",
      "        if noise_std is None:\n",
      "            noise_std = self.noise_std\n",
      "        predictive_likelihoods = np.zeros(self.ncomponents)\n",
      "        Dirichlet_hyperparams = np.array([comp.kappa for comp in self.components])\n",
      "        comps_weights = Dirichlet_hyperparams/Dirichlet_hyperparams.sum()\n",
      "        \n",
      "        predictive_liks = np.array([comp.predictive_loglikelihood(xt, yt, noise_std) for comp in self.components])\n",
      "        w = np.log(comps_weights) + predictive_liks\n",
      "        w -= w.max()\n",
      "        w = np.exp(w)\n",
      "        w /= w.sum()\n",
      "        w *= weight\n",
      "        \n",
      "        for k in range(self.ncomponents):\n",
      "            self.components[k].update(xt, yt, w[k], noise_std)\n",
      "        self.log_w.append(w)\n",
      "\n",
      "    @property\n",
      "    def statistics(self):\n",
      "        \"\"\"Statistics of the mixtures' components\"\"\"\n",
      "        statistics = []\n",
      "        for component in self.components:\n",
      "            statistics.append({'invV': component.prior_invV.copy(),\n",
      "                 'invV_beta': component.prior_invV_beta.copy(),\n",
      "                 'kappa': component.kappa})\n",
      "        return statistics\n",
      "    \n",
      "    def savelog(self):\n",
      "        \"\"\"Force logging\"\"\"\n",
      "        for component in self.components:\n",
      "            component.savelog()\n",
      "        \n",
      "    def adapt(self, xt, yt_array, noise_std_array, adapt_weights):\n",
      "        \"\"\"Diffusion adapt step\"\"\"\n",
      "        for i in range(yt_array.shape[0]):\n",
      "            if adapt_weights[i] != 0:\n",
      "                self.update(xt, yt_array[i], adapt_weights[i], noise_std_array[i])\n",
      "            \n",
      "    def combine(self, statistics, combine_weights):\n",
      "        \"\"\"Diffusion combine step\"\"\"\n",
      "        for k in range(self.ncomponents):\n",
      "            self.components[k].prior_invV *= 0\n",
      "            self.components[k].prior_invV_beta *= 0\n",
      "            self.components[k].kappa = 0.\n",
      "            for i in range(len(statistics)):\n",
      "                if combine_weights[i] != 0:\n",
      "                    self.components[k].prior_invV += combine_weights[i] * statistics[i][k]['invV']\n",
      "                    self.components[k].prior_invV_beta += combine_weights[i] * statistics[i][k]['invV_beta']\n",
      "                    self.components[k].kappa += combine_weights[i] * statistics[i][k]['kappa']\n",
