5 - theano-NN.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Theano\n",
    "\n",
    "Theano is a python library and an optimizing compiler, which allows to define, optimize and compute mathematical expressions effectively using multidimensional arrays.\n",
    "\n",
    "This notebook requires theano (`!pip install theano`) and `gcc` (if you're using windows, it's not that simple).\n",
    "\n",
    "Also, install `hep_ml` (`!pip install hep_ml`) if you haven't done this yet.\n",
    "\n",
    "Theano features:\n",
    "\n",
    "* integration with `NumPy`\n",
    "* effective analytical computation of gradient (can automatically build expressions to compute gradient)\n",
    "* fast and stable optimization (can recognize numerical inaccurate expressions and compute them using more stable algorithms)\n",
    "* transparent usage of GPU\n",
    "* dynamic C++ code generation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import Image\n",
    "import numpy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# next line is a convention\n",
    "import theano.tensor as T\n",
    "import theano"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Symbolic expessions for tensors\n",
    "Theano’s strength is in expressing symbolic calculations involving tensors. There are many types of symbolic expressions for tensors:\n",
    "\n",
    "* scalar\n",
    "* vector\n",
    "* matrix\n",
    "* tensor\n",
    "* ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# create two vectors and one scaler. Those are abstract variables\n",
    "x = T.vector() \n",
    "y = T.vector()\n",
    "alpha = T.scalar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### compute \n",
    "$x + \\alpha y + (\\sum x_i, ... ,\\sum x_i)^T$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# define mathematical expression (you can use any function, which you use for NumPy arrays). \n",
    "z = x + alpha * y + T.sum(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compile defined expression\n",
    "`theano.function`\n",
    "\n",
    "Returns a callable object that will calculate outputs from inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# input variables, output expessions\n",
    "compiled_expr = theano.function([x, y, alpha], z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute compiled expression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x_val = numpy.arange(10)\n",
    "y_val = numpy.arange(10)\n",
    "alpha_val = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 45. ,  46.5,  48. ,  49.5,  51. ,  52.5,  54. ,  55.5,  57. ,  58.5])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "compiled_expr(x_val, y_val, alpha_val)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# create two vectors and two scalars\n",
    "x = T.vector() \n",
    "y = T.vector()\n",
    "alpha = T.scalar()\n",
    "beta = T.scalar()\n",
    "\n",
    "# define values for each variable \n",
    "x_val = numpy.arange(10)\n",
    "y_val = numpy.arange(10)\n",
    "alpha_val = 0.1\n",
    "beta_val = 0.3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* compute $z = (x_1 + y_1^2, x_2 + y_2^2, ...)^T$: define theano function and evaluate it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* compute $||x||$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* compute $(<x, \\alpha y> + <\\beta x, y>)^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Names for variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# define \n",
    "x = T.vector(name='x')\n",
    "y = T.vector(name='y')\n",
    "alpha = T.scalar(name='a')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "z = alpha * x * T.log(y) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `theano.printing.pprint()`\n",
    "Theano provides the functions `theano.printing.pprint()` and `theano.printing.debugprint()` to print a graph to the terminal before or after compilation. `pprint()` is more compact and math-like, `debugprint()` is more verbose. Theano also provides `pydotprint()` that creates an image of the function. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'x'"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theano.pprint(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'((a * x) * log(y))'"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theano.pprint(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "compiled_expr = theano.function(inputs=[x, y, alpha], outputs=[z], name='function')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elemwise{Composite{(log(i0) * i1 * i2)}} [@A] ''   1\n",
      " |y [@B]\n",
      " |InplaceDimShuffle{x} [@C] ''   0\n",
      " | |a [@D]\n",
      " |x [@E]\n"
     ]
    }
   ],
   "source": [
    "theano.printing.debugprint(compiled_expr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The output file is available at graph.png\n"
     ]
    },
    {
     "data": {
