{ "metadata": { "name": "", "signature": "sha256:ce47e05ee3af71f7e4a8011f488e074993accc0a3d9d3ac4066d42a3dfa26d42" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "from IPython.html.widgets import interact\n", "from scipy import stats\n", "import seaborn as sns\n", "import pandas as pd" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Previously, we talk about maximum likelihood estimation and maximum a-posteriori estimation and in each case we started out with a probability density function of some kind and we further assumed that the samples were identically distributed and independent. The idea behind robust statistics is to construct estimators that can survive the weakening of either or both of these assumptions.\n", "\n", "The first idea to consider is the notion of *location*, which is a generalization of the idea of \"central value\". Typically, we just use an estimate of the mean for this, but we will see shortly why that is a bad idea. The general idea of Location satisfies the following requirements\n", "\n", "Let $X$ be a random variable with distribution $F$, and let $\\theta(X)$ be some descriptive\n", "measure of $F$. Then $\\theta(X)$ is said to be a measure of *location* if for any constants *a* and *b*, we have the following:\n", "\n", "$$\\theta(X+b) = \\theta(X) +b$$\n", "\n", "$$\\theta(-X) = -\\theta(X)$$\n", "\n", "$$X \\ge 0 \\Rightarrow \\theta(X) \\ge 0$$\n", "\n", "$$\\theta(a X) = a\\theta(X)$$\n", "\n", "The first condition is called *location equivariance* (or *shift-invariance* in signal processing lingo). The fourth condition is called *scale equivariance*, which means that the units that $X$ is measured in should not effect the value of the location estimator. These Requirements capture the idea of what we intuitively mean by *centrality* of a distribution, or where most of the probability mass is located.\n", "\n", "For example, the mean estimator is $\\hat{\\mu}=\\frac{1}{n}\\sum X_i$. The first requirement is obviously satisfied as $\\hat{\\mu}=\\frac{1}{n}\\sum (X_i+b) = b + \\frac{1}{n}\\sum X_i =b+\\hat{\\mu}$. Let us consider the second requirement:$\\hat{\\mu}=\\frac{1}{n}\\sum -X_i = -\\hat{\\mu}$. Finally, the last requirement is satisfied with $\\hat{\\mu}=\\frac{1}{n}\\sum a X_i =a \\hat{\\mu}$." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "What do we mean by robust estimators?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have the generalized location of centrality embodied in the *location* parameter, what can we do with it? The next idea is to nail down is the concept of * robust* estimators. Previously, we assumed that our samples were all identically distributed. The key idea is that the samples might be actually coming from a distribution that is contaminated by another nearby distribution, as in the following:\n", "\n", "$$F(X) = \\epsilon G(X) + (1-\\epsilon)H(X)$$\n", "\n", "where $\\epsilon$ is between zero and one. This means that our data samples $\\lbrace X_i \\rbrace$ actually derived from two separate distributions, $G(X)$ and $H(X)$. We just don't know how they are mixed together. What we really want is an estimator that captures the location of $G(X)$ in the face of random intermittent contamination by $H(X)$. It can get even worse than that because we don't know that there is only one contaminating $H(X)$ distribution out there. There may be a whole family of distributions that are contaminating $G(X)$ that we don't know of. This means that whatever estimators we construct have to be derived from families of distributions instead of a distribution, which is what we have been assuming for maximum-likelihood estimators. This is what makes robust estimation so difficult --- the extended theory has to deal with spaces of function distributions instead of particular parameters of a particular probability distribution.