fig_8_networkdepth.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Figure 8. Comparing RDD for different network depths"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "pylab.rcParams['figure.figsize'] = (10, 6)\n",
    "\n",
    "#%matplotlib inline\n",
    "\n",
    "import matplotlib\n",
    "import numpy as np\n",
    "import numpy.linalg as la\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy.random as rand\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "\n",
    "from lib.lif import LIF_Recurrent, ParamsLIF_Recurrent\n",
    "from lib.causal import causaleffect_maxv, causaleffect_maxv_linear, causaleffect_maxv_sp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Angle between two vectors\n",
    "def alignment(a,b):\n",
    "    da = np.dot(a,a)\n",
    "    db = np.dot(b,b)\n",
    "    if da > 0 and db > 0:\n",
    "        return 180/np.pi*np.arccos(np.dot(a,b)/np.sqrt(da*db))\n",
    "    else:\n",
    "        return 360.\n",
    "    \n",
    "def mse(pred,true):\n",
    "    return np.mean((pred - true)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Test LIF_Recurrent network\n",
    "nsims = 1\n",
    "\n",
    "cvals = [0.0, 0.7]\n",
    "pvals = np.logspace(-2, 0, 10)\n",
    "#c = 0.9\n",
    "n1 = 200\n",
    "n2 = 10\n",
    "tau_s = 0.020\n",
    "dt = 0.001\n",
    "t = 1   #In seconds\n",
    "sigma = 10\n",
    "x = 0\n",
    "#p = 0.1\n",
    "DeltaT = 10\n",
    "\n",
    "nC = len(cvals)\n",
    "nP = len(pvals)\n",
    "\n",
    "t_filter = np.linspace(0, 1, 1000)\n",
    "exp_filter = np.exp(-t_filter/tau_s)\n",
    "exp_filter = exp_filter/np.sum(exp_filter)\n",
    "ds = exp_filter[0]\n",
    "\n",
    "params = ParamsLIF_Recurrent(exp_filter, sigma = sigma,sigma1=0.1, n1 = n1, n2 = n2)\n",
    "lif = LIF_Recurrent(params, t = t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<lib.lif.ParamsLIF_Recurrent at 0x7f7191ad6690>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test 2 hidden layer network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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    {
     "name": "stderr",
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     "text": [
      "lib/lif.py:780: RuntimeWarning: invalid value encountered in multiply\n",
      "  delta1 = np.multiply(np.dot(delta.T,self.U[self.params.n1:,0:self.params.n1]),padded2)\n",
      "lib/lif.py:706: RuntimeWarning: invalid value encountered in greater\n",
      "  s = vt>self.params.mu\n",
      "lib/lif.py:720: RuntimeWarning: invalid value encountered in less\n",
      "  ut[ut<self.params.reset] = self.params.reset\n",
      "lib/lif.py:719: RuntimeWarning: invalid value encountered in less\n",
      "  vt[vt<self.params.reset] = self.params.reset\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
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      "  second = np.exp(-u**2+ 2*y_r*u)#,dtype=np.float128)\n"
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      "(784, 1000)\n",
      "('y_hat:', array([ 962.70135055,  963.08164479,  959.67011174,  960.9626857 ,\n",
      "        959.87406215,  962.17949563,  962.32365609,  961.29135376,\n",
      "        962.74687754,  961.23650691]))\n",
      "('e shape:', (10, 1))\n",
      "('grad_yhat', (10, 1))\n",
      "(784, 1000)\n",
      "('y_hat:', array([ 963.68186638,  964.06216062,  960.65062757,  961.94320153,\n",
      "        960.85457798,  963.16001146,  963.30417192,  962.27186959,\n",
      "        963.72739337,  962.21702274]))\n",
      "('e shape:', (10, 1))\n",
      "('grad_yhat', (10, 1))\n",
      "(784, 1000)\n",
      "('y_hat:', array([ 964.66238221,  965.04267645,  961.6311434 ,  962.92371736,\n",
      "        961.83509381,  964.14052729,  964.28468775,  963.25238542,\n",
      "        964.7079092 ,  963.19753857]))\n",
      "('e shape:', (10, 1))\n",
      "('grad_yhat', (10, 1))\n",
      "(784, 1000)\n",
      "('y_hat:', array([ 965.64289804,  966.02319228,  962.61165923,  963.90423319,\n",
      "        962.81560964,  965.12104311,  965.26520358,  964.23290125,\n",
      "        965.68842503,  964.1780544 ]))\n",
      "('e shape:', (10, 1))\n",