      "image/png": 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zt7/9bcBkjF4PBv5iRnTCCSf47QqVMV+esNHnPaHRQ/5hedVVV/npxbxPcOS9ZEBvycFa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\n4Ntz12eXlTLPjtbYYP0ntmevz6IBMmed/bN+skaL7fOlNUY4PjMu7di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El8TSgnXzibOX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\nTkSuQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theano.printing.pydotprint(compiled_expr, outfile=\"graph.png\", var_with_name_simple=True)\n",
    "Image('./graph.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gradient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`T.grad` computes symbolic gradients for one or more variables with respect to some cost."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1D gradient (derivative)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = T.scalar(name='x') \n",
    "function1d = x ** 2 + T.log(x)\n",
    "function1d_derivative = T.grad(function1d, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'(((fill(((x ** TensorConstant{2}) + log(x)), TensorConstant{1.0}) * TensorConstant{2}) * (x ** (TensorConstant{2} - TensorConstant{1}))) + (fill(((x ** TensorConstant{2}) + log(x)), TensorConstant{1.0}) / x))'"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# result of analytical differentiation:\n",
    "theano.pprint(function1d_derivative)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# let's compile it\n",
    "compiled_derivative = theano.function([x], function1d_derivative)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elemwise{Composite{((i0 * i1) + inv(i1))}} [@A] ''   0\n",
      " |TensorConstant{2.0} [@B]\n",
      " |x [@C]\n"
     ]
    }
   ],
   "source": [
    "# optimizations were done during compilation\n",
    "theano.printing.debugprint(compiled_derivative)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10a12e450>]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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jrmXz5RPo+fQS/RT4DnBCHvsoih494Cc/geuvDwP8jzsu6hqJSKFs3BiGEM6cCf/8ZxiB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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109f47110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = numpy.linspace(0.1, 2, 100)\n",
    "plt.plot([compiled_derivative(point) for point in x])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### NDimensional gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = T.vector(name='x') \n",
    "function = T.sum(x * x)\n",
    "function_gradient = T.grad(function, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "compiled_gradient = theano.function([x], function_gradient)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.,  4.,  8.,  0.])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "compiled_gradient([1, 2, 4, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elemwise{add,no_inplace} [@A] ''   0\n",
      " |x [@B]\n",
      " |x [@B]\n"
     ]
    }
   ],
   "source": [
    "theano.printing.debugprint(compiled_gradient)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Shared variables\n",
    "`theano.shared` returns a SharedVariable variable, initialized with a copy or reference of `value`.\n",
    "\n",
    "Variable with Storage that is shared between functions that it appears in. These variables are meant to be created by registered shared constructors, i.e. `shared()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "w = theano.shared(numpy.arange(10, dtype=float), name='weight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "weight [ 0.  1.  2.  3.  4.  5.  6.  7.  8.  9.]\n"
     ]
    }
   ],
   "source": [
    "print w, w.get_value()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = T.vector('x')\n",
    "# dotproduct = theano.function([x], T.sum(x * w))\n",
    "dotproduct_grad = theano.function([x], T.grad(T.sum(x * w), x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dotproduct_grad(numpy.arange(10) * 0.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9.])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dotproduct_grad(numpy.arange(10) * 10.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Compute $||Ax||^2$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(8.0)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = T.vector('x')\n",
    "A = T.matrix('A')\n",
    "z = A.dot(x)\n",
    "normAx = theano.function([x, A], z.dot(z))\n",
    "normAx([0, 2], [[1, 1], [1, 1]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* compile a function which takes an array $x$ with three elements and computes $x_0^3 + \\sin{x_1}*\\cos{x_2}$. Check it by computing at any point"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* compute gradient for previous function w.r.t. x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* compute gradient for $||Ax|| + \\alpha * ||x||$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic regression "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# import function to create toy dataset for classification\n",
    "from sklearn.datasets import make_blobs, make_moons\n",
    "from sklearn.cross_validation import train_test_split \n",
    "from sklearn.metrics import roc_auc_score\n",
    "# logistic function (we introduce shortcut sigmoid)\n",