\n", "\n", "* Influence function\n", "* Outlier Detection\n", "* Estimates of location\n", " - definition of location\n", "* Trimmed means\n", "* Windsorized means\n", "* Hodges Lehmann statistics\n", "* Asymptotic efficiency\n", "* Fisher Consistent\n", "\n", "* Robust Regression \n", " \n", "\n", " - least median\n", " - outliers" ] }, { "cell_type": "code", "collapsed": false, "input": [ "n0=stats.norm(0,1)\n", "n1=stats.norm(1,2)\n", "xi = linspace(-5,5,100)\n", "\n", "fig,ax=subplots()\n", "ax.plot(xi,n0.pdf(xi))\n", "ax.plot(xi,n1.pdf(xi))\n", "\n", "def bias_coin(phead = .5):\n", " while True:\n", " yield int( np.random.rand() < phead ) \n", "\n", "pct_mixed = 0.1\n", "bias_coin_gen = bias_coin(pct_mixed) \n", "dual_set = [n0,n1]\n", "samples = [ dual_set[bias_coin_gen.next()].rvs() for i in range(500) ]" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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G93i74T1+f/ARzsw+lW8Xf5MI09JPsCKEJyRZC+ElwTxe3Tvex2OHn6V2oJ64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\nQCgWYnf3fnZ07WFfTxPRRGr6vmpPFSvLlnGBbyn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"text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "hist(samples,bins=20)\n", "title('average = %3.3f, median=%3.3f pct_mixed=%3.3f'%(mean(samples),np.median(samples),pct_mixed))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 3, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "import sympy.stats\n", "from sympy.abc import x\n", "eps = sympy.symbols('epsilon')\n", "\n", "mixed_cdf = sympy.stats.cdf(sympy.stats.Normal('x',0,1),'x')(x)*(1-eps) + eps*sympy.stats.cdf(sympy.stats.Normal('x',1,2),'x')(x)\n", "mixed_pdf = sympy.diff(mixed_cdf,x)\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "def plot_mixed_dist(epsilon=.1):\n", " n1 = stats.norm(1,2)\n", " xi = linspace(-5,5,100)\n", " fig,ax = subplots()\n", " ax.plot(xi,[sympy.lambdify(x,mixed_pdf.subs(eps,epsilon))(i) for i in xi],label='mixed',lw=2)\n", " ax.plot(xi,n0.pdf(xi),label='g(x)',linestyle='--')\n", " ax.plot(xi,n1.pdf(xi),label='h(x)',linestyle='--')\n", " ax.legend(loc=0)\n", " ax.set_title('epsilon = %2.2f'%(epsilon))\n", " ax.vlines(0,0,.4,linestyle='-',color='g')\n", " ax.vlines(epsilon,0,.4,linestyle='-',color='b')\n", "\n", "interact(plot_mixed_dist,epsilon=(0,1,.05))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 5, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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hsP+If8jW4gi/uWy0JcPjrfcdaaG2u4GGniaTIxIiMkiyFiIMHevop7VrgMQ4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\nsUEIcePJBKooAFFvO34pSZpcwsj/vht70YhubVZ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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "M-estimators" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "M-estimators are generalized maximum likelihood estimators. Recall that for maximum likelihood, we want to maximize the likelihood function as in the following:\n", "\n", "$$L_{\\mu}(x_i) = \\prod f_0(x_i-\\mu)$$\n", "\n", "and then to find the estimator $\\hat{\\mu}$ so that\n", "\n", "$$\\hat{\\mu} = \\arg \\max_{\\mu} L_{\\mu}(x_i)$$\n", "\n", "So far, everything is the same as our usual maximum-likelihood derivation except for the fact that we don't know $f_0$, the distribution of the $\\lbrace X_i\\rbrace$. Making the convenient definition of\n", "\n", "$$\\rho = -\\log f_0$$\n", "\n", "we obtain the more convenient form of the likelihood product and the optimal $\\hat{\\mu}$ as\n", "\n", "$$\\hat{\\mu} = \\arg \\min_{\\mu} \\sum \\rho(x_i-\\mu)$$\n", "\n", "If $\\rho$ is differentiable, then differentiating this with respect to $\\mu$ gives\n", "\n", "$$\\sum \\psi(x_i-\\hat{\\mu}) = 0$$\n", "\n", "with $\\psi = \\rho'$ and for technical reasons we will assume that $\\psi$ is increasing. The key idea here is we want to consider general $\\rho$ functions that my not be MLE for *any* distribution.