      "            self.components[k].beta = np.linalg.inv(self.components[k].prior_invV).dot(self.components[k].prior_invV_beta)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Estimation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "prior_invV = np.eye(3) * 1.\n",
      "prior_beta0 = np.array([0.5, 1., -1.])\n",
      "prior_beta1 = np.array([0.5, 0., 1.])\n",
      "\n",
      "diffnet = []\n",
      "\n",
      "for i in range(nnodes):\n",
      "    components = []\n",
      "    components.append(QB_RLS_component(prior_invV.copy(), prior_beta0.copy(), noise_std_array[i], 10.))\n",
      "    components.append(QB_RLS_component(prior_invV.copy(), prior_beta1.copy(), noise_std_array[i], 10.))\n",
      "    diffnet.append(QB_RLS(deepcopy(components)))\n",
      "\n",
      "print('Progress (out of {0}):'.format(ndat))\n",
      "for t in range(ndat):\n",
      "    if t%10 == 0:\n",
      "        print t,\n",
      "    xt = X[t]\n",
      "    yt_array = YY[t]\n",
      "    \n",
      "    # ADAPT\n",
      "    for i in range(nnodes):\n",
      "        diffnet[i].adapt(xt, yt_array, noise_std_array, np.ravel(adapt_weights[i]))\n",
      "    \n",
      "    # COMBINE\n",
      "    if mode == 'ATC':\n",
      "        diff_statistics = [node.statistics for node in diffnet]\n",
      "        for i in range(nnodes):\n",
      "            diffnet[i].combine(diff_statistics, np.ravel(combine_weights[i]))\n",
      "            \n",
      "    for node in diffnet:\n",
      "        node.savelog()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
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      {
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       "text": [
        "590\n"
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      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Printing table of final estimates\n",
      "est_tab = PrettyTable([\"Node\", \"1st component\", \"2nd component\"])\n",
      "for node in range(nnodes):\n",
      "    est_tab.add_row([node+1, diffnet[node].components[0].beta, diffnet[node].components[1].beta])\n",
      "print est_tab\n",
      "\n",
      "# Plotting the evolution at nodes (note: python indexes from 0!)\n",
      "node_to_plot = 10\n",
      "\n",
      "plt.figure(figsize=(14,10))  \n",
      "plt.subplot(4,1,1)\n",
      "plt.title('Evolution of data')\n",
      "for tx in beta0_tuple:\n",
      "    plt.axvline(tx, color='gainsboro')\n",
      "plt.plot(YY[:,node_to_plot])\n",
      "plt.hold(True)\n",
      "plt.grid(True)\n",
      "\n",
      "plt.subplot(4,1,2)\n",
      "plt.title('Evolution of weights (probabilities) of beta0')\n",
      "plt.fill_between(range(2, 2+len(diffnet[node_to_plot].log_w)), \n",
