numerical_simulation-paper-quadratic-4th.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generating Data\n",
    "Like in my post on [building neural networks from scratch](https://beckernick.github.io/neural-network-scratch/), I'm going to use simulated data. I can easily simulate separable data by sampling from a multivariate normal distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import nodepy \n",
    "import matplotlib.pyplot as plt\n",
    "import sys\n",
    "import scipy as sp\n",
    "from scipy import io\n",
    "%matplotlib inline\n",
    "\n",
    "np.random.seed(12)\n",
    "num_observations = 3\n",
    "clusters = 1\n",
    "dim = 10\n",
    "spread = 10\n",
    "margin = np.random.randint(10, size=dim) * 50\n",
    "\n",
    "for i in range(clusters):\n",
    "    if i == 0:\n",
    "        x1 = np.random.multivariate_normal(np.random.randint(spread, size=dim) + margin, np.identity(dim), num_observations)\n",
    "        x2 = np.random.multivariate_normal(np.random.randint(spread, size=dim), np.identity(dim), num_observations)\n",
    "    else:\n",
    "        x1 = np.append(x1, np.random.multivariate_normal(np.random.randint(spread, size=dim) + margin, np.identity(dim), num_observations), axis=0)\n",
    "        x2 = np.append(x2, np.random.multivariate_normal(np.random.randint(spread, size=dim), np.identity(dim), num_observations), axis=0)\n",
    "\n",
    "simulated_separableish_features = np.vstack((x1, x2)).astype(np.float32)\n",
    "simulated_labels = np.hstack((np.zeros(len(x1)),\n",
    "                              np.ones(len(x2))))\n",
    "intercept = np.ones((simulated_separableish_features.shape[0], 2))\n",
    "simulated_separableish_features = np.hstack((intercept, simulated_separableish_features))\n",
    "dim += 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x117017f28>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x113c20828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,8))\n",
    "plt.scatter(simulated_separableish_features[:, -1], simulated_separableish_features[:, 2],\n",
    "            c = simulated_labels, alpha = .4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Quadratic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\n",
    "def grad_logistic(X, Y, w):\n",
    "    pred = np.dot(X, w) - Y\n",
    "    return np.dot(X.T, pred) + 4* np.dot(w[-1].T, w[-1]) * np.hstack([[0]*(dim-1),w[-1]])\n",
    "\n",
    "def loss_logistic(X, Y, w):\n",
    "    pred = Y - np.dot(X, w)\n",
    "    return np.dot(pred.T, pred) + np.dot(w[-1].T, w[-1])**2\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Show that GD works"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def gd(f, df, num_steps, learning_rate, inits, period=5000):\n",
    "    losses = np.zeros(int(num_steps/period))\n",
    "    weights = inits\n",
    "    for step in xrange(num_steps):\n",
    "        # Update weights with log likelihood gradient\n",
    "        gradient = - df(weights)\n",
    "        #gradient = np.dot(features.T, output_error_signal)\n",
    "        weights += learning_rate * gradient\n",
    "        # Print log-likelihood every so often\n",
    "        if step % period == 0:\n",
    "            losses[int(step/period)] = f(weights)\n",
    "        if step % (num_steps/5) == 0:\n",
    "            print losses[int(step/period)]\n",
    "        \n",
    "    return weights, losses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.996290005\n",
      "0.00426339959744\n",
      "0.00173069191139\n",
      "0.000726516873182\n",
      "0.000306737242127\n"
     ]
    }
   ],
   "source": [
    "weights = np.zeros(dim)\n",
    "f = lambda x: loss_logistic(simulated_separableish_features, simulated_labels, x)\n",
    "df = lambda x: grad_logistic(simulated_separableish_features, simulated_labels, x)\n",
    "weights, losses = gd(f, df, num_steps = int(1e6), learning_rate = 1e-6, \n",
    "                     inits=weights, period=500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1099c1b50>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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/lHjG9OrM2N6dGdOrM8nxsR5XLHL2gjoAjtMdgLSmyppa1heUsmZHCat3lLB2ZwnlDXcJ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\nASAiEqYUACIiYer/A2F9OBFlx/jvAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1096f93d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.loglog(losses[:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.000130557066578\n"
