machinelearningproject1count.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.io as sio\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "data=sio.loadmat('PA_1_matlab/count_data.mat')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      "       [-10.0525],\n",
      "       [-10.0525],\n",
      "       [-10.0525]]), 'testx': array([[ 1.71840538,  1.71435392,  1.73471488, ..., -1.1168872 ,\n",
      "        -1.12653584, -1.11876743],\n",
      "       [ 0.63550837,  0.56798578,  0.60446373, ..., -1.11178376,\n",
      "        -1.10236248, -1.10643402],\n",
      "       [-0.53764695, -0.54446318, -0.90091259, ..., -0.6308237 ,\n",
      "        -0.62259792, -0.49482174],\n",
      "       ...,\n",
      "       [ 0.84563072,  0.94763762,  1.22829541, ..., -0.88884166,\n",
      "        -0.94822055, -0.9716274 ],\n",
      "       [ 1.08367608,  1.01472573,  1.09587867, ..., -1.03400009,\n",
      "        -1.01395503, -1.0210064 ],\n",
      "       [-1.98763845, -2.04531886, -2.0284462 , ...,  1.22249187,\n",
      "         1.33951875,  1.25987542]]), '__header__': 'MATLAB 5.0 MAT-file, Platform: PCWIN, Created on: Thu Sep 13 17:24:03 2012', '__globals__': [], '__version__': '1.0', 'trainx': array([[-0.93896716, -0.96200988, -0.980555  , ...,  1.62394219,\n",
      "         1.70552069,  1.73774133],\n",
      "       [-0.84457345, -0.9232998 , -0.95890429, ...,  0.78163425,\n",
      "         0.85620397,  0.84933258],\n",
      "       [-0.79296073, -1.25768828, -1.26703836, ..., -0.70245778,\n",
      "        -0.42018279,  0.25436494],\n",
      "       ...,\n",
      "       [-0.76662328, -0.69537714, -0.68786399, ...,  0.926296  ,\n",
      "         1.1074946 ,  0.98860488],\n",
      "       [-0.20254792, -0.34836888, -0.26605002, ...,  0.34433165,\n",
      "         0.11780671, -0.29971809],\n",
      "       [ 0.99700929,  0.86680129,  0.85642082, ..., -1.77500257,\n",
      "        -1.77772332, -1.8113235 ]]), 'trainy': array([[ -8.0525],\n",
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      "       [ 15.9475],\n",
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      "       [ 15.9475],\n",
      "       [ 14.9475],\n",
      "       [ 14.9475]])}\n"
     ]
    }
   ],
   "source": [
    "print data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "testx=data['testx']\n",
    "testy=data['testy']\n",
    "trainy=data['trainy']\n",
    "trainx=data['trainx']\n",
    "ym=data['ym']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(9, 600)\n",
      "(600, 1)\n",
      "(9, 400)\n",
      "(400, 1)\n",
      "(1, 1)\n"
     ]
    }
   ],
   "source": [
    "print testx.shape\n",
    "print testy.shape\n",
    "print trainx.shape\n",
    "print trainy.shape\n",
    "print ym.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "600\n"
     ]
    }
   ],
   "source": [
    "print len(testy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(18, 1)\n",
      "(400, 1)\n",
      "24.357632762377484\n",
      "593.294273786845\n"
     ]
    }
   ],
   "source": [
    "#φ(x) = [x1,x2,x3,x4...x9,]\n",
    "#so Phi=trainx\n",
    "def phi(trainx):\n",
    "    d,m=trainx.shape\n",
    "    phi=np.zeros((2*d,m))\n",
    "    temp2=np.zeros((d,m))\n",
    "    temp1=np.zeros((d,m))\n",
