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@csferrie
Last active March 22, 2017 11:50
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Supplementary and source for https://arxiv.org/abs/1612.07946.
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Bayes estimator for multinomial parameters and Bhattacharyya distances\n",
"\n",
"[Christopher Ferrie](http://csferrie.com) *(University of Sydney)* and Robin Blume-Kohout (*Sandia National Lab*)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This notebook is supplementary information for [arXiv:1612.07946](https://arxiv.org/abs/1612.07946), wherein we derived the Bayes estimator for the parameters of a multinomial distribution under two loss functions ($1-B$ and $1-B^2$) that are based on the Bhattacharyya coefficient $B(\\vec{p},\\vec{q}) = \\sum{\\sqrt{p_kq_k}}$. \n",
"\n",
"Here we apply the theory to find Bayes and minimax estimators for a binomial parameter under Bhattacharyya loss ($1-B^2$)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Preamble\n",
"\n",
"Before jumping into the code, there's a few housekeeping things to take care of. The main bulk of this notebook continues below."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"\n",
"%matplotlib inline\n",
"from __future__ import division\n",
"import matplotlib.pyplot as plt\n",
"from mpl_toolkits.mplot3d import Axes3D # for 3D figures\n",
"plt.style.use('ggplot')\n",
"\n",
"from scipy.stats import binom #binomial distribution\n",
"import scipy.linalg as la #linear algebra rountines\n",
"from scipy.optimize import minimize #self-explanatory\n",
"from scipy.special import beta # beta function"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We'll want to set some sensible defaults for matplotlib, too, that are nice for making printed figures."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"plt.rcParams['axes.labelsize'] = 20\n",
"plt.rcParams['axes.titlesize'] = 22\n",
"plt.rcParams['legend.fontsize'] = 18\n",
"plt.rcParams['xtick.labelsize'] = 14\n",
"plt.rcParams['ytick.labelsize'] = 14"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Bayes estimators for Bhattacharyya loss"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Consider a Binomial parameter $p$. The Bhattacharyya loss is\n",
"$$\n",
"L_2 = 1- B^2(p,\\hat p) = 1 - (\\sqrt{p \\hat p} +\\sqrt{(1-p)(1-\\hat p)})^2. \n",
"$$\n",
"\n",
"We wish to estimate $p$ from $N$ trials, where success was obtained $n$ times (and failure $N-n$).\n",
"Standard estimators of $p$ are maximum likelihood (MLE)\n",
"$$\n",
"\\hat p_{\\rm MLE}(n) = \\frac nN,\n",
"$$\n",
"and \"add-$\\beta$\"\n",
"$$\n",
"\\hat p_\\beta(n) = \\frac{n+\\beta}{N+ 2\\beta}.\n",
"$$\n",
"\n",
"The later can be derived as the mean of the posterior distribution assuming the canonical Beta prior\n",
"$$\n",
"\\Pr(p) = \\frac{p^{\\beta-1}(1-p)^{\\beta-1}}{{\\rm Beta(\\beta,\\beta)}}.\n",
"$$\n",
"\n",
"The Bayes estimator is the one which minimizes the average of $L_2$ with respect to the posterior distribution. As derived in TODO:cite_paper, this turns out to be the eigenvector $(\\hat p_2,1-\\hat p_2)$ of the matrix\n",
"$$\n",
"\\left( \\begin{array}{cc}\n",
"{\\rm Beta}(\\beta+n+1,\\beta+N-n) & {\\rm Beta}(\\beta+n+1/2,\\beta+N-n+1/2) \\\\\n",
"{\\rm Beta}(\\beta+n+1/2,\\beta+N-n+1/2) & {\\rm Beta}(\\beta+n,\\beta+N-n+1) \\end{array} \\right)/{\\rm Beta}(\\beta+n,\\beta+N-n),\n",
"$$\n",