\n" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "The distribution of M-estimates " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For a given distribution $F$, we define $\\mu_0=\\mu(F)$ as the solution to the following \n", "\n", "$$\\mathbb{E}_F(\\psi(x-\\mu_0))= 0$$\n", "\n", "It is technical to show, but it turns out that $\\hat{\\mu} \\sim \\mathcal{N}(\\mu_0,\\frac{v}{n})$ with\n", "\n", "$$v = \\frac{\\mathbb{E}_F(\\psi(x-\\mu_0)^2)}{(\\mathbb{E}_F(\\psi^\\prime(x-\\mu_0)))^2}$$\n", "\n", "Thus, we can say that $\\hat{\\mu}$ is asymptotically normal with asymptotic value $\\mu_0$ and asymptotic variance $v$. This leads to the efficiency ratio which is defined as the following:\n", "\n", "$$\\texttt{Eff}(\\hat{\\mu})= \\frac{v_0}{v}$$\n", "\n", "where $v_0$ is the asymptotic variance of the MLE and measures how near $\\hat{\\mu}$ is to the optimum. for example, if for two estimates with asymptotic variances $v_1$ and $v_2$, we have $v_1=3v_2$, then first estimate requires three times as many observations to obtain the same variance as the second.\n", "\n", "For example, for the sample mean (i.e. $\\hat{\\mu}=\\frac{1}{n} \\sum X_i$) with $F=\\mathcal{N}$, we have $\\rho=x^2/2$ and $\\psi=x$ and also $\\psi'=1$. Thus, we have $v=\\mathbb{V}(x)$. Alternatively, using the sample median as the estimator for the location, we have $v=\\frac{1}{4 f(\\mu_0)^2}$. Thus, if we have $F=\\mathcal{N}(0,1)$, for the sample median, we obtain $v=\\frac{2\\pi}{4} \\approx 1.571$. This means that the sample median takes approximately 1.6 times as many samples to obtain the same variance for the location as the sample mean." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One way to think about M-estimates is a weighted means. Most of the time, we have $\\psi(0)=0$ and $\\psi'(0)$ exists so that $\\psi$ is approximately linear at the origin. Using the following definition:\n", "\n", "\n", "$$W(x) = \\begin{cases}\n", " \\psi(x)/x & \\text{if} \\: x \\neq 0 \\\\\n", " \\psi'(x) & \\text{if} \\: x =0 \n", " \\end{cases}\n", "$$\n", "\n", "We can write our earlier equation as follows:\n", "\n", "$$\\sum W(x_i-\\hat{\\mu})(x_i-\\hat{\\mu}) = 0$$\n", "\n", "Solving this for $\\hat{\\mu}$ yields the following,\n", "\n", "$$\\hat{\\mu} = \\frac{\\sum w_{i} x_i}{\\sum w_{i}}$$\n", "\n", "where $w_{i}=W(x_i-\\hat{\\mu})$. The question that remains is how to pick the $\\psi$ functions." ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Huber functions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The family of Huber function is defined by the following:\n", "\n", "$$\\rho_k(x ) = \\begin{cases}\n", " x^2 & \\text{if} \\: |x|\\le k \\\\\n", " 2 k |x|-k^2 & \\text{if} \\: |x| \\gt k\n", " \\end{cases}\n", "$$\n", "\n", "with corresponding derivatives $2\\psi_k(x)$ with\n", "\n", "$$\\psi_k(x ) = \\begin{cases}\n", " x & \\text{if} \\: |x|\\le k \\\\\n", " \\text{sgn}(x)k & \\text{if} \\: |x| \\gt k\n", " \\end{cases}\n", "$$\n", "where the limiting cases $k \\rightarrow \\infty$ and $k \\rightarrow 0$ correspond to the mean and median, respectively. To see this, take $\\psi_{\\infty} = x$ and therefore $W(x) = 1$ and thus the defining equation results in\n", "\n", "$$\\sum_{i=1}^{n} (x_i-\\hat{\\mu}) = 0$$\n", "\n", "and then solving this leads to $\\hat{\\mu} = \\frac{1}{n}\\sum x_i$. Note that choosing $k=0$ leads to the sample median, but that is not so straightforward to solve for." ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig,ax=subplots()\n", "colors=['b','r']\n", "for k in [1,2]:\n", " ax.plot(xi,np.ma.masked_array(xi,abs(xi)>k),color=colors[k-1])\n", " ax.plot(xi,np.ma.masked_array(np.sign(xi)*k,abs(xi)" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The $W$ function corresponding to Huber's $\\psi$ is the following:\n", "\n", "$$W_k(x) = \\min\\Big{\\lbrace} 1, \\frac{k}{|x|} \\Big{\\rbrace}$$\n", "\n", "which is plotted in the following cell for a few values of $k$." ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig,ax=subplots()\n", "ax.plot(xi,np.vstack([np.ones(xi.shape),2/abs(xi)]).min(axis=0),label='k=2')\n", "ax.plot(xi,np.vstack([np.ones(xi.shape),1/abs(xi)]).min(axis=0),label='k=1')\n", "ax.axis(ymax=1.1)\n", "ax.legend(loc=0)\n", "ax.set_title(\"Huber's weight function\")" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 7, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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uO5v3teC12JahYnZIURZhNeH28MGBNlITXSwuTjc6zklrHGwmxZVMkivR6ChR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\nqlhZsIo91Qdoc7VZHa3P0pmyh3O2OllftoVdVfs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"text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another alternative intuitive way to interpret the M-estimate is to rewrite the following:\n", "\n", "$$\\hat{\\mu} = \\hat{\\mu} +\\frac{1}{n}\\sum_i \\psi(x_i-\\hat{\\mu}) = \\frac{1}{n} \\sum_i \\zeta(x_i,\\hat{\\mu})$$\n", "\n", "which for the Huber family of functions takes on the form :\n", "\n", "$$\\zeta(x,\\mu) = \\begin{cases}\n", " \\mu - k & \\text{if} \\: x \\lt \\mu-k \\\\\n", " x & \\text{if} \\: \\mu-k \\le x \\le \\mu+k \\\\\n", " \\mu+k & \\text{if} \\: x \\gt \\mu \\\\\n", " \\end{cases}\n", "$$\n", "\n", "Thus, the interpretation here is that $\\hat{\\mu}$ is the average of the truncated pseudo-observations $\\zeta_i$ where the observations beyond a certain point are clipped at the $k$-offset of the $\\hat{\\mu}$. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "kvals= [.001,0.3,0.5,.7,1.00001,1.4,1.7,2,3,4,5]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "import pythonica\n", "mma=pythonica.Pythonica()\n", "mma.plot_dir='.'" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 15 }, { "cell_type": "code", "collapsed": false, "input": [ "def closure_variance(mn=(0,1),std=(1,1)):\n", " # close over specific F-distribution and integral terms\n", " mma.eval('Clear[\"`*\"]') # clear workspace\n", " mma.eval('lpdf=D[CDF[NormalDistribution[%g,%g], x](1-Epsilon)+Epsilon*CDF[NormalDistribution[%g,%g],x],x]'%(mn[0],std[0],mn[1],std[1]))\n", " denom=mma.eval('Integrate[lpdf,{x,-k,k},Assumptions -> k > 0]^2')\n", " numer=mma.eval('Integrate[lpdf*Piecewise[{{x, Abs[x] < k},{k*Sign[x],Abs[x] >= k}}]^2, {x, -Infinity, Infinity}, Assumptions -> k > 0]')\n", " def asymp_variance(kval,eps=0.01):\n", " mma.push('k',kval)\n", " mma.push('Epsilon',eps)\n", " mma.eval('numer ='+numer) # used closure string\n", " mma.eval('denom ='+denom)\n", " mma.eval('Clear[k,Epsilon]')\n", " return float(mma.eval('N[numer/denom]'))\n", " return asymp_variance" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 }, { "cell_type": "code", "collapsed": false, "input": [ "asympt_var_case1 = closure_variance((0,1),(1,2)) # case 1 with N(0,1) + N(1,2)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 17 }, { "cell_type": "code", "collapsed": false, "input": [ "fig,ax=subplots()\n", "ax.plot(kvals,[asympt_var_case1(k,0) for k in kvals],'-o',label='eps=0')\n", "ax.plot(kvals,[asympt_var_case1(k,.05) for k in kvals],'-o',label='eps=.05')\n", "ax.plot(kvals,[asympt_var_case1(k,.1) for k in kvals],'-o',label='eps=0.1')\n", "ax.set_xlabel(\"k\")\n", "ax.set_ylabel(\"relative asymptotic efficiency \")\n", "ax.legend(loc=0)\n", "ax.set_title(r\"$\\mathcal{N}(0,1) , \\mathcal{N}(1,2)$ mixed\",fontsize=18)\n", "ax.grid()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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PzQ5h5EIIIUT4GNnPfLRS6nOl1A7f75OVUveFOa4OWcxmpoxO40hNI3r3Ib/l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\nbcPwEwgxdBLmI1QgGOKhFz9na42Lr80v5/LTp6Z1DWNv837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"text": [ "" ] } ], "prompt_number": 18 }, { "cell_type": "code", "collapsed": false, "input": [ "asympt_var_case2 = closure_variance((0,0),(1,10)) # case 1 with N(0,1) + N(0,10)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 20 }, { "cell_type": "code", "collapsed": false, "input": [ "fig2,ax=subplots()\n", "ax.plot(kvals,[asympt_var_case2(k,0) for k in kvals],'-o',label='eps=0')\n", "ax.plot(kvals,[asympt_var_case2(k,.05) for k in kvals],'-o',label='eps=.05')\n", "ax.plot(kvals,[asympt_var_case2(k,.1) for k in kvals],'-o',label='eps=0.1')\n", "ax.set_xlabel(\"k\")\n", "ax.set_ylabel(\"relative asymptotic efficiency \")\n", "ax.legend(loc=0)\n", "ax.set_title(r\"$\\mathcal{N}(0,1) , \\mathcal{N}(0,10)$ mixed\",fontsize=18)\n", "ax.grid()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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ZtI1WZACcEEJ0HIbLRc6bq8h/7x2s4eGkzLqZ0IGDzA6rQ2nVADhgAjAeOBb3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\nNUQXHR0lcOok/T/850w35SKTKe0tecnd9lzsVVV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BXwALgf8HTAFe6k4BRUREpPu87Jr2R+B44J/AydbaOe6pR40xC7JZOBEREemc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\n57uy+Ewy9S31zF7zObMqZ/PlxkUJ85T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"prompt_number": 22, "text": [ "" ] } ], "prompt_number": 22 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Computable Example" ] }, { "cell_type": "code", "collapsed": false, "input": [ "nsamples = 200\n", "xs = np.array([dual_set[bias_coin_gen.next()].rvs() for i in range(200)*nsamples ]).reshape(nsamples,-1)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 23 }, { "cell_type": "code", "collapsed": false, "input": [ "fig,ax=subplots()\n", "ax.hist(np.mean(xs,0),20,alpha=0.8,label = 'mean')\n", "ax.hist(np.median(xs,0),20,alpha=0.3,label ='median')\n", "ax.legend()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 24, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 24 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "References" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Maronna, R. A., R. D. Martin, and V. J. Yohai. \"Robust Statistics: Theory and Methods\". 2006." ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig,ax=subplots()\n", "sns.violinplot(np.vstack([np.median(xs,axis=0),np.mean(xs,axis=0)]).T,ax=ax,names=['median','mean']);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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rqqrk1df+zI7tW7Cl5ePuNExmdKegaKC26dp1oJZhw0cx7bob5b7rBNqxYzsv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\nnE7ZcCNVSFCnoNGjT+fee+/DCDfi2z1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"text": [ "" ] } ], "prompt_number": 25 }, { "cell_type": "code", "collapsed": false, "input": [ "mma.push('data',xs[:,0].tolist())\n", "mma.eval('psi[k_] := Function[x, Piecewise[{{x, Abs[x] < k}, {k*Sign[x], Abs[x] > k}}]]')" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 26 }, { "cell_type": "code", "collapsed": false, "input": [ "def psi_est(k,x):\n", " if x.ndim ==2 : # loop over columns\n", " out = []\n", " for i in range(x.shape[1]):\n", " data = x[:,i]\n", " out.append( psi_est(k,data) ) # recurse\n", " return np.array(out)\n", " else: \n", " mma.push('data',x.tolist())\n", " return float(mma.eval('\\[Mu] /. FindRoot[Plus @@ (psi[%d] /@ (data - \\[Mu])) == 0, {\\[Mu], 0}]'%(k)))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 27 }, { "cell_type": "code", "collapsed": false, "input": [ "hist(psi_est(1,xs),alpha=.7,label='k=1')\n", "hist(psi_est(2,xs),alpha=.7,label='k=2')\n", "hist(psi_est(3,xs),alpha=.7,label='k=3')\n", "legend(loc=0)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 28, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 28 }, { "cell_type": "code", "collapsed": false, "input": [ "huber_est={k:psi_est(k,xs) for k in [1,1.5,2,3]}\n", "huber_est[0] = np.median(xs,axis=0)\n", "huber_est[4] = np.mean(xs,axis=0)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 29 }, { "cell_type": "code", "collapsed": false, "input": [ "fig,ax=subplots()\n", "sns.violinplot(pd.DataFrame(huber_est),ax=ax)\n", "ax.set_xticklabels(['median','1','1.5','2','3','mean']);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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2OlVxrRLQ092BpjrQtJi1qCghioqKMiyVtWhuqiMvx4EyJJq5INfBhap6Cgs9SNfSC2Ys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\nEtm6czf9phl3CcwLwSBulysvF25Jl9bWdlwuF6O++2+oMaYZwh8cdnR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"text": [ "" ] } ], "prompt_number": 30 }, { "cell_type": "code", "collapsed": false, "input": [ "from sympy import mpmath, symbols, diff, Piecewise, sign, lambdify\n", "from sympy.stats import density, cdf, Normal\n", "from sympy.abc import k,x" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 31 }, { "cell_type": "code", "collapsed": false, "input": [ "eps = symbols('epsilon')\n", "lpdf=diff(cdf(Normal('x',0,1))(x)*(1-eps)+ eps*cdf(Normal('x',0,10))(x),x)\n", "p = Piecewise((x,abs(x)" ] } ], "prompt_number": 76 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }