1-DL-intro-preamble.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Introduction into Deep Learning\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "### Andrey Ustyuzhanin<sup>1,2</sup>\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "###### ICCUB School, 2016-10, Institute of Cosmos sciences, Barcelona\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "#### <sup>1</sup> Yandex School of Data Analysis,\n",
    "#### <sup>2</sup> Higher School of Economics\n",
    "<img src=\"imgs/YSDA_logo.png\" height=20>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## whoami, Yandex\n",
    "\n",
    "- A Dutch company (according to NASDAQ)\n",
    "- The leading web search engine in Russia\n",
    "- Image search\n",
    "- Speech recognition\n",
    "- Car traffic prediction\n",
    "- Mail and spam filtering\n",
    "- Natural language translation\n",
    "- Yandex Data Factory - data science for business\n",
    "- Yandex School of Data Analysis (YSDA)\n",
    "\n",
    "<!-- img src=\"http://www.marekrei.com/blog/wp-content/uploads/2016/01/CYh2GMnWkAELDTL.jpg\" -->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## whoami, YSDA\n",
    "\n",
    "- Education:\n",
    "    - Curricula in Data & Computer Science\n",
    "    - Free tuition\n",
    "    - No employment obligations on part of the students (yet many go to Yandex)\n",
    "    - 500+ students graduated since 2007\n",
    "- Research\n",
    "    - Organizes Machine Learning Conference\n",
    "    - Interest in interdisciplinary research (eScience)\n",
    "    - A full member of LHCb and SHiP"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Goals\n",
    "\n",
    "- understand Deep Learning landscape\n",
    "- understand basics, terminology\n",
    "- understand toolboxes/frameworks\n",
    "- get hands-on experience with some problems\n",
    "- know where to look for more"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Why deep learning\n",
    "\n",
    "  - image recognition\n",
    "  - text recognition\n",
    "  - voice recognition\n",
    "  - Go\n",
    "  - ...(you name it)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Physics examples\n",
    "\n",
    "- Higgs boson exotic decay (ATLAS, simulated dataset)\n",
    "- Jet tagging (CMS)\n",
    "- muon track identification (CRAYFIS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Not so long time ago, 1965\n",
    "<img src=https://devblogs.nvidia.com/parallelforall/wp-content/uploads/2015/12/GMDH-network.png>\n",
    "<small>The architecture of the first known deep network which was trained by Alexey Grigorevich Ivakhnenko in 1965. The feature selection steps after every layer lead to an ever-narrowing architecture which terminates when no further improvement can be achieved by the addition of another layer. Image of Prof. Alexey Ivakhnenko courtesy of Wikipedia.\n",
    "</small>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Short history, continued\n",
    "\n",
    "- The earliest convolutional networks were used by Fukushima, 1979\n",
    "- Backpropagation in the modern form was derived first by Linnainmaa, 1970\n",
    "- Rumelhart, Hinton, and Williams, 1985 backpropagation in neural networks could yield interesting representations\n",
    "- LeCunn, 1989 convolutional networks + backpropagation = LeNet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/https://www.youtube.com/watch?v=FwFduRA_L6Q&feature=youtu.be\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7fc0642ec690>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo(\"https://www.youtube.com/watch?v=FwFduRA_L6Q&feature=youtu.be\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## a few more milestones\n",
    "\n",
    "- Schmidhuber 1992, pretraining approaches for RNN\n",
    "- Schmidhuber and Hochreiter in 1997, LSTM (Long-Short Term Memory)\n",
    "- 2011, 2012 Ciresan et al, won character recognition, traffic sign, medical imaging competitions with convolutional architecture\n",
    "- Krizhevsky, Sutskever, Hinton, 2012, CNN + ReLU + dropout = won ImageNet competition (AlexNet)\n",
    "- Google, Facebook, Microsoft made major acquisitions in 2012-2014 of deep learning startups"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "## References\n",
    "\n",
    "- https://devblogs.nvidia.com/parallelforall/deep-learning-nutshell-history-training/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Basic concepts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Logistic regression\n",