"which has the larger eigenvalue."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# the mean of the posterior with a canonical Beta prior (note MLE corresponds to beta = 0)\n",
"def mean_est(N,n,beta):\n",
" return (n+beta)/(N+2*beta)\n",
"\n",
"# the Bayes estimator\n",
"def bayes_est_canon(N,n,b):\n",
" \n",
" est = np.empty(n.shape[0])\n",
" \n",
" if len(b)>0:\n",
" b = b[0]\n",
" \n",
" for idx in range(n.shape[0]):\n",
" T = np.array([[beta(b+n[idx]+1,b+N-n[idx]),beta(b+n[idx]+0.5,b+N-n[idx]+0.5)],\n",
" [beta(b+n[idx]+0.5, b+N-n[idx]+0.5),beta(b+n[idx],b+N-n[idx]+1)]])/beta(b+n[idx],b+N-n[idx])\n",
" \n",
" eigs = la.eig(T)\n",
" \n",
" a = eigs[1][np.argmax(eigs[0])]\n",
" \n",
" est[idx]= a[0]**2/np.sum(a**2)\n",
" return est"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Below is a routine to simplify code for plotting estimators as a function of $n$."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def plot_estimator(N,ests,end = None, savename = None, title = None):\n",
" \n",
" if end == None:\n",
" end = N\n",
" \n",
" n = np.arange(0,end+1)\n",
" \n",
" plt.figure(figsize=(9, 5))\n",
"\n",
" for key in ests.keys():\n",
" est = ests[key](n)\n",
" plt.plot(n, est, linewidth = 2, marker = 'o', markersize = 10, label = key, clip_on = False)\n",
" \n",
" plt.ylabel('$\\hat p$')\n",
" plt.xlabel('$n$')\n",
"\n",
" ax = plt.gca()\n",
" ax.yaxis.grid(color='gray', linestyle='dotted')\n",
" ax.legend(loc = 4)\n",
" \n",
" if title!=None:\n",
" plt.title(title)\n",
" \n",
" if savename!=None:\n",
" plt.savefig(savename+'.pdf',format='pdf',bbox_inches='tight')\n",
" plt.show() "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Some examples"
]
},
{
"cell_type": "code",
"execution_count": 120,
"metadata": {
"collapsed": false
},
"outputs": [
{
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NpRS2Q3tRud8QesPd1Hn3AGBkYABDlB/1te51/f0hoWILvTa9hWYY7uLom2dI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\nhFv7/2PwXCmalnM9AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1fa066949e8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"N = 10\n",
"plot_estimator(N,{'Bayes':lambda n:bayes_est_canon(N,n,np.array([0.5])),\n",
" 'Mean':lambda n:mean_est(N,n,0.5),'MLE':lambda n:mean_est(N,n,0)},\n",
" end=5, savename='N10_jeff', title = 'Jeffreys Prior ($\\\\beta=1/2$)')"
]
},
{
"cell_type": "code",
"execution_count": 121,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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GbUMjGVprwV2hcKMIDNJJybC26iBvGAZv/eh5/jSqgW17XuOTHX+EgEBorGey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\nbbhQYnVNTY4WQgghHJnTBUMPjkvgpV0/oOvSo9429S11NBgsnE03cO6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"text/plain": [
"<matplotlib.figure.Figure at 0x1fa055b01d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"N = 10\n",
"plot_estimator(N,{'Bayes':lambda n:bayes_est_canon(N,n,np.array([1])),\n",
" 'Mean':lambda n:mean_est(N,n,1),'MLE':lambda n:mean_est(N,n,0)},\n",
" end=5, savename='N10_lap', title = 'Laplace Prior ($\\\\beta=1$)')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Comparing the loss between estimators\n",
"\n",
"Here we compare Bayes risk of mean estimator and the Bayes estimator for several values of $N$ and $\\beta$."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def loss(p,q):\n",
" return 1-(np.sqrt(p*q)+np.sqrt((1-p)*(1-q)))**2\n",
"\n",
"def ave_loss(N, p, est):\n",