      "('grad_yhat', (10, 1))\n",
      "(784, 1000)\n",
      "('y_hat:', array([ 966.62341387,  967.00370811,  963.59217506,  964.88474902,\n",
      "        963.79612547,  966.10155894,  966.24571941,  965.21341708,\n",
      "        966.66894086,  965.15857022]))\n",
      "('e shape:', (10, 1))\n",
      "('grad_yhat', (10, 1))\n",
      "(784, 1000)\n",
      "('y_hat:', array([ 967.6039297 ,  967.98422394,  964.57269089,  965.86526485,\n",
      "        964.77664129,  967.08207477,  967.22623524,  966.19393291,\n",
      "        967.64945669,  966.13908605]))\n",
      "('e shape:', (10, 1))\n",
      "('grad_yhat', (10, 1))\n",
      "(784, 1000)\n",
      "('y_hat:', array([ 968.58444553,  968.96473976,  965.55320672,  966.84578068,\n",
      "        965.75715712,  968.0625906 ,  968.20675107,  967.17444874,\n",
      "        968.62997252,  967.11960188]))\n",
      "('e shape:', (10, 1))\n",
      "('grad_yhat', (10, 1))\n",
      "(784, 1000)\n",
      "('y_hat:', array([ 969.56496136,  969.94525559,  966.53372255,  967.82629651,\n",
      "        966.73767295,  969.04310643,  969.1872669 ,  968.15496457,\n",
      "        969.61048835,  968.10011771]))\n",
      "('e shape:', (10, 1))\n",
      "('grad_yhat', (10, 1))\n",
      "(784, 1000)\n",
      "('y_hat:', array([ 970.54547719,  970.92577142,  967.51423838,  968.80681234,\n",
      "        967.71818878,  970.02362226,  970.16778273,  969.1354804 ,\n",
      "        970.59100417,  969.08063354]))\n",
      "('e shape:', (10, 1))\n",
      "('grad_yhat', (10, 1))\n",
      "(784, 1000)\n",
      "('y_hat:', array([ 971.52599301,  971.90628725,  968.49475421,  969.78732817,\n",
      "        968.69870461,  971.00413809,  971.14829856,  970.11599622,\n",
      "        971.57152   ,  970.06114937]))\n",
      "('e shape:', (10, 1))\n",
      "('grad_yhat', (10, 1))\n",
      "(784, 1000)\n",
      "('y_hat:', array([ 972.50650884,  972.88680308,  969.47527004,  970.767844  ,\n",
      "        969.67922044,  971.98465392,  972.12881439,  971.09651205,\n",
      "        972.55203583,  971.0416652 ]))\n",
      "('e shape:', (10, 1))\n",
      "('grad_yhat', (10, 1))\n",
      "(784, 1000)\n",
      "('y_hat:', array([ 973.48702467,  973.86731891,  970.45578587,  971.74835983,\n",
      "        970.65973627,  972.96516975,  973.10933022,  972.07702788,\n",
      "        973.53255166,  972.02218103]))\n",
      "('e shape:', (10, 1))\n",
      "('grad_yhat', (10, 1))\n",
      "(784, 1000)\n",
      "('y_hat:', array([ 974.4675405 ,  974.84783474,  971.4363017 ,  972.72887566,\n",
      "        971.6402521 ,  973.94568558,  974.08984605,  973.05754371,\n",
      "        974.51306749,  973.00269686]))\n",
      "('e shape:', (10, 1))\n",
      "('grad_yhat', (10, 1))\n"
     ]
    }
   ],
   "source": [
    "inp,v, h, u, sh,st_actv,st_err,st_x,st_y = lif.simulate()\n",
    "#bp,hidd=lif.backprop()\n",
    "# results=lif.simulate()\n",
    "#np.nonzero(results[3][0,:])[0].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "a=array([12,123,12,3,4,21,23,3,12,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 12, 123,  12,   3,   4,  21,  23,   3,  12,   3])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000, 1)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(np.power(st_err,1),1).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f718a785650>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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UO8IfAACPIfwBAPAYwh8AAI8h/AEA8BjCHwAAjyH8AQDwGMIfAACPIfwBAPAY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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7191ad1b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.mean(np.power(st_err,1),1))\n",
    "plt.title(\"mean squared error\")\n",
    "plt.xlabel(\"iterations\")\n",
    "plt.ylabel(\"Error\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ -5.49827084e-002],\n",
       "       [  5.57832671e-005],\n",
       "       [  3.83800434e-002],\n",
       "       [ -1.09443692e-001],\n",
       "       [ -3.63042882e-001],\n",
       "       [ -8.68851926e-001],\n",