    "    for i in range(d):\n",
    "        for j in range(m):\n",
    "            temp2[i][j]=np.power(trainx[i][j],2)\n",
    "            temp1[i][j]=trainx[i][j]\n",
    "    phi=np.vstack((temp1,temp2))\n",
    "    return phi\n",
    "\n",
    "def meanabsoluteerror(testy,f_l):\n",
    "    sum=0\n",
    "    m=len(testy)\n",
    "    for i in range(m):\n",
    "        error=np.absolute(f_l[i][0]-testy[i][0])\n",
    "        sum+=error\n",
    "    mae=sum/m\n",
    "    return mae\n",
    "\n",
    "def meansquareerror(polyy,f_l):\n",
    "    sum=0\n",
    "    m=len(polyy)\n",
    "    for i in range(m):\n",
    "        error=f_l[i][0]-polyy[i][0]\n",
    "        sum+=np.power(error,2)\n",
    "    mse=sum/m\n",
    "    return mse\n",
    "\n",
    "def paraestimate(Phi,sampy):\n",
    "    A=np.linalg.inv(np.dot(Phi,Phi.T))\n",
    "    theta_ls=np.dot(np.dot(A,Phi),sampy)\n",
    "    return theta_ls\n",
    "Phi=phi(trainx)\n",
    "theta_real=paraestimate(Phi,trainy)\n",
    "print theta_real.shape\n",
    "f_ls=np.dot(Phi.T,theta_real)\n",
    "print f_ls.shape\n",
    "print meanabsoluteerror(testy.T,f_ls)\n",
    "print meansquareerror(testy.T,f_ls)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(9, 1)\n",
      "(600, 1)\n",
      "1.282432855732885\n",
      "2.6187339222418937\n"
     ]
    }
   ],
   "source": [
    "##LR\n",
    "def paraestimateReg(Phi,sampy,lmb=1):\n",
    "    A=np.linalg.inv(np.dot(Phi,Phi.T)+lmb*np.eye(9))\n",
    "    theta_ls=np.dot(np.dot(A,Phi),sampy)\n",
    "    return theta_ls\n",
    "theta_ls=paraestimateReg(trainx,trainy)\n",
    "print theta_ls.shape\n",
    "f_lr=np.dot(testx.T,theta_ls)\n",
    "print f_lr.shape\n",
    "print meanabsoluteerror(testy,f_lr)\n",
    "print meansquareerror(testy,f_lr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(600, 1)\n",
      "1.3008913835130993\n",
      "2.7828235164999673\n"
     ]
    }
   ],
   "source": [
    "#LASSO\n",
    "import scipy.optimize as opt\n",
    "\n",
    "def paraestimateLasso(Phi,sampy,lmb=1):\n",
    "    H=np.hstack((np.vstack((np.dot(Phi,Phi.T),np.dot(-Phi,Phi.T))),np.vstack((np.dot(-Phi,Phi.T),np.dot(Phi,Phi.T)))))\n",
    "    fa=np.vstack((np.dot(Phi,sampy),-np.dot(Phi,sampy)))\n",
    "    f=lmb*np.ones((18,1))-fa\n",
    "    x_ans=np.zeros((18,1))\n",
    "    fun=lambda x: float(0.5*np.dot((np.dot(x.T,H)),x)+np.dot(f.T,x))\n",
    "    cons=({'type': 'ineq', 'fun': lambda x: x})\n",
    "    x_ans_true=opt.minimize(fun,x_ans,constraints=cons,method=\"SLSQP\")# these 3 lines use Opt way to get the min of function\n",
    "    \n",
    "    theta_plus=x_ans_true.x[0:9]\n",
    "    theta_sub=x_ans_true.x[9:18]\n",
    "    theta=theta_plus-theta_sub\n",
    "    theta=np.expand_dims(theta, axis=1)\n",
    "    return theta\n",
    "\n",
    "theta_lasso=paraestimateLasso(trainx,trainy,lmb=1)\n",
    "f_lasso=np.dot(testx.T,theta_lasso)\n",
    "print f_lasso.shape\n",
    "print meanabsoluteerror(testy,f_lasso)\n",
    "print meansquareerror(testy,f_lasso)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(600, 1)\n",
      "1.3645672474557409\n",
      "3.1189980526815244\n"
     ]
    }
   ],
   "source": [
    "def ArrayToList(array):\n",
    "    list=[]\n",
    "    for i in range(len(array)):\n",
