{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Neural Network Fundamentals\n",
    "\n",
    "## Gradient Descent Introduction:\n",
    "https://www.youtube.com/watch?v=IxBYhjS295w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "np.random.seed(1)\n",
    "\n",
    "%matplotlib inline\n",
    "np.random.seed(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 100\n",
    "x = np.random.rand(N,1)*5\n",
    "# Let the following command be the true function\n",
    "y = 2.3 + 5.1*x\n",
    "# Get some noisy observations\n",
    "y_obs = y + 2*np.random.randn(N,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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T8FoSngRamHYY0xoAXhdDU415DBQMSCaom0BEpAWxsw3CvBu4zzeX4uI40w6d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\nks1GL7ZenAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119130ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x,y_obs,label='Observations')\n",
    "plt.plot(x,y,c='r',label='True function')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gradient Descent\n",
    "\n",
    "We are trying to minimise $\\sum \\xi_i^2$.\n",
    "\n",
    "\\begin{align}\n",
    "\\mathcal{L} & = \\frac{1}{N}\\sum_{i=1}^N (y_i-f(x_i,w,b))^2 \\\\\n",
    "\\frac{\\delta\\mathcal{L}}{\\delta w} & = -\\frac{1}{N}\\sum_{i=1}^N 2(y_i-f(x_i,w,b))\\frac{\\delta f(x_i,w,b)}{\\delta w} \\\\ \n",
    "& = -\\frac{1}{N}\\sum_{i=1}^N 2\\xi_i\\frac{\\delta f(x_i,w,b)}{\\delta w}\n",
    "\\end{align}\n",
    "where $\\xi_i$ is the error term $y_i-f(x_i,w,b)$ and \n",
    "$$\n",
    "\\frac{\\delta f(x_i,w,b)}{\\delta w} = x_i\n",
    "$$\n",
    "\n",
    "Similar expression can be found for $\\frac{\\delta\\mathcal{L}}{\\delta b}$ (exercise).\n",
    "\n",
    "Finally the weights can be updated as $w_{new} = w_{current} - \\gamma \\frac{\\delta\\mathcal{L}}{\\delta w}$ where $\\gamma$ is a learning rate between 0 and 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Helper functions\n",
    "def f(w,b):\n",
    "    return w*x+b\n",
    "\n",
    "def loss_function(e):\n",
    "    L = np.sum(np.square(e))/N\n",
    "    return L\n",
    "\n",
    "def dL_dw(e,w,b):\n",
    "    return -2*np.sum(e*df_dw(w,b))/N\n",
    "\n",
    "def df_dw(w,b):\n",
    "    return x\n",
    "\n",
    "def dL_db(e,w,b):\n",
    "    return -2*np.sum(e*df_db(w,b))/N\n",
    "\n",
    "def df_db(w,b):\n",
    "    return np.ones(x.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The Actual Gradient Descent\n",
    "def gradient_descent(iter=100,gamma=0.1):\n",
    "    # get starting conditions\n",
    "    w = 10*np.random.randn()\n",
    "    b = 10*np.random.randn()\n",
    "    \n",
    "    params = []\n",
    "    loss = np.zeros((iter,1))\n",
    "    for i in range(iter):\n",
    "#         from IPython.core.debugger import Tracer; Tracer()()\n",
    "        params.append([w,b])\n",
    "        e = y_obs - f(w,b) # Really important that you use y_obs and not y (you do not have access to true y)\n",
    "        loss[i] = loss_function(e)\n",
    "\n",
    "        #update parameters\n",
    "        w_new = w - gamma*dL_dw(e,w,b)\n",
    "        b_new = b - gamma*dL_db(e,w,b)\n",
    "        w = w_new\n",
    "        b = b_new\n",
    "        \n",
    "    return params, loss\n",
    "        \n",
    "params, loss = gradient_descent()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "iter=100\n",
    "gamma = 0.1\n",
    "w = 10*np.random.randn()\n",
    "b = 10*np.random.randn()\n",
    "\n",
    "params = []\n",
    "loss = np.zeros((iter,1))\n",
    "for i in range(iter):\n",
    "#         from IPython.core.debugger import Tracer; Tracer()()\n",
    "    params.append([w,b])\n",
    "    e = y_obs - f(w,b) # Really important that you use y_obs and not y (you do not have access to true y)\n",
    "    loss[i] = loss_function(e)\n",
    "\n",
    "    #update parameters\n",
    "    w_new = w - gamma*dL_dw(e,w,b)\n",
    "    b_new = b - gamma*dL_db(e,w,b)\n",
    "    w = w_new\n",
    "    b = b_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0078296405377948283"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dL_dw(e,w,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1184f7be0>]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hSZJyK3WQcLKlJEnFKmWQmDQpWxyRkCSpWKUMEpBNuDRISJJUrNIGCR/cJUlS8UobJHp6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\nIDroFwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1186b3b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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swIH0n3f8uNnkyWZnn83ndOpk9ssvwX0fiYlm33xjNnCgWZUqfJ0GDcyeesos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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115ba20b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "params = np.array(params)\n",
    "plt.plot(params[:,0],params[:,1])\n",
    "plt.title('Gradient descent')\n",
    "plt.xlabel('w')\n",
    "plt.ylabel('b')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.98099133,  2.75130442])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params[-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multivariate case\n",
    "\n",
    "We are trying to minimise $\\sum \\xi_i^2$. This time $ f = Xw$ where $w$ is Dx1 and $X$ is NxD.\n",
    "\n",
    "\\begin{align}\n",
    "\\mathcal{L} & = \\frac{1}{N} (y-Xw)^T(y-Xw) \\\\\n",