" dist = binom(N,p)\n",
" pn = dist.pmf(np.repeat([np.arange(N+1)],p.shape[0],axis = 0).T)\n",
" estn = est(np.arange(N+1))[:,np.newaxis]\n",
" return np.sum(pn*loss(p,estn),axis = 0)\n",
"\n",
"def bayes_ave_loss(N,est,b, res = 1000):\n",
" p = np.linspace(0,0.5,res)\n",
" prior = p**(b-1)*(1-p)**(b-1)/beta(b,b)\n",
" prior[np.isinf(prior)] = 0\n",
" loss = ave_loss(N,p,est)\n",
" return np.sum(prior*loss)/res"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"C:\\Users\\csfer\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:12: RuntimeWarning: divide by zero encountered in power\n"
]
}
],
"source": [
"n_N = 90\n",
"n_b = 10\n",
"\n",
"Ns = np.linspace(10,n_N+10,n_N).astype(int)\n",
"betas = np.linspace(0.5,1,n_b)\n",
"\n",
"mean_loss = np.zeros([n_N,n_b])\n",
"bme_loss = np.zeros([n_N,n_b])\n",
"\n",
"for idx in range(n_N):\n",
" for idy in range(n_b):\n",
" \n",
" mean_loss[idx,idy] = bayes_ave_loss(Ns[idx],lambda n:mean_est(Ns[idx],n,betas[idy]),betas[idy])\n",
" bme_loss[idx,idy] = bayes_ave_loss(Ns[idx],lambda n:bayes_est_canon(Ns[idx],n,np.array([betas[idy]])),betas[idy])"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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BoB+FYk5SbryOkTWLwJLARg+SVSIUdIui6tFLEABIkoR0Oi3kQyrskVU/tm/cF0vDaLVa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\n+Zg+fTp33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6PSMrdFJaFq5phX4jRbJU89+eST+MEPfoAvfelLuO6663z9nG7JXi1YDUjE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\nBAKH5f8BYGrdzHTSOBYAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1fa0677ef98>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(12, 8),facecolor='w')\n",
"ax = fig.add_subplot(111,projection='3d')\n",
"Y,X = np.meshgrid(Ns,betas)\n",
"\n",
"rel_err = ((mean_loss-bme_loss)/bme_loss)\n",
"surf = ax.plot_surface(X,Y,rel_err.T,rstride=1, cstride=1, cmap=plt.cm.RdBu,\n",
" linewidth=0, antialiased=False, )\n",
"\n",
"ax.set_ylabel('\\n$N$')\n",
"ax.set_xlabel('\\n$\\\\beta$')\n",
"ax.set_zlabel('\\nRelative Loss')\n",
"\n",
"#fig.colorbar(surf, shrink = 0.75)\n",
"\n",
"ax.view_init(azim=125.)\n",
"ax.set_axis_bgcolor((1.0, 1.0, 1.0, 1.0))\n",
"\n",
"plt.savefig('3ddiff.pdf',format='pdf',bbox_inches='tight')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Plotting the Bhattacharyya risk as a function of $p$"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def plot_est(N,ests,res = 1000, end = 0.5, savename=None, title=None):\n",
" \n",
" p = np.linspace(0,end,res)\n",
" \n",
" plt.figure(figsize=(9, 5))\n",
"\n",
" for key in ests.keys():\n",
" \n",
" loss = ave_loss(N,p,ests[key])\n",
" \n",
" plt.plot(p, loss , linewidth = 3.5, label = key, clip_on = False)\n",
" \n",
" plt.ylabel('Average $1-B^2$')\n",
" plt.xlabel('$p$')\n",
"\n",
" ax = plt.gca()\n",
" ax.legend(loc = 'best')\n",
" \n",
" if title!=None:\n",
" plt.title(title)\n",
" \n",
" if savename!=None:\n",
" plt.savefig(savename+'.pdf',format='pdf',bbox_inches='tight')\n",
" \n",
" plt.show() "
]
},
{
"cell_type": "code",
"execution_count": 118,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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gvPAOxnNvWRLdTTddv/R09NrlmF96nMxPpqEPR5eq/29CiKLRt29fEhMTWbly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\nAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1fa04b31748>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"N = 10\n",
"plot_est(N, {'Bayes':lambda n:bayes_est_canon(N,n,np.array([0.5])),\n",
" 'Mean':lambda n:mean_est(N,n,0.5),'MLE':lambda n:mean_est(N,n,0)},end = 0.5,\n",
" savename='N10_jeff_loss', title = 'Jeffreys Prior ($\\\\beta=1/2$)')"
]
},
{
"cell_type": "code",
"execution_count": 117,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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B3d1dp0muQmhoKJycnLBhwwaMGzcOdnZ2WvtLSkpQXl4OKysrCAQCAIBKpV0D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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1fa07acff28>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_est(N, {'Bayes':lambda n:bayes_est_canon(N,n,np.array([1])),\n",
" 'Mean':lambda n:mean_est(N,n,1),'MLE':lambda n:mean_est(N,n,0)},end = 0.5,\n",
" savename='N10_lap_loss', title = 'Laplace Prior ($\\\\beta=1$)')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Finding the minimax estimators\n",
"\n",
"The minimax estimator is the one whose maximum risk (over $p$) is as small as possible. A remarkable result in statistics is Bayes-minimax duality which states that there exists a prior (called the *least favorable prior*) whose Bayes estimator coincides with minimax estimator. Thus, provided we know the Bayes estimator (which we now do), we can find minimax estimators by searching over priors, rather than estimators. \n",
"\n",
"Before we find the minimax estimator, though, we consider finding the prior which is least favorable *among the subclass of canonical priors*. This amounts to finding the *optimal* $\\beta$. A further interesting restriction is to do so with the sub-optimal mean estimator. Why? Well, if the mean and Bayes estimator are close, then the mean estimator is \"good enough\" and in fact preferable since it is easier to calculate."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def find_max_loss(N,est):\n",
" p0 = 1/N\n",
" sol = minimize(lambda p:(-ave_loss(N, p, est)), p0, bounds = ((0,0.5),))\n",
" return sol\n",
"\n",
"def find_opt_beta(N,est,b0 = 0.1):\n",
" \n",
" sol = minimize(lambda b: np.abs(-ave_loss(N,np.array([0]),lambda n:est(N,n,b)) - find_max_loss(N,lambda n:est(N,n,b)).fun),b0)\n",
"\n",
" return sol.x"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The optimal value of beta for the Bayes estimator is: 0.441469767921\n",
"The optimal value of beta for the mean estimator is: 0.26103491116\n"
]
}
],
"source": [
"N = 10\n",
"\n",
"opt_beta_bayes = find_opt_beta(N,bayes_est_canon)[0]\n",
"opt_beta_mean = find_opt_beta(N,mean_est)[0]\n",
"print(\"The optimal value of beta for the Bayes estimator is:\", opt_beta_bayes)\n",
"print(\"The optimal value of beta for the mean estimator is:\", opt_beta_mean)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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GRgb8/f0RFBQk1ktLS8PGjRvx6quvYvjw4Vbv9dVXX2H37t1YtmwZwsPD7xpr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\nRGQg/w+Wdagql1/T3gAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x2496e76fcf8>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"The Bayes risk for the Bayes estimator is: 0.0188771733906\n",
"The Bayes risk for the mean estimator is: 0.0159362928329\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"C:\\Users\\csfer\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:12: RuntimeWarning: divide by zero encountered in power\n"
]
}
],
"source": [