      "                 np.array(diffnet[node_to_plot].log_w)[:,0], np.zeros(len(diffnet[node_to_plot].log_w)), color='red')\n",
      "plt.hold(True)\n",
      "plt.grid(True)\n",
      "plt.xlim(xmax=len(diffnet[node_to_plot].log_w))\n",
      "\n",
      "plt.subplot(4,1,3)\n",
      "plt.plot(diffnet[node_to_plot].components[0].log_beta)\n",
      "plt.title('Estimates of beta0')\n",
      "plt.grid(True)\n",
      "\n",
      "plt.subplot(4,1,4)\n",
      "plt.plot(diffnet[node_to_plot].components[1].log_beta)\n",
      "plt.title('Estimates of beta1')\n",
      "plt.grid(True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "+------+---------------------------+---------------------------+\n",
        "| Node |       1st component       |       2nd component       |\n",
        "+------+---------------------------+---------------------------+\n",
        "|  1   | [ 0.3217  1.2882 -0.8867] | [ 0.2982 -0.0046  0.8928] |\n",
        "|  2   | [ 0.3217  1.2882 -0.8867] | [ 0.2982 -0.0045  0.8926] |\n",
        "|  3   | [ 0.3217  1.2882 -0.8867] | [ 0.2982 -0.0043  0.8925] |\n",
        "|  4   | [ 0.3217  1.2882 -0.8867] | [ 0.2982 -0.0043  0.8924] |\n",
        "|  5   | [ 0.3217  1.2882 -0.8867] | [ 0.2981 -0.0041  0.8922] |\n",
        "|  6   | [ 0.3217  1.2882 -0.8867] | [ 0.2981 -0.0042  0.8924] |\n",
        "|  7   | [ 0.3217  1.2882 -0.8867] | [ 0.2981 -0.0041  0.8923] |\n",
        "|  8   | [ 0.3217  1.2882 -0.8867] | [ 0.2981 -0.0039  0.8921] |\n",
        "|  9   | [ 0.3217  1.2882 -0.8867] | [ 0.2982 -0.0041  0.8922] |\n",
        "|  10  | [ 0.3217  1.2882 -0.8867] | [ 0.2982 -0.0044  0.8925] |\n",
        "|  11  | [ 0.3217  1.2882 -0.8867] | [ 0.2981 -0.0042  0.8923] |\n",
        "|  12  | [ 0.3217  1.2882 -0.8867] | [ 0.2982 -0.0042  0.8923] |\n",
        "|  13  | [ 0.3217  1.2882 -0.8867] | [ 0.2981 -0.0043  0.8924] |\n",
        "|  14  | [ 0.3217  1.2882 -0.8867] | [ 0.2981 -0.0041  0.8923] |\n",
        "|  15  | [ 0.3217  1.2882 -0.8867] | [ 0.2982 -0.0042  0.8923] |\n",
        "|  16  | [ 0.3217  1.2882 -0.8867] | [ 0.2981 -0.004   0.8922] |\n",
        "|  17  | [ 0.3217  1.2882 -0.8867] | [ 0.2982 -0.0043  0.8923] |\n",
        "|  18  | [ 0.3217  1.2882 -0.8867] | [ 0.2982 -0.0042  0.8923] |\n",
        "|  19  | [ 0.3217  1.2882 -0.8867] | [ 0.2982 -0.0043  0.8924] |\n",
        "|  20  | [ 0.3217  1.2882 -0.8867] | [ 0.2981 -0.0042  0.8922] |\n",
        "|  21  | [ 0.3217  1.2882 -0.8867] | [ 0.2981 -0.0042  0.8923] |\n",
        "|  22  | [ 0.3217  1.2882 -0.8867] | [ 0.2981 -0.0042  0.8924] |\n",
        "|  23  | [ 0.3217  1.2882 -0.8867] | [ 0.2982 -0.0044  0.8925] |\n",
        "|  24  | [ 0.3217  1.2882 -0.8867] | [ 0.2981 -0.0042  0.8923] |\n",