    "\\frac{\\delta\\mathcal{L}}{\\delta w} & = -\\frac{1}{N} 2\\left(\\frac{\\delta f(X,w)}{\\delta w}\\right)^T(y-Xw) \\\\ \n",
    "& = -\\frac{2}{N} \\left(\\frac{\\delta f(X,w)}{\\delta w}\\right)^T\\xi\n",
    "\\end{align}\n",
    "where $\\xi_i$ is the error term $y_i-f(X,w)$ and \n",
    "$$\n",
    "\\frac{\\delta f(X,w)}{\\delta w} = X\n",
    "$$\n",
    "\n",
    "Finally the weights can be updated as $w_{new} = w_{current} - \\gamma \\frac{\\delta\\mathcal{L}}{\\delta w}$ where $\\gamma$ is a learning rate between 0 and 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N = 1000\n",
    "D = 5\n",
    "X = 5*np.random.randn(N,D)\n",
    "w = np.random.randn(D,1)\n",
    "y = X.dot(w)\n",
    "y_obs = y + np.random.randn(N,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.19670626],\n",
       "       [-0.74645194],\n",
       "       [ 0.93774813],\n",
       "       [-2.62540124],\n",
       "       [ 0.74616483]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000, 5)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5, 1)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000, 5)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(X*w.T).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Helper functions\n",
    "def f(w):\n",
    "    return X.dot(w)\n",
    "\n",
    "def loss_function(e):\n",
    "    L = e.T.dot(e)/N\n",
    "    return L\n",
    "\n",
    "def dL_dw(e,w):\n",
    "    return -2*X.T.dot(e)/N "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent(iter=100,gamma=1e-3):\n",
    "    # get starting conditions\n",
    "    w = np.random.randn(D,1)\n",
    "    params = []\n",
    "    loss = np.zeros((iter,1))\n",
    "    for i in range(iter):\n",
    "        params.append(w)\n",
    "        e = y_obs - f(w) # Really important that you use y_obs and not y (you do not have access to true y)\n",
    "        loss[i] = loss_function(e)\n",
    "\n",
    "        #update parameters\n",
    "        w = w - gamma*dL_dw(e,w)\n",
    "        \n",
    "    return params, loss\n",
    "        \n",
    "params, loss = gradient_descent()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x119a10940>]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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kqZlVM7QxGfg9eVJlAn5S2v9L4AsppTMjYihwIbABcAdwQEqpfKWDTmAZcBUw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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119806240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.18613581],\n",
       "       [-0.74929568],\n",
       "       [ 0.95245495],\n",
       "       [-2.602146  ],\n",
       "       [ 0.73246543]])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.19670626],\n",
       "       [-0.74645194],\n",
       "       [ 0.93774813],\n",
       "       [-2.62540124],\n",
       "       [ 0.74616483]])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = LinearRegression(fit_intercept=False)\n",
    "model.fit(X,y)\n",
    "model.coef_.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.93191854,  0.93774813],\n",
       "       [-2.62216904, -2.62540124],\n",
       "       [ 0.74418434,  0.74616483],\n",
       "       [ 0.64963419,  0.67411002],\n",
       "       [ 1.00760672,  1.0142675 ]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compare parameters side by side\n",
    "np.hstack([params[-1],model.coef_.T])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stochastic Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dL_dw(X,e,w):\n",
    "    return -2*X.T.dot(e)/len(X)\n",
    "\n",
    "def gradient_descent(gamma=1e-3, n_epochs=100, batch_size=20, decay=0.9):\n",
    "    epoch_run = int(len(X)/batch_size)\n",
    "    \n",
    "    # get starting conditions\n",
    "    w = np.random.randn(D,1)\n",
    "    params = []\n",
    "    loss = np.zeros((n_epochs,1))\n",
    "    for i in range(n_epochs):\n",
    "        params.append(w)\n",
    "        \n",
    "        for j in range(epoch_run):\n",
    "            idx = np.random.choice(len(X),batch_size,replace=False)\n",
    "            e = y_obs[idx] - X[idx].dot(w) # Really important that you use y_obs and not y (you do not have access to true y)\n",
    "            #update parameters\n",
    "            w = w - gamma*dL_dw(X[idx],e,w)\n",
    "        loss[i] = e.T.dot(e)/len(e)    \n",
    "        gamma = gamma*decay #decay the learning parameter\n",
    "        \n",
    "    return params, loss\n",
    "        \n",
    "params, loss = gradient_descent()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1197dd278>]"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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JsOGJcePSC0/QaSCE1BqFFw0i6jZkJRr69NHPHz5cX9uxI/39WHbuVIEyZIg+98bRSXWx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\nQghxgqKBEEIIIU5QNBBCCCHEif8fEPh9jWDwqCMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1196e0588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.18387464, -0.19670626],\n",
       "       [-0.74895223, -0.74645194],\n",
       "       [ 0.9476572 ,  0.93774813],\n",
       "       [-2.62055252, -2.62540124],\n",
       "       [ 0.75009766,  0.74616483]])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.hstack([params[-1],model.coef_.T])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  },
  "latex_envs": {
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 0
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}