    "from scipy.special import expit as sigmoid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### generate toy samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n_features = 10 # number of features\n",
    "centers = 2 # number of classes\n",
    "X, y = make_blobs(n_samples=10000, centers=centers, n_features=n_features, random_state=42)\n",
    "trainX, testX, trainY, testY = train_test_split(X, y, train_size=0.5, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logistic regression description:\n",
    "\n",
    "$p_i = \\sigma(\\sum_k X_{ik} w_k)$\n",
    "\n",
    "$\\text{llh}=\\sum_i y_i \\log{p_i} + (1-y_i)\\log{(1 - p_i)}\\qquad$  (here $y \\in \\{0, 1\\}$)\n",
    "\n",
    "$loss = -\\text{llh}, \\qquad loss \\to \\min$\n",
    "\n",
    "## Exercise \n",
    "\n",
    "Write loss function and its gradient using theano (create compiled expressions).\n",
    "\n",
    "**Use** `T.nnet.sigmoid`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# create theano objects for data(they should be shared because we know X, y)\n",
    "X_ = theano.shared(trainX, name='X')\n",
    "y_ = theano.shared(trainY, name='y')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# define vector of weights, we don't know it, that is why:\n",
    "w = T.vector(name='w')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# write expression for probabilities\n",
    "# TODO"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# write expression for loss\n",
    "# loss = ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# compile loss expression, compile gradient expression for loss\n",
    "loss_function = theano.function([w], loss)\n",
    "loss_grad = theano.function([w], theano.grad(loss, w))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "loss_function(numpy.random.random(n_features))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have expessions for loss and its gradient and we need to use some optimization method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.optimize import minimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# minimize loss function using its gradient\n",
    "result = minimize(fun=loss_function, jac=loss_grad, x0=numpy.zeros(n_features))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "w_optimal = result['x']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Now predict output of logistic regression for the test sample and compute AUC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pred = testX.dot(w_optimal)\n",
    "roc_auc_score(testY, pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Neural Network with theano\n",
    "\n",
    "## NN with one hidden layer\n",
    "This is a simple NN description with one hidden layer:\n",
    "\n",
    "Parameters: \n",
    "\n",
    "* $W$, $v$\n",
    "\n",
    "Calculations:\n",
    "\n",
    "* hidden activations: h = $\\sigma$(X_.dot(W))\n",
    "* output = v.dot(h)\n",
    "* $p_{sig}$ = $\\sigma$(output)\n",
    "* $p_{bck} = 1 - p_{sig}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# number of neurons in the hidden layer\n",
    "n_hidden = 10\n",
    "\n",
    "X_ = theano.shared(trainX, name='X')\n",
    "y_ = theano.shared(trainY, name='y')\n",
    "param = T.vector()\n",
    "\n",
    "# scipy.optimize operates with functions that depend on the vector\n",
    "# we pack all weights into one vector, and we need to extract matrix and vector from it\n",
    "W_ = param[:n_features * n_hidden].reshape((n_features, n_hidden))\n",
    "v_ = param[n_features * n_hidden:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise: \n",
    "\n",
    "Write 1-hidden layer NN using theano"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# define loss here\n",
    "loss = ...\n",
    "\n",
    "loss_function = theano.function([param], loss)\n",
    "loss_grad = theano.function([param], theano.grad(loss, param))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# minimize log loss using scipy.minimize\n",
    "result = minimize(loss_function, numpy.random.random(n_features*n_hidden + n_hidden), jac=loss_grad)\n",
    "# Why putting random numbers not zero?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# transform result into matrix and vector\n",
    "optimal_params = result['x']\n",
    "W = optimal_params[:n_features * n_hidden].reshape(n_features, n_hidden)\n",
    "v = optimal_params[n_features * n_hidden:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pred = sigmoid(testX.dot(W))\n",
    "pred = pred.dot(v)\n",
    "roc_auc_score(testY, pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## NN with two hidden layers\n",
    "first let's take another dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X, y = make_moons(n_samples=20000, noise=0.1)\n",
    "trainX, testX, trainY, testY = train_test_split(X, y, train_size=0.5, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], c=y, alpha=0.05, linewidths=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_ = theano.shared(trainX, name='X')\n",
    "y_ = theano.shared(trainY, name='y')\n",
    "param = T.vector()\n",
    "\n",
    "n_hidden_1 = 10\n",
    "n_hidden_2 = 6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise\n",
    "\n",