     ]
    }
   ],
   "source": [
    "print(losses[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (<ipython-input-7-59cf23a778b2>, line 13)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-7-59cf23a778b2>\"\u001b[0;36m, line \u001b[0;32m13\u001b[0m\n\u001b[0;31m    print losses[int(step/period)]\u001b[0m\n\u001b[0m               ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "def rgd4(f, df, num_steps, learning_rate, inits, period=5000):\n",
    "    losses = np.zeros(int(num_steps/period))\n",
    "    weights = inits\n",
    "    for step in xrange(num_steps):\n",
    "        # Update weights with log likelihood gradient\n",
    "        gradient = - df(weights)\n",
    "        #gradient = np.dot(features.T, output_error_signal)\n",
    "        weights += learning_rate * gradient/(np.linalg.norm(gradient)^{3/2})\n",
    "        # Print log-likelihood every so often\n",
    "        if step % period == 0:\n",
    "            losses[int(step/period)] = f(weights)\n",
    "        if step % (num_steps/5) == 0:\n",
    "            print losses[int(step/period)]\n",
    "        \n",
    "    return weights, losses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (<ipython-input-8-5edfda6c148f>, line 15)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-8-5edfda6c148f>\"\u001b[0;36m, line \u001b[0;32m15\u001b[0m\n\u001b[0;31m    print losses[int(k/period)]\u001b[0m\n\u001b[0m               ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "def nag(f, df, num_steps, learning_rate, inits, period=5000):\n",
    "    losses = np.zeros(int(num_steps/period))\n",
    "    x = inits\n",
    "    x_prev = inits\n",
    "    y = inits\n",
    "    for k in xrange(num_steps):\n",
    "        # Update weights with log likelihood gradient\n",
    "        x, x_prev = y - learning_rate * df(y), x\n",
    "        y = x + (k-1.0)/(k+2.0)*(x-x_prev)\n",
    "\n",
    "        # Print log-likelihood every so often\n",
    "        if k % period == 0:\n",
    "            losses[int(k/period)] = f(x)\n",
    "        if k % (num_steps/10) == 0:\n",
    "            print losses[int(k/period)]\n",
    "        \n",
    "    return x, losses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.996290005\n",
      "1.38626699619e-08\n",
      "6.76037577688e-10\n",
      "8.0899051656e-11\n",
      "4.06784246467e-12\n",
      "1.57940380124e-12\n",
      "5.11492031801e-12\n",
      "4.71804759185e-12\n",
      "2.45015735692e-12\n",
      "6.84502471145e-13\n"
     ]
    }
   ],
   "source": [
    "weights = np.zeros(dim)\n",
    "f = lambda x: loss_logistic(simulated_separableish_features, simulated_labels, x)\n",
    "df = lambda x: grad_logistic(simulated_separableish_features, simulated_labels, x)\n",
    "weights, losses = nag(f, df, num_steps = int(1e6), learning_rate = 1e-6, \n",
    "                     inits=weights, period=500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x109ec9bd0>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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dDhc8/i4AG6eMIrwRzNpWnx7CViC53HKSr01ExFM9OsSSfV9gR0qtjW6Ts3lq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\nCgQREfH5fyi369iDx7acAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109b78450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.loglog(losses[:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simulate ODE flow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\n",
    "import nodepy.runge_kutta_method as rk\n",
    "import nodepy.convergence as cv\n",
    "from nodepy import ivp\n",
    "\n",
    "class ODE_IVP(nodepy.ivp.IVP):\n",
    "    \n",
    "    def __init__(self, X, Y, p, u0, t0=0., T=1000000., desc='', name=''):\n",
    "        \n",
    "        #intercept = np.ones((X.shape[0], 1))\n",
    "        #self.X = np.hstack((intercept, X))\n",
    "        self.Y = Y\n",
    "        self.X = X\n",
    "        self.p = float(p)\n",
    "        self.u0  = u0\n",