    "        list.append(float(array[i]))\n",
    "    return list\n",
    "\n",
    "def paraestimateRobustreg(Phi,sampy,lmb=1):\n",
    "    m=len(sampy)\n",
    "    k=len(Phi)\n",
    "    temp1=np.row_stack((-Phi.T,Phi.T))\n",
    "    temp2=np.row_stack((-np.eye(m),-np.eye(m)))\n",
    "    A=np.column_stack((temp1,temp2))\n",
    "    b=np.row_stack((-sampy,sampy))\n",
    "    f=np.row_stack((np.zeros((k,1)),np.ones((m,1))))\n",
    "    X=np.zeros((m+k, 1))\n",
    "    B=ArrayToList(b)\n",
    "    fun=lambda x:np.dot(f.T,x)\n",
    "    cons=({'type': 'ineq', 'fun': lambda x:B-np.dot(A, x)})#B should be list then can get constraint\n",
    "    x_ans=opt.minimize(fun,X,constraints=cons, method=\"SLSQP\")\n",
    "    \n",
    "    theta=x_ans.x[0:k]\n",
    "    theta=np.expand_dims(theta, axis=1)\n",
    "    return theta\n",
    "theta_rr=paraestimateRobustreg(trainx,trainy,lmb=1)\n",
    "f_rr=np.dot(testx.T,theta_rr)\n",
    "print f_rr.shape\n",
    "print meanabsoluteerror(testy,f_rr)\n",
    "print meansquareerror(testy,f_rr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.4486049524761022\n",
      "3.1462528214455157\n"
     ]
    }
   ],
   "source": [
    "def esitmatesigma(Phi,alpha=1,sigma_square=5):\n",
    "    temp=(1/float(sigma_square))*np.dot(Phi,Phi.T)\n",
    "    m=len(Phi)\n",
    "    SIGMA=np.linalg.inv(temp+(1/float(alpha))*np.eye(m))\n",
    "    return SIGMA\n",
    "\n",
    "def estimatemju(sampy,Phi,SIGMA,sigma_square=5):\n",
    "    mju=(1/float(sigma_square))*np.dot(np.dot(SIGMA,Phi),sampy)\n",
    "    return mju\n",
    "\n",
    "def gaussianpredictedsigma(SIGMA,polyx_l):\n",
    "    polyphi=np.zeros((1,6))\n",
    "    for i in range(6):\n",
    "        polyphi[0][i]=np.power(polyx_l,i)\n",
    "    res=np.dot(np.dot(polyphi,SIGMA),polyphi.T)\n",
    "    return res\n",
    "\n",
    "SIGMA=esitmatesigma(trainx,alpha=1,sigma_square=5)\n",
    "mju=estimatemju(trainy,trainx,SIGMA,sigma_square=5)\n",
    "f_br=np.dot(testx.T,mju)\n",
    "print meanabsoluteerror(testy,f_br)\n",
    "print meansquareerror(testy,f_br)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6287867148877597\n",
      "-0.7929607272039138\n"
     ]
    }
   ],
   "source": [
    "temp1=np.zeros((len(trainx),len(trainx[0])))\n",
    "for j in range(len(trainx[0])):\n",
    "    for i in range(len(trainx)):\n",
    "        temp1[i][j]=np.power(trainx[i][j],2)\n",
    "phi=np.row_stack((trainx,temp1))\n",
    "\n",
    "temp2=np.zeros((len(testx),len(testx[0])))\n",
    "for j in range(len(testx[0])):\n",
    "    for i in range(len(testx)):\n",
    "        temp2[i][j]=np.power(testx[i][j],2)\n",
    "test_phi=np.row_stack((testx,temp2))\n",
    "\n",
    "phi=np.row_stack((trainx,temp1))\n",
    "print phi[11][0]\n",
    "print trainx[2][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(18, 1)\n",
      "(600, 1)\n",
      "1.3267461241105298\n",
      "2.9235940267301013\n"
     ]
    }
   ],
   "source": [
    "#LS\n",
    "theta_real=paraestimate(phi,trainy)\n",
    "print theta_real.shape\n",
    "f_ls=np.dot(test_phi.T,theta_real)\n",
    "print f_ls.shape\n",
    "print meanabsoluteerror(testy,f_ls)\n",
    "print meansquareerror(testy,f_ls)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(18, 1)\n",