    "Write 2 hidden layers NN (use code from 1-hidden layer NN)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# TODO"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define special function for NNs\n",
    "\n",
    "This function simplifies experiments with functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def fit_predict_NN(trainX, trainY, testX, activate_functions, hidden_layers):\n",
    "    X_ = theano.shared(trainX, name='X')\n",
    "    y_ = theano.shared(trainY, name='y')\n",
    "    param = T.vector()\n",
    "    dim = X.shape[1]\n",
    "    \n",
    "    def activation(data_, parameter):\n",
    "        n_previous = 0\n",
    "        dim_previous = dim\n",
    "        h = data_\n",
    "        for n_hidden, func in zip(hidden_layers, activate_functions):\n",
    "            N = dim_previous * n_hidden\n",
    "            W_ = parameter[n_previous:n_previous + N].reshape((dim_previous, n_hidden))\n",
    "            h = func(h.dot(W_))\n",
    "            dim_previous = n_hidden\n",
    "            n_previous += N\n",
    "\n",
    "        # output     \n",
    "        v_ = parameter[n_previous:]\n",
    "        output = h.dot(v_)\n",
    "        n_previous = n_previous + dim_previous\n",
    "        \n",
    "        return T.nnet.sigmoid(output), n_previous\n",
    "\n",
    "    p_sig = activation(X_, param)[0]\n",
    "    p_bck = 1 - p_sig\n",
    "    llh_ = y_.dot(T.log(p_sig)) + (1 - y_).dot(T.log(p_bck))\n",
    "    loss = -llh_\n",
    "    \n",
    "    # optimize\n",
    "    loss_function = theano.function([param], loss)\n",
    "    loss_grad = theano.function([param], theano.grad(loss, param))\n",
    "    result = minimize(loss_function, jac=loss_grad, x0=numpy.random.normal(size=activation(X_, param)[1]))\n",
    "    optimal_params = result['x']\n",
    "    \n",
    "    # predict data\n",
    "    data = T.matrix()\n",
    "    compiled_activation = theano.function([data, param], activation(data, param)[0])\n",
    "    \n",
    "    return compiled_activation(testX, optimal_params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# generate another dataset with more noise\n",
    "X, y = make_moons(n_samples=1000, noise=0.3)\n",
    "\n",
    "trainX, testX, trainY, testY = train_test_split(X, y, train_size=0.5)\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y, alpha=0.5, linewidths=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pred = fit_predict_NN(trainX, trainY, testX, [T.nnet.sigmoid] * 3, [20, 10, 5])\n",
    "roc_auc_score(testY, pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Popular activation functions\n",
    "\n",
    "* **Sigmoid**:\n",
    "\n",
    "    $f(x) = \\frac{1}  {1+e^{-x}}$\n",
    "\n",
    "\n",
    "* **ReLU - rectifier linear unit**\n",
    "\n",
    "    In the context of artificial neural networks, the rectifier is an activation function defined as\n",
    "\n",
    "    $f(x) = \\max(0, x)$\n",
    "\n",
    "    where x is the input to a neuron. This activation function has been argued to be more biologically plausible than the widely used logistic sigmoid (which is inspired by probability theory; see logistic regression) and its more practical counterpart, the hyperbolic tangent. The rectifier is the most popular activation function for deep neural networks.\n",
    "\n",
    "    A unit employing the rectifier is also called a rectified linear unit (ReLU).\n",
    "\n",
    "\n",
    "* **Softplus**\n",
    "    A smooth approximation to the rectifier is the analytic function\n",
    "\n",
    "    $f(x) = \\ln(1 + e^x)$\n",
    "\n",
    "    which is called the softplus function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise: \n",
    "\n",
    "Compare different intermediate activation functions:\n",
    "\n",
    "* sigmoid (which we used, `T.nnet.sigmoid`)\n",
    "* leaky ReLU (defined below)\n",
    "* softplus (`T.nnet.softplus`)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def LeakyReLU(x):\n",
    "    return T.switch(x > 0, x, 0.5 * x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# TODO"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multiclassification  Problem\n",
    "\n",
    "In this case we need use `softmax` activation function for the last layer to get probabilities.\n",
    "\n",
    "\n",
    " * Exercise (optional): write multiclassification NN\n",
    "\n",
    "## Neural Net interface in `hep_ml`\n",
    "\n",
    "The only thing needed is to write activation function using `theano`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X, y = make_moons(n_samples=2000, noise=0.25, random_state=42)\n",
    "trainX, testX, trainY, testY = train_test_split(X, y, train_size=0.5, random_state=42)\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y, alpha=0.5, linewidths=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import hep_ml\n",
    "from hep_ml import nnet\n",
    "from hep_ml.nnet import AbstractNeuralNetworkClassifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class SimpleNeuralNetwork(AbstractNeuralNetworkClassifier):\n",
    "    def prepare(self):\n",