"ests = {'Bayes':lambda x:bayes_est_canon(N,x,np.array([opt_beta_bayes])),'Mean':lambda x:mean_est(N,x,opt_beta_mean)}\n",
" \n",
"plot_est(N,ests,end = 0.5,savename=None)\n",
"\n",
"print(\"The Bayes risk for the Bayes estimator is:\", bayes_ave_loss(N,ests['Bayes'],opt_beta_bayes))\n",
"print(\"The Bayes risk for the mean estimator is:\", bayes_ave_loss(N,ests['Mean'],opt_beta_mean))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A nice algorithm for doing so was introduced by [Kempthorne](http://dx.doi.org/10.1137/0908028).\n",
"\n",
"For reasons (see the paper), it turns out that least favorable prior will be discrete and support on only a few points. So first, we provide some functions which use this assumption to make the calculation of the Bayes risk simple."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def Tmtx(pr_dist):\n",
" \n",
" # unpack the distribution\n",
" locs = pr_dist['Locations']\n",
" weights = pr_dist['Weights']\n",
" \n",
" on_diag = np.sum(weights*locs)\n",
" off_diag = np.sum(weights*np.sqrt(locs*(1-locs)))\n",
" \n",
" return np.array([[on_diag,off_diag],[off_diag,1-on_diag]])\n",
" \n",
"def bayes_est(N, n, pr_dist):\n",
" \n",
" # Calculate likelihoods\n",
" dist = binom(N,pr_dist['Locations'])\n",
" \n",
" est = np.empty(n.shape[0])\n",
" \n",
" for idx in range(n.shape[0]):\n",
" new_dist = np.copy(pr_dist)\n",
" \n",
" # update sans normalization\n",
" weights = dist.pmf(n[idx])*pr_dist['Weights']\n",
" \n",
" # normalize\n",
" weights = weights/np.sum(weights)\n",
" \n",
" new_dist['Weights'] = weights\n",
" \n",
" # Calculate T matrix and find the eigenvectors\n",
" T = Tmtx(new_dist)\n",
" eigs = la.eigh(T)\n",
" \n",
" a = eigs[1][np.argmax(eigs[0])]\n",
" \n",
" est[idx] = a[0]**2/np.sum(a**2)\n",
" \n",
" return est\n",
"\n",
"def dist_dtype():\n",
" return [('Locations','float'),('Weights','float')]\n",
"\n",
"def symmetrize(pr_dist):\n",
" # unpack the distribution\n",
" locs = pr_dist['Locations']\n",
" weights = pr_dist['Weights']\n",
" \n",
" new_dist = np.empty(2*locs.shape[0], dist_dtype())\n",
" new_dist['Locations'] = np.concatenate((locs,1-locs))\n",
" new_dist['Weights'] = np.concatenate((weights/2,weights/2))\n",
" \n",
" return new_dist\n",
" \n",
"def vec2prior(x):\n",
" n = x.shape[0]/2\n",
" new_dist = np.empty(n, dist_dtype())\n",
" new_dist['Locations'] = x[:n]\n",
" new_dist['Weights'] = x[n:]\n",
" return new_dist\n",
" \n",
"def bayes_loss(N,pr_dist):\n",
" return np.sum(pr_dist['Weights']*ave_loss(N,pr_dist['Locations'], lambda n:bayes_est(N,n,symmetrize(pr_dist))))\n",
" \n",
"def find_minimax(N, tol = 1e-3):\n",
" \n",
" # let's not add too many points\n",
" max_iter = N/2\n",
" \n",
" # Start with a prior support on 0 and 0.25\n",
" pr_dist = np.array([(1e-10,1/3),(0.1,1/3),(0.49,1/3)],dist_dtype())\n",
" \n",
" iterations = 0\n",
" not_stop = True\n",
" while not_stop:\n",
" iterations += 1\n",
" \n",
" # minimize the loss over the locations and weights\n",
" x0 = np.append(pr_dist['Locations'],pr_dist['Weights'])\n",
" \n",
" bounds = np.zeros([x0.shape[0],2])\n",
" bounds[:x0.shape[0]/2,1] = 0.5\n",
" bounds[x0.shape[0]/2:,1] = 1\n",
" constraints = {'type': 'eq', 'fun': lambda x: np.sum(x[x.shape[0]/2:]) - 1}\n",
" ave = minimize(lambda x: -bayes_loss(N,vec2prior(x)),x0, bounds = bounds, constraints = constraints)\n",
" pr_dist = vec2prior(ave.x)\n",
" \n",
" # Calculate the max fidelity\n",
" sol = find_max_loss(N,lambda n:bayes_est(N,n,symmetrize(pr_dist)))\n",