       "       [ -1.71233921e+000],\n",
       "       [ -5.53835462e+000],\n",
       "       [ -1.41287566e+001],\n",
       "       [ -2.93649778e+001],\n",
       "       [ -5.20824927e+001],\n",
       "       [ -8.49114847e+001],\n",
       "       [ -1.27394034e+002],\n",
       "       [ -1.82521315e+002],\n",
       "       [ -2.56085767e+002],\n",
       "       [ -3.46028445e+002],\n",
       "       [ -4.65221133e+002],\n",
       "       [ -6.18079275e+002],\n",
       "       [ -8.14879036e+002],\n",
       "       [ -1.08040197e+003],\n",
       "       [ -1.43419206e+003],\n",
       "       [ -1.91357928e+003],\n",
       "       [ -2.59134897e+003],\n",
       "       [ -3.53462579e+003],\n",
       "       [ -4.88800290e+003],\n",
       "       [ -6.90687216e+003],\n",
       "       [ -9.87601840e+003],\n",
       "       [ -1.44755686e+004],\n",
       "       [ -2.15561070e+004],\n",
       "       [ -3.28698251e+004],\n",
       "       [ -5.10880360e+004],\n",
       "       [ -8.15176785e+004],\n",
       "       [ -1.31865400e+005],\n",
       "       [ -2.18542008e+005],\n",
       "       [ -3.71045323e+005],\n",
       "       [ -6.41602177e+005],\n",
       "       [ -1.13002186e+006],\n",
       "       [ -2.02549345e+006],\n",
       "       [ -3.73505818e+006],\n",
       "       [ -7.00749812e+006],\n",
       "       [ -1.33399769e+007],\n",
       "       [ -2.61197597e+007],\n",
       "       [ -5.18102350e+007],\n",
       "       [ -1.05414311e+008],\n",
       "       [ -2.17936584e+008],\n",
       "       [ -4.59974068e+008],\n",
       "       [ -9.88668814e+008],\n",
       "       [ -2.17529034e+009],\n",
       "       [ -4.85112458e+009],\n",
       "       [ -1.10598917e+010],\n",
       "       [ -2.58796682e+010],\n",
       "       [ -6.12105596e+010],\n",
       "       [ -1.48182975e+011],\n",
       "       [ -3.67131740e+011],\n",
       "       [ -9.23494014e+011],\n",
       "       [ -2.36008365e+012],\n",
       "       [ -6.18597241e+012],\n",
       "       [ -1.65088057e+013],\n",
       "       [ -4.50502887e+013],\n",
       "       [ -1.25074652e+014],\n",
       "       [ -3.53711505e+014],\n",
       "       [ -1.02072515e+015],\n",
       "       [ -2.99598511e+015],\n",
       "       [ -8.97489982e+015],\n",
       "       [ -2.75135375e+016],\n",
       "       [ -8.55467268e+016],\n",
       "       [ -2.72374699e+017],\n",
       "       [ -8.79961964e+017],\n",
       "       [ -2.92168285e+018],\n",
       "       [ -9.82612626e+018],\n",
       "       [ -3.38013367e+019],\n",
       "       [ -1.18386479e+020],\n",
       "       [ -4.22316856e+020],\n",
       "       [ -1.53911116e+021],\n",
       "       [ -5.68896123e+021],\n",
       "       [ -2.16298817e+022],\n",
       "       [ -8.32360667e+022],\n",
       "       [ -3.28220498e+023],\n",
       "       [ -1.31488134e+024],\n",
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       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf],\n",
       "       [             -inf]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(np.power(st_err,1),1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2000, 1)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# store_tmp[0]\n",
    "np.sum(st_err*2,1).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# plt.plot(tograph[0,:])\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "ename": "IndexError",
     "evalue": "tuple index out of range",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-11-b0a4600edf14>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mscatter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mtograph\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxlabel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"MNIST number averaged over T steps\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mylabel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Activation mu\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtitle\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Activation vs input\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda/miniconda2/lib/python2.7/site-packages/numpy/core/fromnumeric.pyc\u001b[0m