    "        # getting number of layers in input, hidden, output layers\n",
    "        # note that we support only one hidden layer here\n",
    "        n1, n2, n3 = self.layers_\n",
    "        \n",
    "        # creating parameters of neural network\n",
    "        W1 = self._create_matrix_parameter('W1', n1, n2)\n",
    "        W2 = self._create_matrix_parameter('W2', n2, n3)\n",
    "        \n",
    "        # defining activation function\n",
    "        def activation(input):\n",
    "            first = T.nnet.sigmoid(T.dot(input, W1))\n",
    "            return T.dot(first, W2)\n",
    "\n",
    "        return activation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "nnet_simple = SimpleNeuralNetwork()\n",
    "nnet_simple.fit(trainX, trainY)\n",
    "\n",
    "print roc_auc_score(testY, nnet_simple.predict_proba(testX)[:, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Rewrite `SimpleNeuralNetwork` to support arbitrary number of layers \n",
    "\n",
    "Here is you don't need to add `b` parameter, this interface does it and includes additional column in `X`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class MyNeuralNetwork(AbstractNeuralNetworkClassifier):\n",
    "    def prepare(self):\n",
    "        # TODO\n",
    "        \n",
    "        def activation(input):\n",
    "            # TODO\n",
    "\n",
    "        return activation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "nnet_my = MyNeuralNetwork(layers=[15, 10, 5])\n",
    "nnet_my.fit(trainX, trainY)\n",
    "\n",
    "print roc_auc_score(testY, nnet_my.predict_proba(testX)[:, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Run the same code, results are very different (NN strongly depends on the initial parameters)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "nnet_my = MyNeuralNetwork(layers=[15, 10, 5])\n",
    "nnet_my.fit(trainX, trainY)\n",
    "print roc_auc_score(testY, nnet_my.predict_proba(testX)[:, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## NNs available in `hep_ml`\n",
    "library has some examples of neural networks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from hep_ml.nnet import PairwiseNeuralNetwork, RBFNeuralNetwork, MLPClassifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "for models in [PairwiseNeuralNetwork(random_state=42), RBFNeuralNetwork(random_state=42), MLPClassifier(random_state=42)]:\n",
    "    models.fit(trainX, trainY)\n",
    "    pred = models.predict_proba(testX)[:, 1]\n",
    "    print roc_auc_score(testY, pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.ensemble import RandomForestClassifier, GradientBoostingClassifier\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "\n",
    "knn_clf = KNeighborsClassifier(n_neighbors=15)\n",
    "knn_clf.fit(trainX, trainY)\n",
    "print 'KNN', roc_auc_score(testY, knn_clf.predict_proba(testX)[:, 1])\n",
    "\n",
    "log_clf = LogisticRegression(C=100)\n",
    "log_clf.fit(trainX, trainY)\n",
    "print 'logistic regression', roc_auc_score(testY, log_clf.predict_proba(testX)[:, 1])\n",
    "\n",
    "rf_clf = RandomForestClassifier(n_estimators=100, max_depth=20)\n",
    "rf_clf.fit(trainX, trainY)\n",
    "print 'random forest', roc_auc_score(testY, rf_clf.predict_proba(testX)[:, 1])\n",
    "\n",
    "gb_clf = GradientBoostingClassifier(n_estimators=200, max_depth=5, learning_rate=0.1)\n",
    "gb_clf.fit(trainX, trainY)\n",
    "print 'GB', roc_auc_score(testY, gb_clf.predict_proba(testX)[:, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bagging over NN - using sklearn's meta algorithms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.ensemble import AdaBoostClassifier, BaggingClassifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "base = RBFNeuralNetwork()\n",
    "meta_ada = AdaBoostClassifier(base_estimator=base, n_estimators=10, learning_rate=0.05, random_state=42)\n",
    "meta_ada.fit(trainX, trainY)\n",
    "\n",
    "print roc_auc_score(testY, meta_ada.predict_proba(testX)[:, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "base = RBFNeuralNetwork()\n",
    "meta_bagging = BaggingClassifier(base_estimator=base, n_estimators=50, max_samples=0.7, random_state=42)\n",
    "meta_bagging.fit(trainX, trainY)\n",
    "\n",
    "print roc_auc_score(testY, meta_bagging.predict_proba(testX)[:, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Ok! This really works for simple datasets! Maybe try this for some other data? **"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# NN in theanets\n",
    "\n",
    "This also requires `theanets`and `rep` (latest shall be installed without dependencies, otherwise it is likely to downgrade some of libraries)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from rep.estimators import TheanetsClassifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "knn_clf = TheanetsClassifier(layers=[20, 10, 5], trainers=[{'algo': 'adadelta', 'learning_rate': 0.05}])\n",
    "knn_clf.fit(trainX, trainY)\n",
    "\n",
    "print 'Theanets', roc_auc_score(testY, knn_clf.predict_proba(testX)[:, 1])"
   ]
  }
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