scale_intercept.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.linear_model import LinearRegression\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.linspace(50,90)\n",
    "intercept = 60\n",
    "slope = 300\n",
    "y = intercept + slope*x + np.random.normal(0,3,size=len(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def splot(x,y):\n",
    "    fig,ax = plt.subplots()\n",
    "    ax.scatter(x,y)\n",
    "    plt.show()\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def lr(x,y):\n",
    "    if len(x.shape) == 1:\n",
    "        X = x[:,np.newaxis]\n",
    "    else:\n",
    "        X = x\n",
    "    model = LinearRegression()\n",
    "    model.fit(X,y)\n",
    "    print(\"Intercept: {}, Slope: {}\".format(model.intercept_,model.coef_))\n",
    "    return model.intercept_,model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept: 58.594482157404855, Slope: [ 300.02477645]\n"
     ]
    }
   ],
   "source": [
    "a0,b0 = lr(x,y);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a13bfb320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "splot(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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x65c07qq6BpDAdyMigS9n5s6K5l02s35J427RBhARdwMn9njq6sy8Y8B5zsnM2Yg4Abgr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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a13a9db00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scalex = StandardScaler().fit(x[:,np.newaxis])\n",
    "xs = scalex.transform(x[:,np.newaxis])\n",
    "scaley = StandardScaler().fit(y[:,np.newaxis])\n",
    "ys = scaley.transform(y[:,np.newaxis])[:,0]\n",
    "splot(xs,ys)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept: 4.618528082144806e-16, Slope: [ 0.9999996]\n"
     ]
    }
   ],
   "source": [
    "a,b = lr(xs,ys)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "60 58.5944821574 [ 58.59448216]\n"
     ]
    }
   ],
   "source": [
    "print(intercept,a0,(a*scaley.scale_) + y.mean() - (b*(scaley.scale_/scalex.scale_)*x.mean()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pymc3 as pm\n",
    "import theano.tensor as ttens\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "def linear_regression(X, y, \n",
    "                      n_features = None, n_samples = None,\n",
    "                      alpha_prior = None, beta_prior = None, sigma_prior = None,\n",
    "                      samples = 1000, njobs = 2):\n",
    "    if not alpha_prior:\n",
    "        alpha_prior = {'mu':0, 'sd':10}\n",
    "    if not beta_prior:\n",
    "        beta_prior = {'mu':np.zeros((n_features)), 'sd':3*np.ones((n_features))}\n",
    "    if not sigma_prior:\n",
    "        sigma_prior = {'sd': 3}\n",
    "    if not n_features:\n",
    "        n_features = X.shape[1]\n",
    "    if not n_samples:\n",
    "        n_samples = X.shape[0]\n",
    "\n",
    "    with pm.Model() as model: \n",
    "        #Specify priors\n",
    "        alpha = pm.Normal('alpha', mu = alpha_prior['mu'], sd = alpha_prior['sd'])\n",
    "        beta = pm.Normal('beta', mu = beta_prior['mu'], sd = beta_prior['sd'], shape = int(n_features))\n",
    "        sigma = pm.HalfNormal('sigma', sd = sigma_prior['sd'])\n",
    "        \n",
    "        # Specify regression relationship in mu\n",
    "        mu = alpha + ttens.dot(beta,X.T)\n",
    "        \n",
    "        # Specify likelihood\n",
    "        Y_obs = pm.Normal('Y_obs', mu = mu, sd = sigma, observed = y)\n",
    "        \n",
    "        # Fit the model\n",
    "        trace = pm.sample(draws = samples, njobs = njobs)\n",
    "        \n",
    "        # Generate data from the model\n",
    "        simulate_data = pm.sample_ppc(trace=trace,model=model)\n",
    "    return model, trace, simulate_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [sigma_log__, beta, alpha]\n",
      "100%|██████████| 1500/1500 [00:06<00:00, 240.30it/s]\n",
      "The acceptance probability does not match the target. It is 0.909026258446, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The acceptance probability does not match the target. It is 0.896167383666, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "100%|██████████| 1000/1000 [00:02<00:00, 466.01it/s]\n"
     ]
    }
   ],
   "source": [
    "model, trace, simulate_data = linear_regression(xs[:,np.newaxis],ys)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "def _to_dataframe(trace):\n",
    "    ft = pd.DataFrame()\n",
    "    param_list = trace.varnames\n",
    "    for idx,param_name in enumerate(param_list):\n",
    "        if \".\" not in param_name:\n",
    "            ft[param_name] = trace.get_values(param_name)\n",
    "        else:\n",
    "            param_short_name, feature_index = param_name.split(\".\")\n",
    "            feature_index = int(feature_index) -1\n",
    "            if len(fit.extract(param_short_name)[param_short_name].shape) < 2:\n",
    "                ft[param_name] = fit.extract(param_short_name)[param_short_name]\n",
    "            else:\n",
    "                ft[param_name] = fit.extract(param_short_name)[param_short_name][:,feature_index]\n",
    "    return ft\n",
    "\n",
    "# Extract the samples to a dataframe called ft\n",
    "ft = _to_dataframe(trace)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [],
   "source": [
    "ft['alpha_original'] = scaley.mean_ - ft.beta*(scaley.scale_/scalex.scale_)*scalex.mean_\n",
    "ft['beta_original'] = ft.beta*(scalex.scale_/scaley.scale_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1c1f01e550>"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c1f4a2390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ft.alpha_original.hist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1c1f04f668>"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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A/cCZpft1wKnADuAHwNuXIbMkaUgWLRqZ+ZY9vHRyl74JnL/UUJKkdvKKcElSNYuGJKma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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c1f2ceba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ft.beta_original.hist(bins=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -3.47290517e-12])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(a*scaley.scale_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.99965192])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 20925.30186394])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b*(scaley.scale_/scalex.scale_)*x.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "bayes",
   "language": "python",
   "name": "bayes"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}