" \n",
" # add a new point if we are too far away\n",
" final_tol = np.abs((sol.fun-ave.fun)/ave.fun)\n",
" \n",
" if final_tol > tol and iterations < max_iter:\n",
" new_dist = np.empty(pr_dist['Locations'].shape[0]+1, dist_dtype())\n",
" new_dist['Locations'] = np.append(pr_dist['Locations'],sol.x)\n",
" new_dist['Weights'] = np.append(pr_dist['Weights'],0.01)\n",
" new_dist['Weights'] = new_dist['Weights']/np.sum(new_dist['Weights'])\n",
" pr_dist = new_dist\n",
" else:\n",
" not_stop = False\n",
" \n",
" return pr_dist, final_tol"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"C:\\Users\\csfer\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:81: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
"C:\\Users\\csfer\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:82: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
"C:\\Users\\csfer\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:83: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
"C:\\Users\\csfer\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:56: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
"C:\\Users\\csfer\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:57: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
"C:\\Users\\csfer\\Anaconda3\\lib\\site-packages\\ipykernel\\__main__.py:58: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n"
]
}
],
"source": [
"lfp = find_minimax(N, tol = 1e-10)[0]"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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/BpZWN74oaYOlRT5ZPyFJhRszGhH7198BDZflB+XcCO57z4DFJfZ5+3qKMQa1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"text/plain": [
"<matplotlib.figure.Figure at 0x2496e892588>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"The max. loss for Bayes estimator with optimal beta is: [ 0.02520802]\n",
"The max. loss for mean estimator with optimal beta is: [ 0.02480832]\n",
"The max. loss for minimax estimator is: [ 0.02305672]\n"
]
}
],
"source": [
"ests = {'Bayes':lambda x:bayes_est_canon(N,x,np.array([opt_beta_bayes])),'Mean':lambda x:mean_est(N,x,opt_beta_mean),\n",
" 'Minimax':lambda x:bayes_est(N,x,symmetrize(lfp))}\n",
" \n",
"plot_est(N,ests,end = 0.5, savename = 'minimax_loss')\n",
"\n",
"print(\"The max. loss for Bayes estimator with optimal beta is:\", -find_max_loss(N,ests['Bayes']).fun)\n",
"print(\"The max. loss for mean estimator with optimal beta is:\", -find_max_loss(N,ests['Mean']).fun)\n",
"print(\"The max. loss for minimax estimator is:\", -find_max_loss(N,ests['Minimax']).fun)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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FtuzYSdvwqT2C0NkMphDCc24g6MwRvrFiMTckRxBk6DnR2e3SKD/WyYnjLrwYAYWk2j1k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\nL90AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x2496e1eabe0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_estimator(N,{'Bayes':lambda n:bayes_est_canon(N,n,np.array([opt_beta_bayes])),\n",
" 'Mean':lambda n:mean_est(N,n,opt_beta_mean),'Minimax':lambda n:bayes_est(N,n,symmetrize(lfp))},\n",
" end = 5, savename = 'minimax_est')"
]
}
],
"metadata": {
"anaconda-cloud": {},
"kernelspec": {
"display_name": "Python [default]",
"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": "3.5.2"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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