        "|  25  | [ 0.3217  1.2882 -0.8867] | [ 0.2981 -0.0039  0.892 ] |\n",
        "+------+---------------------------+---------------------------+\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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150gVn9xceh6rNbKxt6cHeP31/pWRwW4HensXjgjiYzBQmuprryVlTw02W3DF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\naPzUBqJgjQ9AWp3zzpMXJ5T9h8lEi48XXaQfAZI16LQI4Pk8J08m0yJ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EaqXxfdgwOv6f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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xbe1ebcc>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Mean square errors"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "est_errors_beta0_norm = np.zeros((ndat, nnodes))\n",
      "est_errors_beta1_norm = np.zeros((ndat, nnodes)) \n",
      "\n",
      "for i in range(nnodes):\n",
      "    est_errors_beta0_norm[:,i] += np.sum((np.array(diffnet[i].components[0].log_beta) - beta0) ** 2, axis = 1)\n",
      "    MSE_beta0_nodes = np.cumsum(est_errors_beta0_norm, axis=1) / np.arange(1, ndat+1)[:,newaxis]\n",
      "    MSE_beta0_net = np.mean(MSE_beta0_nodes, axis=1)\n",
      "    est_errors_beta1_norm[:,i] += np.sum((np.array(diffnet[i].components[1].log_beta) - beta1) ** 2, axis = 1)\n",
      "    MSE_beta1_nodes = np.cumsum(est_errors_beta1_norm, axis=1) / np.arange(1, ndat+1)[:,newaxis]\n",
      "    MSE_beta1_net = np.mean(MSE_beta1_nodes, axis=1)\n",
      "    np.save('{0}.npy'.format(mode), [MSE_beta0_net, MSE_beta1_net])\n",
      "    np.save('nodes_{0}.npy'.format(mode), [MSE_beta0_nodes, MSE_beta1_nodes])\n",
      "\n",
      "# In this figure, betas correspond to the paper!\n",
      "plt.figure(figsize=(8, 4.5))\n",
      "for tx in beta0_tuple:\n",
      "    plt.axvline(tx, color='gainsboro')\n",
      "plt.hold(True)\n",
      "plt.plot(np.log10(MSE_beta1_net), 'g', label=r'$\\beta_2$')\n",
      "plt.plot(np.log10(MSE_beta0_net), 'r', label=r'$\\beta_1$')\n",
      "plt.grid(True)\n",
      "plt.legend()\n",
      "plt.ylabel(r'log(MSE) of $\\beta_{1}, \\beta_{2}$', fontsize=14)\n",
      "plt.xlabel('Time $t$', fontsize=14)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "<matplotlib.text.Text at 0xd074eec>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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jGuldq5E8qZOxZx8NFv5FixYRHR3N/Pnz6du3L8uXL+eXX35hz549/PLLL7z9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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xbdfbcac>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(np.arange(1, nnodes+1), np.log(MSE_beta0_nodes[-1,:]), 'v--', label=r'$MSE(\\beta_0)$')\n",
      "plt.hold(True)\n",
