Robust regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "using PyPlot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "plotline (generic function with 2 methods)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"plot line y = w*x+b\"\"\"\n",
    "function plotline(w::Number,b::Number;\n",
    "                  xmin=-100,xmax=100)\n",
    "    xsamples = [xmin, xmax]\n",
    "    plot(xsamples, [w*x+b for x in xsamples], color=\"black\")\n",
    "end\n",
    "plotline(w::Array{Float64,1}; kwargs...) = \n",
    "    plotline(w[1], w[2], kwargs...)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "plotfunc"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"plot function y=f(x)\"\"\"\n",
    "function plotfunc(f;\n",
    "                  xmin=-100,xmax=100,nsamples=100)\n",
    "    xsamples = linspace(xmin,xmax,nsamples)\n",
    "    plot(xsamples, [f(x) for x in xsamples], color=\"black\")\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO: Recompiling stale cache file /Users/madeleine/.julia/lib/v0.5/LowRankModels.ji for module LowRankModels.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "proxgrad_const (generic function with 1 method)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# proximal gradient method\n",
    "include(\"proxgrad.jl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x31a645650>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(-0.24743830553517399,10.188192417379238)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Generate and plot data\n",
    "srand(2)\n",
    "n = 30\n",
    "function sample_data(num_points)\n",
    "    x = rand(num_points)*10\n",
    "    y = .2*x + .3*randn(num_points)\n",
    "    return x,y\n",
    "end\n",
    "x,y = sample_data(n)\n",
    "\n",
    "\"\"\"function to plot the above data\"\"\"\n",
    "function plotdata(x=x,y=y; margin=.05)\n",
    "    hold(true)\n",
    "    plot(x,y,\"o\")\n",
    "    xlabel(\"x\")\n",
    "    ylabel(\"y\")\n",
    "    range_y = maximum(y) - minimum(y)\n",
    "    range_x = maximum(x) - minimum(x)\n",
    "    ylim([minimum(y)-margin*range_y,maximum(y)+margin*range_y])\n",
    "    xlim([minimum(x)-margin*range_x,maximum(x)+margin*range_x])\n",
    "end\n",
    "plotdata()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# mess up the data\n",
    "outliers=true\n",
    "if outliers\n",
    "    y[3] = 5\n",
    "    y[4] = -2\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Least squares"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Float64,1}:\n",
       " 0.124325\n",
       " 0.407174"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = length(y)\n",
    "X = [x ones(length(x))]\n",
    "w_quad = proxgrad(1/n*QuadLoss(), ZeroReg(), X, y, maxiters=200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x31a8a7650>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Array{Any,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x31a5dda50>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# plot the fit\n",
    "clf() # clears the previous figure\n",
    "plotdata()\n",
    "plotline(w_quad)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ℓ_1 regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x31a6b2f90>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Array{Any,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x31a7335d0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w_l1 = proxgrad(1/n*L1Loss(), ZeroReg(), X, y, \n",
    "                maxiters=200)\n",
    "\n",
    "# plot the fit\n",
    "clf() # clears the previous figure\n",
    "plotdata()\n",
    "plotline(w_l1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Huber regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x31a804410>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Array{Any,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x31a8ce5d0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w_huber = proxgrad(1/n*HuberLoss(), ZeroReg(), X, y, maxiters=200)\n",
    "\n",
    "# plot the fit\n",
    "clf() # clears the previous figure\n",
    "plotdata()\n",
    "plotline(w_huber)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Quantile regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x31a733e50>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Array{Any,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x31a9942d0>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w_10 = proxgrad(1/n*QuantileLoss(quantile=.7), ZeroReg(), X, y, maxiters=1000)\n",
    "\n",
    "# plot the fit\n",
    "clf() # clears the previous figure\n",
    "plotdata()\n",
    "plotline(w_10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w_quad = [0.124325,0.407174]\n",
      "w_l1 = [0.207355,0.0116781]\n",
      "w_huber = [0.201982,0.036572]\n",
      "w_10 = [0.239954,0.0109669]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "2-element Array{Float64,1}:\n",
       " 0.239954 \n",
       " 0.0109669"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@show w_quad\n",
    "@show w_l1\n",
    "@show w_huber\n",
    "@show w_10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot quantiles of distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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WAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOKJVgAA4olWAADiiVYAAOL9B7uyKW8hP7m0AAAAAElFTkSuQmCC",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x31da80110>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.patches.FancyArrow object at 0x31dcad150>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/madeleine/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/madeleine/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/madeleine/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/madeleine/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/madeleine/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/madeleine/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/madeleine/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/madeleine/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/madeleine/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/madeleine/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/madeleine/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/madeleine/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/madeleine/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "in show at /Users/madeleine/.julia/v0.5/PyCall/src/PyCall.jl\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/madeleine/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "in show at /Users/madeleine/.julia/v0.5/PyCall/src/PyCall.jl\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/madeleine/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "in show at /Users/madeleine/.julia/v0.5/PyCall/src/PyCall.jl\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/madeleine/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "in show at /Users/madeleine/.julia/v0.5/PyCall/src/PyCall.jl\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/madeleine/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "in show at /Users/madeleine/.julia/v0.5/PyCall/src/PyCall.jl\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/madeleine/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "in show at /Users/madeleine/.julia/v0.5/PyCall/src/PyCall.jl\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/madeleine/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "in show at /Users/madeleine/.julia/v0.5/PyCall/src/PyCall.jl\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/madeleine/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "in show at /Users/madeleine/.julia/v0.5/PyCall/src/PyCall.jl\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/madeleine/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "in show at /Users/madeleine/.julia/v0.5/PyCall/src/PyCall.jl\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/madeleine/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "in show at /Users/madeleine/.julia/v0.5/PyCall/src/PyCall.jl\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/madeleine/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "in show at /Users/madeleine/.julia/v0.5/PyCall/src/PyCall.jl\n",
      "WARNING: Base.writemime is deprecated.\n",
      "  likely near /Users/madeleine/.julia/v0.5/IJulia/src/kernel.jl:31\n",
      "in show at /Users/madeleine/.julia/v0.5/PyCall/src/PyCall.jl\n"
     ]
    }
   ],
   "source": [
    "q = .1\n",
    "l = QuantileLoss(quantile=q)\n",
    "ch = ConvergenceHistory(\"quantile\")\n",
    "w_nocov = proxgrad(1/n*l, ZeroReg(), ones(n,1), y, stepsize=.9, maxiters=50, ch=ch)\n",
    "\n",
    "clf() # clears the previous figure\n",
    "plot(y, zeros(n), \".\")\n",
    "plot(w_nocov, 0, \"rx\")\n",
    "axis(\"off\")\n",
    "ylim(-1,1)\n",
    "m,M = minimum(y), maximum(y)\n",
    "xlim(minimum(y)-(M-m)/10, maximum(y)+(M-m)/10)\n",
    "arrow(0, 0, maximum(y)+(M-m)/20, 0, head_width=0.05, head_length=0.1, fc=\"k\", ec=\"k\")\n",
    "arrow(0, 0, minimum(y)-(M-m)/20, 0, head_width=0.05, head_length=0.1, fc=\"k\", ec=\"k\")\n",
    "# savefig(\"quantile_$(q).pdf\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 0.5.0",
   "language": "julia",
   "name": "julia-0.5"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "0.5.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}