in \u001b[0;36mmean\u001b[0;34m(a, axis, dtype, out, keepdims)\u001b[0m\n\u001b[1;32m   2887\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2888\u001b[0m     return _methods._mean(a, axis=axis, dtype=dtype,\n\u001b[0;32m-> 2889\u001b[0;31m                           out=out, **kwargs)\n\u001b[0m\u001b[1;32m   2890\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2891\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda/miniconda2/lib/python2.7/site-packages/numpy/core/_methods.pyc\u001b[0m in \u001b[0;36m_mean\u001b[0;34m(a, axis, dtype, out, keepdims)\u001b[0m\n\u001b[1;32m     55\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     56\u001b[0m     \u001b[0mis_float16_result\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mFalse\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 57\u001b[0;31m     \u001b[0mrcount\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_count_reduce_items\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     58\u001b[0m     \u001b[0;31m# Make this warning show up first\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     59\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mrcount\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda/miniconda2/lib/python2.7/site-packages/numpy/core/_methods.pyc\u001b[0m in \u001b[0;36m_count_reduce_items\u001b[0;34m(arr, axis)\u001b[0m\n\u001b[1;32m     48\u001b[0m     \u001b[0mitems\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     49\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0max\u001b[0m \u001b[0;32min\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 50\u001b[0;31m         \u001b[0mitems\u001b[0m \u001b[0;34m*=\u001b[0m \u001b[0marr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0max\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     51\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mitems\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     52\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mIndexError\u001b[0m: tuple index out of range"
     ]
    }
   ],
   "source": [
    "plt.scatter(np.mean(x,1),tograph[0,:])\n",
    "plt.xlabel(\"MNIST number averaged over T steps\")\n",
    "plt.ylabel(\"Activation mu\")\n",
    "plt.title(\"Activation vs input\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "scrolled": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plt.imshow(inp[1,:,:])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#print('Firing rates:',np.sum(h[0], 1)/t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "fig, axes = plt.subplots(3,1,figsize = (15, 15), sharex = True)\n",
    "axes[0].imshow(inp[0], aspect = 'auto', interpolation = 'nearest')\n",
    "axes[1].imshow(v, aspect = 'auto', interpolation = 'nearest')\n",
    "im2 = axes[2].imshow(h, aspect = 'auto', interpolation = 'nearest')\n",
    "axes[0].set_ylabel('voltage')\n",
    "axes[1].set_ylabel('spike raster')\n",
    "axes[2].set_ylabel('synaptic input')\n",
    "axes[2].set_xlabel('time bin')\n",
    "plt.colorbar(im2, ax = axes[2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Causal effect estimation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "U = np.eye(n2)\n",
    "target = .02*np.ones((n2,1))\n",
    "target[0] = 0\n",
    "C_orig = lambda s: np.sum((np.dot(U, s) - target)**2,0)\n",
    "nsims = 50\n",
    "beta_rd_c = np.zeros((nC, nsims, nP, n1))\n",
    "beta_rd_c_linear = np.zeros((nC, nsims, nP, n1))\n",
    "beta_fd_c = np.zeros((nC, nsims, nP, n1))\n",
    "beta_fd_c_linear = np.zeros((nC, nsims, nP, n1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "cvals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#Compute causal effects\n",
    "for i,c in enumerate(cvals):\n",
    "    print(\"Running %d simulations with c=%s\"%(nsims, c))\n",
    "    params.c = c\n",
    "    lif.setup(params)\n",
    "    for j in range(nsims):\n",
    "        (inp,v, h, u, sh) = lif.simulate(DeltaT)\n",
    "        cost = C_orig(sh[n1:,:])\n",
    "        for k,p in enumerate(pvals):\n",
    "            #a = causaleffect_maxv(u[0:n1,:], cost, DeltaT, p, params)\n",