      "plt.plot(np.arange(1, nnodes+1), np.log(MSE_beta1_nodes[-1,:]), '^--', label=r'$MSE(\\beta_1)$')\n",
      "plt.grid()\n",
      "plt.legend(loc=4)\n",
      "plt.xlim(xmin=1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "(1, 25.0)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ydHPhQhwZGX25995IW3dF1LHSK04Tvksg91yu7ntub3U7e57ew56/7iGyJJKj\nbY46VAlGCHtk8xE9GAgPn8LmzfZ/H9iakPm/5R29cJT+/9Ofg60P4rbPjbYj27L3mb00dm1cYZuG\nNAtGjhd9EhdzDnllrIdHCs8/P8SpknxDUJOlBaI+i2LTfzdxpeUVABp1a8TcznMrTfIgdzYSwlps\nPqIPD5/kdKN5Z6dXa1dKUaJKaORiPnY4cOYAo54cRXqgLMcrRG05ZI1eRvOOp7TWviRhCcv3LOeJ\nlU/Q8a2OLN6xWPf9OzbuILu5XHEqhK3YfERvMBicMtE7a21RKUXAnwP4OfRnXNa4MPjpwUR1iSLK\nLwr/lv66/5Zla+3n8s7hfYu309baLeWsx0ttSVzMOWSN3hmTvCOp6TK+Cd8lkNsyFzRoclsTxnuN\nJ7ZP5XPTyyZz+cEVov7ZfEQva93YTkXz2g3KwJYjW9hyZAtT+k4p93659Z0QtuWQNXphO2VvZl1c\nUsy6g+v46+q/0m5BOyasmsD5K+cxKEO598vqjkI4HhnR1xF7L1GUHZ2H7w7HMNh4rmS4/3Duv/1+\nut3czayNNea123tcbEXiok/iYs4ha/TCNsqOzrObZfPBzR8wavioStvIiVMhHJOM6J1EVSdVc8/l\n8ulPn/IHzz8wLmSc1NqFcFBSo2+gSk+q3viPf/7KeT7a/hEDPh5A7w97c+LyCUL/ECq1diEaGEn0\ndaQ+19Eue1K11KHzh+j4Vkf+s/8/TO4zmaNTjvLen94j+JZg0zK+A3IGmB5hhjBWrVlV532V9cX1\nSVz0SVysQ2r0Du7Ge6MOv3c4mqbRvnl7cp7Nwaepj1kbqbUL0bBYPKJftmwZAQEBuLq6sn37drPX\nDx06RLNmzZg/f36tOuio6mOmQGFxIX9792/sbLbTrPyiaZpukrc1mUGhT+KiT+JiHRYn+qCgIBIT\nE+nfv7/u61OmTCEmJsbijomKHThzgOfXPE/7N9vz+YrPKexYCEBBxwLd2+0JIRo2ixO9v78/3bqZ\nz7UG+Oabb+jcuTPdu3e3uGOOztLaYmVJes+pPUR/Hk2fj/oAENcujuLOxQ51UlVqrvokLvokLtZh\n9ZOxly5dYs6cOcTFxVn7o51eRbNnSjVr3IwHAx7k0KRDzB08l8zNmTY7qSqEcByVnowdNGgQeXl5\nZttnzJjB0KFDddvExcUxefJkPDw8qlVCGDt2LL6+vgB4e3sTHBxsqsuV/jZ3xOcRERE1bv/6jNf5\nctOXRH8fe0A8AAAYBUlEQVQXTezQWNavX1/u9YM7DuKLL03dmgIwJnaM3XzfmjwvZS/9sYfnlhwv\nDeV5KXvpjy2+f1paGrm5uViq1hdMRUZGMn/+fHr16gVA//79OXz4MADnzp3DxcWFN954g6efftp8\n53LBlIlSij4j+7A1cCse//Vg3efr6NO+j627JYSwMza7YKrsTn/44QdycnLIyclh0qRJTJs2TTfJ\nO7sbRyOVKSguYNz8cWxtuhU0KOlcwpEdR+quczZUk7g0JBIXfRIX67A40ScmJtK+fXu2bNlCTEwM\n0dHR1uxXg5F+JJ3Ob3fm29Xfgp9xW5FvEfM+nSf/2xFCWIWsdWNjF4ou8OHXH/JK2isUdCwwbffI\n9WDJ8CXEDq38ph5CiIZFVq+0I9W9c1Nz9+bs2raLsJIwtJzyy/+uWrNKEr0QotZkRF8HlFLEDIth\n9Ter0TSN0wWneXPLm/Rp14d7u91r6+7ZVJqsL65L4qJP4mJOVq+0EwnfJZCWm0b88nj+sfYfdHuv\nGycvnySwdaCtuyaEaIBkRG9lSinuGHEHGUEZuK5x5cmXnuTFu1+kg1cHW3dNCOEEZERvBxK+S2CP\n1x7QwP02d+5R90iSF0LYlCR6KypdMrigQwHkyCJjemRetD6Jiz6Ji3VIorciuXOTEMIeSY2+FpL3\nJzNr4yySRiXR1K0pjz3zGAcvHCw3rVIpRefmneVmH0IIq7Akb0qit8Cxi8eYlDyJzOOZvBf9HtFd\n5apgIUT9kJOxdaBsQEsMJbyb/i49/t2Dbjd3Y9dfdlWY5KW2qE/iok/iok/iYh2S6Ctx4/rwW45s\nIeHnBDY8toHpA6eblgsWQgh7JqWbSixfuZxx88cR/1y8aSmC6i5tIIQQdUFq9FaklKLvA31JD0gn\nfHc4m5dulgQvGqQWLVpw9uxZW3ejwfHx8eHMmTNm26VGbyVKKWZ/PNs0VdKSKZJSW9QncdFnz3E5\ne/YsSil51PPDmr9cJdHfoKC4gFErRjE9frrxwifkwichhGOT0k0ZB88eZPjXw2l+uDmZxzNlfXgh\nsL+f04aiorjLevS1kLw/mTHfjOF/7/5ftu/ajlaiyfrwQginICN6oLC4kLvi7+LNqDfp