    "        self.dim = len(u0)/2\n",
    "        self.rhs = self.dynamics\n",
    "        self.T   = T\n",
    "        self.exact = None\n",
    "        self.description = desc\n",
    "        self.t0 = t0\n",
    "        self.name = name\n",
    "    \n",
    "    def dynamics(self, t, u):\n",
    "        x = u[:self.dim]\n",
    "        v = u[self.dim:]\n",
    "        p = self.p\n",
    "        dv = - (p+1) / (t) * v - p**2 * t**(p-2) * grad_logistic(self.X, self.Y, x)\n",
    "        return np.append(v, dv)\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# Same integrator on different ODE\n",
    "\n",
    "def simulate(p, s, N, period, step, inits):\n",
    "    h = step\n",
    "    if s==1:\n",
    "        name = 'FE'\n",
    "    elif s==2:\n",
    "        name = 'SSP22'\n",
    "    elif s==4:\n",
    "        name = 'RK44'\n",
    "    elif s==8:\n",
    "        name = 'PD8'\n",
    "    else:\n",
    "        return None\n",
    "    u = [inits]\n",
    "    integrator =rk.loadRKM(name)\n",
    "    loop = N/period\n",
    "    losses = np.zeros(int(N/period))\n",
    "    ode_ivp = ODE_IVP(simulated_separableish_features, simulated_labels, p, u0=u[-1])\n",
    "    for j in range(loop):\n",
    "        losses[j] = loss_logistic(simulated_separableish_features, simulated_labels, u[-1][:dim])\n",
    "        t,u = integrator(ode_ivp, t0= 0.1 + j * period * h, dt=h, max_steps=period)\n",
    "        ode_ivp = ODE_IVP(simulated_separableish_features, simulated_labels, p, u0=u[-1])\n",
    "    return losses\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N = int(1e4)\n",
    "truncate = 0\n",
    "period = 500\n",
    "pvalues = [1,2,4]\n",
    "nrange = period * np.arange(int(N/period)) - period + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python2.7/site-packages/ipykernel/__main__.py:4: RuntimeWarning: overflow encountered in multiply\n",
      "/usr/local/lib/python2.7/site-packages/ipykernel/__main__.py:4: RuntimeWarning: invalid value encountered in multiply\n",
      "/usr/local/lib/python2.7/site-packages/matplotlib/ticker.py:2041: UserWarning: Data has no positive values, and therefore cannot be log-scaled.\n",
      "  \"Data has no positive values, and therefore cannot be \"\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10806f390>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ARiQDAEAjkgEAoBHJAADQiGQAAGhEMgAANCIZAAAakQwAAI1IBgCARiQDAEAjkgEAoBHJ\nAADQiGQAAGhEMgAANCIZAAAakQwAAI1IBgCARiQDAEAjkgEAoBHJAADQiGQAAGhEMgAANCIZAAAa\nkQwAAI1IBgCARiQDAEAjkgEAoBHJAADQnLPUF6yq85N8NcmLSf5njPHtpX4OAAA4nRa0klxV91bV\nc1X1aDt+fVUdqKqnquozxw7fmGTPGOPjSW5Y4nkBAOC0W+h2i91Jrj/xQFWtSXJPkg8k2ZLklqra\nkmR9kqePnfby0owJAADLZ0GRPMZ4MMmf2uG3JHlqjPGbMcaLSb6b5INJZnM0lP/p9atqZ1Xtq6p9\nBw8ePPnJAQDgNFnMB/cuz99XjJOjcXx5kvuT3FRVX0uy99UePMbYNcbYPsbYfskllyxiDAAAWFpL\n/sG9McZfkty21NcFAIDlspiV5GeSvP6E2+uPHQMAgFVtMZH8iyRXVNXGqjovyYeT/GBpxgIAgOks\n9CvgvpPkoSSbqmq2qm4fY7yU5M4kP0zyeJLvjTEeO32jAgDA8ljQnuQxxi2vcvyBJA8s6UQAADAx\n/5YaAAAakQwAAI1IBgCARiQDAEAjkgEAoBHJAADQiGQAAGhEMgAANCIZAAAakQwAAI1IBgCAZtJI\nrqodVbVrbm5uyjEAAGCeSSN5jLF3jLFzZmZmyjEAAGCeGmNMPUOq6mCS3x27OZNkuZaWL07y/DI9\nFyy35fxdYnH8rE7O2fR+rfbXuhrmX0kzTjnLcj/3lA32hjHGJa910oqI5BNV1a4xxs5leq59Y4zt\ny/FcsNyW83eJxfGzOjln0/u12l/raph/Jc045SzL/dyrocFW4gf39k49AJwh/C6tHn5WJ+dser9W\n+2tdDfOvpBmnnGUlvQ8rwopbSV5Oq+GvGACAM81qaLCVuJK8nHZNPQAAwFloxTfYWb2SDAAA/8jZ\nvpIMAACvIJIBAKARyQAA0IjkE1TV+VX1X1X1n1V169TzAACcDarqjVX1zaraM/Us/++Mj+Squreq\nnquqR9vx66vqQFU9VVWfOXb4xiR7xhgfT3LDsg8LAHCGOJkGG2P8Zoxx+zST/mNnfCQn2Z3k+hMP\nVNWaJPck+UCSLUluqaotSdYnefrYaS8v44wAAGea3Vl4g604Z3wkjzEeTPKndvgtSZ469lfLi0m+\nm+SDSWZzNJSTs+C9AQA4XU6ywVacszUEL8/fV4yTo3F8eZL7k9xUVV+Lf88IALDU/mGDVdVFVfX1\nJFdV1WenGW2+c6YeYCUZY/wlyW1TzwEAcDYZYxxKcsfUc5zobF1JfibJ60+4vf7YMQAATp9V02Bn\nayT/IskVVbWxqs5L8uEkP5h4JgCAM92qabAzPpKr6jtJHkqyqapmq+r2McZLSe5M8sMkjyf53hjj\nsSnnBAA4k6z2BqsxxtQzAADAinLGryQDAMDJEskAANCIZAAAaEQyAAA0IhkAABqRDAAAjUgGAIBG\nJAMAQCOSAQCg+T/6L0UgjVK5AQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108aee1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (12, 8))\n",
    "losses = simulate(2, 8, N, period, 1e-2, np.zeros(dim * 2))\n",
    "plt.loglog(nrange, losses[truncate:], label=str(2) + 'th order')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.996290005\n",