      "(600, 1)\n",
      "1.213698757046865\n",
      "2.467773902567654\n"
     ]
    }
   ],
   "source": [
    "def paraestimateReg(Phi,sampy,lmb=1):\n",
    "    A=np.linalg.inv(np.dot(Phi,Phi.T)+lmb*np.eye(18))\n",
    "    theta_ls=np.dot(np.dot(A,Phi),sampy)\n",
    "    return theta_ls\n",
    "theta_ls=paraestimateReg(phi,trainy)\n",
    "print theta_ls.shape\n",
    "f_lr=np.dot(test_phi.T,theta_ls)\n",
    "print f_lr.shape\n",
    "print meanabsoluteerror(testy,f_lr)\n",
    "print meansquareerror(testy,f_lr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(600, 1)\n",
      "1.2425737603631541\n",
      "2.545271416551002\n"
     ]
    }
   ],
   "source": [
    "#LASSO\n",
    "import scipy.optimize as opt\n",
    "\n",
    "def paraestimateLasso(Phi,sampy,lmb=1):\n",
    "    H=np.hstack((np.vstack((np.dot(Phi,Phi.T),np.dot(-Phi,Phi.T))),np.vstack((np.dot(-Phi,Phi.T),np.dot(Phi,Phi.T)))))\n",
    "    fa=np.vstack((np.dot(Phi,sampy),-np.dot(Phi,sampy)))\n",
    "    f=lmb*np.ones((36,1))-fa\n",
    "    x_ans=np.zeros((36,1))\n",
    "    fun=lambda x: float(0.5*np.dot((np.dot(x.T,H)),x)+np.dot(f.T,x))\n",
    "    cons=({'type': 'ineq', 'fun': lambda x: x})\n",
    "    x_ans_true=opt.minimize(fun,x_ans,constraints=cons,method=\"SLSQP\")# these 3 lines use Opt way to get the min of function\n",
    "    \n",
    "    theta_plus=x_ans_true.x[0:18]\n",
    "    theta_sub=x_ans_true.x[18:36]\n",
    "    theta=theta_plus-theta_sub\n",
    "    theta=np.expand_dims(theta, axis=1)\n",
    "    return theta\n",
    "\n",
    "theta_lasso=paraestimateLasso(phi,trainy,lmb=1)\n",
    "f_lasso=np.dot(test_phi.T,theta_lasso)\n",
    "print f_lasso.shape\n",
    "print meanabsoluteerror(testy,f_lasso)\n",
    "print meansquareerror(testy,f_lasso)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(600, 1)\n",
      "1.307928627386951\n",
      "2.898128040979179\n"
     ]
    }
   ],
   "source": [
    "\n",
    "theta_rr=paraestimateRobustreg(phi,trainy,lmb=1)\n",
    "f_rr=np.dot(test_phi.T,theta_rr)\n",
    "print f_rr.shape\n",
    "print meanabsoluteerror(testy,f_rr)\n",
    "print meansquareerror(testy,f_rr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.2968993099372872\n",
      "2.913107415872251\n"
     ]
    }
   ],
   "source": [
    "def esitmatesigma(Phi,alpha=1,sigma_square=5):\n",
    "    temp=(1/float(sigma_square))*np.dot(Phi,Phi.T)\n",
    "    m=len(Phi)\n",
    "    SIGMA=np.linalg.inv(temp+(1/float(alpha))*np.eye(m))\n",
    "    return SIGMA\n",
    "\n",
    "def estimatemju(sampy,Phi,SIGMA,sigma_square=5):\n",
    "    mju=(1/float(sigma_square))*np.dot(np.dot(SIGMA,Phi),sampy)\n",
    "    return mju\n",
    "\n",
    "def gaussianpredictedsigma(SIGMA,polyx_l):\n",
    "    polyphi=np.zeros((1,6))\n",
    "    for i in range(6):\n",
    "        polyphi[0][i]=np.power(polyx_l,i)\n",
    "    res=np.dot(np.dot(polyphi,SIGMA),polyphi.T)\n",
    "    return res\n",
    "\n",
    "SIGMA=esitmatesigma(phi,alpha=1,sigma_square=5)\n",
    "mju=estimatemju(trainy,phi,SIGMA,sigma_square=5)\n",
    "f_br=np.dot(test_phi.T,mju)\n",
    "print meanabsoluteerror(testy,f_br)\n",
    "print meansquareerror(testy,f_br)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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