37G/VT5T\n1tHWJ3HRZ89xsZef04ZGRvRW1tStKdue2IaLJqcshBDOR0b0QohKyc+pvpycHDp16mRR2+PHj+Pl\n5YWHh0eF77HmiL7BDGHlQBVCWMvBgwfZsmWLxe1btWrFnDlzrNijyjWIRF+6lMG1kmtMWzeNuZvm\n1vk+7XletC1JXPRJXBzLwoULeeihhyxu36hRI2JiYliyZIkVe1XJ/uplLzaW8F0CS3cvJfMfmfgE\n+fD1iK9t3SUhhJVt376dmTNnkpGRQU5OTrnXjhw5Qr9+/RgxYgSjRo0iJCSEd955By8vLzRN48qV\nK5w8eZKXX36ZzMxMXnnlFc6cOcP48ca1rs6dO8f777/PunXruHDhAu3atdPtQ1ZWFgcPHgRg3759\n/OMf/6iwv7179+bdd99l9OjR1gtCBZw+0SulmBE/g0uRlzix6QTbZm/DzdWtzvdrrzMobE3ios8R\n4/LYYy9y8KC7+f0XOhcRHz+r3j6jVK9evRg8eDC7du3i8uXL3HTTTabXMjIyKCwsZM6cObi6uvLK\nK68wcOBAU9w/++wzOnfuDEBoaCienp48/PDDjBo1yvQZzZo14w9/+ANffPEFw4YNM9t/dnY2586d\nY/jw4QAMHDiw0kQPxhLO/v376dKlS42+a005faL/ePnHZHlmgQYX2l1g5X9Wylx4IawgJiaCMWM0\nCgqiTNs8PJKZOLH6a0JZ4zPK0jQNPz8/9u/fT8+ePQHYsGEDjRs3JiwsDFdXVwBWrFhRLlkHBATQ\ntm1b0/MffviB9957D4DPP/+cUaNGMXDgQNzd3dm2bRsvvfSS2b737NnDgw8+CEBmZiaBgYFV9rdn\nz55kZmbWeaJ36hq9Uor3vnwP1dl4IrY+lzKQmqs+iYs+R4xLbGwUQUHJQOnPkyIoKIXhwwfX62eU\n2rt3L/7+/qZED3Dy5Eluuukmtm7dysCBA03vjYmJoX///gwbNoxFixbRs2dPWrduDcDu3btxc3Nj\n+fLlPPHEE2RnZwPQrVs3AAoKCswWODx+/Dht27YlOzubZ599ltdee42pU6dW2WcfHx+OHDlS4+9a\nU06d6BO+S+AX71/kHq5C1AFN03juuSg8PNb8viWF9PQhuLhoaBpoGsTF6beNizO+7uKikZ4eBRg/\nw8MjheefH2LRSrHp6emEh4fj5+fHgQMHAGPJplevXqSmppZL9LNnz2bjxo0MGDCAuLg40+gdIDU1\nldjYWJ566immTp1KZGQkAMeOHQOgpKREd999+vQhKCiIt99+m+joaBYvXlxln5s2bcrVq1dr/F1r\nyqkT/eq1qwkrCWNAzgDTI8wQxqo1q+p8345Yc60PEhd9jhqXsiPy8PAUDIbBKIXpUVmiL32PwRBF\neLjxMywdzQMUFxfj5uZmGtFv3ryZfv36UVhYyK+//kqvXr0ASElJASA4OJjJkyczffp00wlUMP7v\nql+/fgC0bduWe+65h9OnT5ORkQEYZ8zc6MqVK+W279mzB09PT86ePcvs2bOJj48nMzPTrN358+dp\n0aKFRd+3RpSFli5dqrp3765cXFxUZmamaXtOTo5q0qSJCg4OVsHBweovf/lLhZ9Ri90LIepJVT+n\ny5YlKU/PSWr58mSL91HbzygpKVGLFy9WSin1888/q169eqnNmzcrpZT6/vvv1X333aeUUqqwsFA9\n+OCD5do+/fTTKjs7WymllMFgUC1btlTHjx8v955p06apq1evKqWUGj16tLp48WK518vmuVOnTqnQ\n0FB14cIFNX/+fJWenq6Ki4vVww8/bNbvd999V33//fe636miuFuSNy0+GRsUFERiYiITJkwwe61L\nly7s2LHD4l8+tfH9we8Z2GmgzZczsOe1S2xJ4qLPkeMSGxtFUpLlI/HafsZPP/3ErFmzuHbtGpGR\nkXTu3Jnbb7+dPn36kJiYyMKFC3FxcWHr1q0UFBQQGhrKW2+9xU033cTp06cZOXIkgYGB7Ny5ky++\n+IIrV66wevVqAC5fvkxSUhJBQUG4uRln6w0YMKBczX/37t1ERUXx2Wef4eHhwc6dO0lMTMTT05Oc\nnBxGjhxJo0aNdG8ikpWVxfjx4y2OW7XV+FfDDSIiIsxG9IGBgdVqa4Xdl/PR9o9Uxzc7qpOXTlr1\ncy2Rmppq6y7YJYmLPnuOS3V+Tg0GQ633Y43PqA9nz55V06ZNMz3/+uuvK3zv008/rY4ePaqUUio6\nOrrca4WFhWry5MkVtq0o7pbkzToZ9ubk5BASEkJERAQbN26si12YWbl3JdP+O42UR1JodVOretln\nZRx1dFbXJC76HD0u1rjNpqPcqtPb25uWLVuSn58PgItLxWn0tttu48SJE1y5coXmzZuXe+2rr77S\nrYjUhUoXNRs0aBB5eXlm22fMmMHQoUMBiIyMZP78+aYTHVevXuXy5cv4+Piwfft2hg0bxu7du/H0\n9DTfuZUWS9rw2waGLx3Ofx7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       "text": [
        "<matplotlib.figure.Figure at 0xbe2012c>"
       ]
      }
     ],
     "prompt_number": 10
    }
   ],
   "metadata": {}
  }
 ]
}