      "3.6871400954e-06\n",
      "1.90475854593e-06\n",
      "1.86854255901e-06\n",
      "1.83449406397e-06\n",
      "2.996290005\n",
      "3.60781312976e-14\n",
      "1.06248687312e-14\n",
      "3.27922370106e-16\n",
      "3.19990141623e-19\n",
      "1.64917222249e-18\n",
      "3.42816518866e-19\n",
      "1.06162618868e-20\n",
      "2.97335324638e-21\n",
      "1.74384380306e-21\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(1e-20, 100)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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4aXxc8DF3jr3zuMuoN3oa2VOzh7HRY096QKbQv4ZSD4XBSoTps4zepCU2TUts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1YMrHYCJJkLl3kQERGR+cSMALr1Q2uvo9UKaQCI8vsKvQP+rimY45bP3IRvvj6pOwYZjMU0ERER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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b7a3910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = int(1e7)\n",
    "truncate = 0\n",
    "period = 100\n",
    "pvalues = [1,2,4]\n",
    "nrange = period * np.arange(int(N/period))- period + 1\n",
    "\n",
    "svals = [1,2,4]\n",
    "steps = [1e-6, 1e-5, 1e-3]\n",
    "plt.figure(figsize = (12, 8))\n",
    "loss_matrix = np.zeros((len(svals)+2, len(nrange)))\n",
    "\n",
    "\n",
    "weights = np.zeros(dim)\n",
    "f = lambda x: loss_logistic(simulated_separableish_features, simulated_labels, x)\n",
    "df = lambda x: grad_logistic(simulated_separableish_features, simulated_labels, x)\n",
    "\n",
    "_, gdlosses = gd(f, df, num_steps = N, learning_rate = 1e-6, \n",
    "                     inits=weights, period=period)\n",
    "loss_matrix[0] = gdlosses\n",
    "\n",
    "weights = np.zeros(dim)\n",
    "plt.loglog(nrange, gdlosses[truncate:], label='GD')\n",
    "_, naglosses = nag(f, df, num_steps = N, learning_rate = 1e-6, \n",
    "                     inits=weights, period=period)\n",
    "loss_matrix[1] = naglosses\n",
    "\n",
    "plt.loglog(nrange, naglosses[truncate:], label='NAG')\n",
    "\n",
    "losslst = []\n",
    "for i, s in enumerate(svals):\n",
    "    losses = simulate(2, s, N, period, steps[i], np.zeros(dim * 2))\n",
    "    losslst.append(losses)\n",
    "    loss_matrix[i+2, :] = losses\n",
    "    plt.loglog(nrange, losses[truncate:], label=str(s) + 'th order')\n",
    "plt.legend()\n",
    "plt.ylim(1e-20, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sp.io.savemat('quad-4th.mat', {'loss_matrix': loss_matrix})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python2.7/site-packages/ipykernel/__main__.py:28: RuntimeWarning: overflow encountered in multiply\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(1e-10, 100)"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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baVTv+jI/O/nnXDvxWp7c/CSbKjf18AElmhSmJZYUpkVEhNPbRpwPt7X4om0V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\nO4iIiIg6vN+NTFE7BMUkF69SOwSftWVrvLcAfA4gVQhRLoSYKaVsBPA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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1115d1490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Different choice of p\n",
    "N = int(1e7)\n",
    "truncate = 0\n",
    "period = 100\n",
    "pvalues = [2, 3, 4]\n",
    "nrange = period * np.arange(int(N/period))- period + 1\n",
    "\n",
    "svals = [2, 2, 2]\n",
    "steps = [1e-5, 1e-5, 1e-5]\n",
    "plt.figure(figsize = (12, 8))\n",
    "\n",
    "\n",
    "weights = np.zeros(dim)\n",
    "f = lambda x: loss_logistic(simulated_separableish_features, simulated_labels, x)\n",
    "df = lambda x: grad_logistic(simulated_separableish_features, simulated_labels, x)\n",
    "\n",
    "losslst = []\n",
    "for i, s in enumerate(svals):\n",
    "    losses = simulate(pvalues[i], s, N, period, steps[i], np.zeros(dim * 2))\n",
    "    losslst.append(losses)\n",
    "    plt.loglog(nrange, losses[truncate:], label=str(pvalues[i]) + 'th acceleration')\n",
    "plt.legend()\n",
    "plt.ylim(1e-10, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.16"
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
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   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}