    "            #print(a.shape)\n",
    "            beta_rd_c[i,j,k,:] = causaleffect_maxv(u[0:n1,:], cost, DeltaT, p, params)\n",
    "            beta_rd_c_linear[i,j,k,:] = causaleffect_maxv_linear(u[0:n1,:], cost, DeltaT, p, params)\n",
    "        beta_fd_c[i,j,:] = causaleffect_maxv(u[0:n1,:], cost, DeltaT, 1, params)\n",
    "        beta_fd_c_linear[i,j,:] = causaleffect_maxv_linear(u[0:n1,:], cost, DeltaT, 1, params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "#Plot the causal effects as a function of p\n",
    "for u in range(10):\n",
    "    #u = 1\n",
    "    fig,ax = plt.subplots(1,1,figsize=(4,4))\n",
    "    #for i in range(len(cvals)):\n",
    "    #    #sns.tsplot(data = beta_rd_c[i,:,:,u], ax = ax, ci='sd', time=pvals)#, color='C%d'%i)\n",
    "    #    sns.tsplot(data = beta_rd_c[i,:,:,u], ax = ax, time=pvals)#, color='C%d'%i)\n",
    "    #    #ax.plot(pvals, m_beta_rd_c[i,-1,u]*ones(pvals.shape), '-.', color='C%d'%i)\n",
    "    sns.tsplot(data = beta_rd_c[0,:,:,u], ax = ax, time=pvals, color='red')\n",
    "    sns.tsplot(data = beta_rd_c[1,:,:,u], ax = ax, time=pvals, color='blue')\n",
    "    #sns.tsplot(data = beta_rd_c_linear[0,:,:,u], ax = ax, time=pvals, color='red')\n",
    "    #sns.tsplot(data = beta_rd_c_linear[1,:,:,u], ax = ax, time=pvals, color='blue')\n",
    "    ax.set_xlabel('window size $p$');\n",
    "    ax.set_ylabel('average causal effect');\n",
    "    ax.set_title('Constant RD estimator');\n",
    "    #ax.plot(pvals, beta_sp_c[0,u]*ones(pvals.shape), color=(0,0,0));\n",
    "    #ax.set_ylim([3, 7])\n",
    "    #ax.set_ylim([5.4, 5.9])\n",
    "    #ax.set_xlim([0, 1])\n",
    "    ax.set_xscale('log')\n",
    "    #ax.set_yticks([2, 3, 4, 5, 6])\n",
    "    sns.despine(trim=True)\n",
    "    ax.legend([\"c = %.2f\"%i for i in cvals]);\n",
    "    #plt.savefig('./fig_2a.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A. Dependence on $N$ and $c$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nsims = 5\n",
    "cvals = np.array([0.01, 0.25, 0.5, 0.75, 0.99])\n",
    "#cvals = np.array([0.01, 0.25, 0.5])\n",
    "#Nvals = np.logspace(1, 3, 6, dtype = int)\n",
    "Nvals = np.logspace(1, 3, 4, dtype = int)\n",
    "\n",
    "tau_s = 0.020\n",
    "dt = 0.001\n",
    "t = 100\n",
    "sigma = 10\n",
    "x = 0\n",
    "p = 0.1\n",
    "DeltaT = 20\n",
    "\n",
    "W = np.array([12, 9])\n",
    "\n",
    "params = ParamsLIF(sigma = sigma)\n",
    "lif = LIF(params, t = t)\n",
    "lif.W = W\n",
    "\n",
    "t_filter = np.linspace(0, 1, 2000)\n",
    "exp_filter = np.exp(-t_filter/tau_s)\n",
    "exp_filter = exp_filter/np.sum(exp_filter)\n",
    "ds = exp_filter[0]\n",
    "\n",
    "#c (correlation between noise inputs)\n",
    "beta_mse_rd_c = np.zeros((len(cvals), len(Nvals), nsims))\n",
    "beta_mse_fd_c = np.zeros((len(cvals), len(Nvals), nsims))\n",
    "beta_mse_bp_c = np.zeros((len(cvals), len(Nvals), nsims))\n",
    "\n",
    "beta_mse_rd_c_linear = np.zeros((len(cvals), len(Nvals), nsims))\n",
    "beta_mse_fd_c_linear = np.zeros((len(cvals), len(Nvals), nsims))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#beta_sp_c = np.zeros((len(cvals), params.n))\n",
    "\n",
    "target = 0.1\n",
    "W = 10*np.ones(int(Nvals[-1]))\n",
    "#W = np.random.randn(int(Nvals[-1]))*5\n",
    "V = np.random.randn(int(Nvals[-1]))*5\n",
    "\n",
    "cost = lambda s,a: (np.dot(a[0:len(s)], s) - len(s)*target)**2\n",
    "\n",
    "#Cost function\n",
    "#B1 = 1\n",
    "#B2 = 2\n",
    "#x = .01\n",
    "#y = 0.1\n",
    "#z = 0\n",
    "\n",
    "#cost = lambda s1, s2: (B1*s1-x)**2 + (z+B2*s2 - B2*(B1*s1-y)**2)**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "params.c = 0.99\n",
    "params.n = 10\n",
    "lif.setup(params)\n",
    "lif.W = W[0:10]\n",
    "(v, h, _, _, u) = lif.simulate(DeltaT)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "h.shape\n",
    "n_units = 10\n",
    "s = np.zeros(h.shape)\n",
    "for l in range(10):\n",
    "    s[l,:] = np.convolve(h[l,:], exp_filter)[0:h.shape[1]]\n",
    "cost_s = cost(s,V[0:n_units])"
   ]
  }
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