    "\n",
    "### $p_i = \\sigma(\\sum_k X_{ik} w_k) + b$\n",
    "\n",
    "### $\\text{LogLikelihood}=\\sum_i y_i \\log{p_i} + (1-y_i)\\log{(1 - p_i)}\\qquad y \\in \\{0, 1\\}$\n",
    "\n",
    "### $Loss = -\\text{LogLikelihood}, \\qquad Loss \\to \\min$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Artificial neuron, unit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img  src=\"imgs/Perceptron.png\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Activation function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "hide_input": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlsAAAHfCAYAAABnDB0iAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f4be6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pylab as plt\n",
    "import numpy as np\n",
    "x = np.linspace(-3, 3, 100)\n",
    "plt.figure(figsize=(10,8))\n",
    "plt.plot(x, 1/(1+np.exp(-x)), lw=4, label=\"sigmoid\")\n",
    "plt.plot(x, np.tanh(x), lw=4, label=\"tanh\")\n",
    "plt.plot(x, np.maximum(0, x), lw=4, label=\"ReLU\")\n",
    "plt.plot(x, np.log(1+np.exp(x)), lw=4, label=\"softplus\")\n",
    "plt.hlines(0, xmin=x[0], xmax=x[-1])\n",
    "plt.hlines(1, xmin=x[0], xmax=x[-1], linestyles='--')\n",
    "\n",
    "plt.legend(loc=\"upper left\", fontsize=16);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "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",
    "    (argued to be more biologically plausible than the widely used logistic sigmoid (which is inspired by probability theory; see logistic regression)). The most popular activation function for deep neural networks.\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": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Layer\n",
    "\n",
    "Layer - a building block for Neural Networks :\n",
    "- \"Dense layer\": $f(x) = Wx+b$\n",
    "- \"Nonlinearity layer\": $f(x) = \\sigma(x)$, where $\\sigma$ could be any of activation functions\n",
    "- Input layer, output layer\n",
    "- A few more we gonna cover later\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<img  src=\"imgs/MLP.png\" width=\"60%\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Backpropagation (aka backprop)\n",
    "\n",
    "method for finding the gradient of the error with respect to weights over a neural network. The gradient signifies how the error of the network changes with changes to the network’s weights."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img  src=\"imgs/backprop-step.png\" width=60%/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<img  src=\"imgs/backprop.png\" width=60%/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Optimizers\n",
    "\n",
    "Algorithms for updating network weights to minimize errors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Gradient descent\n",
    "\n",
    "repeat until convergence:\n",
    "\n",
    "$$X_i = X_{i-1} - \\alpha \\frac{\\partial f}{\\partial x}$$\n",
    "<img src=\"imgs/gradient-descent.png\">\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Other kinds of optimizers\n",
    "\n",
    "- Stochastic gradient descent:\n",
    "    - calculate error using subsample of training set\n",
    "- Stochastic gradient descent with momentum: \n",
    "    - move towards \"overall gradient direction\", Not just current gradient\n",
    "- AdaGrad:\n",
    "    - decrease learning rate individually for each parameter in proportion to sum of it's gradients so far.\n",
    "- RMSProp:\n",
    "    - make sure all gradient steps have approximately same magnitude (by keeping moving average of magnitude)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<img  src=\"imgs/optimizers-stochastic.gif\" width=\"50%\"/>\n",
    "\n",
    "<small> Behavior of different methods to accelerate gradient descent</small>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Theoretical Motivations for depth"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">Much has been studied about the depth of neural nets. Is has been proven mathematically[1] and empirically that convolutional neural network benefit from depth! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[1] - On the Expressive Power of Deep Learning: A Tensor Analysis - Cohen, et al 2015"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "´"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}