{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "UFF logo\n", "\n", "\n", "IC logo\n", "\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Machine Learning\n", "# 1. Introduction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### [Luis Martí](http://lmarti.com)\n", "#### [Instituto de Computação](http://www.ic.uff)\n", "#### [Universidade Federal Fluminense](http://www.uff.br)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### About the notebook/slides\n", "\n", "* The slides are _programmed_ as a [Jupyter](http://jupyter.org)/[IPython](https://ipython.org/) notebook.\n", "* **Feel free to try them and experiment on your own by launching the notebooks.**\n", "\n", "* You can run the notebook online: [![Binder](http://mybinder.org/badge.svg)](http://mybinder.org/repo/lmarti/machine-learning)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "If you are using [nbviewer](http://nbviewer.jupyter.org) you can change to slides mode by clicking on the icon:\n", "\n", "
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" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## [Machine learning](https://en.wikipedia.org/wiki/Machine_learning)\n", "\n", "Programs with **parameters** that **automatically** **adjust** by **adapting** to previously seen **data**.\n", "
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" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "* Machine learning can be considered a subfield of **artificial intelligence**...\n", "* ...since those algorithms can be seen as building blocks to make computers learn to behave more intelligently.\n", "* **Generalize** instead of that just storing and retrieving data items like a database system would do." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Machine learning: A modern alchemy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
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  • Data is more abundant -and least expensive- than knowledge.
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  • Professionals from various areas of industry work on a particular philosopher's stone:
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Turn data into knowledge!

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\n", " \n", " Alchemic treatise of [Ramon Llull](https://en.wikipedia.org/wiki/Ramon_Llull).\n", "
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" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "**Intelligent systems** find patterns and discover relations that are latent in large volumes of data.\n", "\n", "Features of intelligent systems:\n", "\n", "* Learning\n", "* Adaptation\n", "* Flexibility and robustness\n", "* Provide explanations\n", "* Discovery/creativity" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Learning\n", "\n", "> Learning is the act of acquiring new, or modifying and reinforcing, existing knowledge, behaviors, skills, values, or preferences and may involve synthesizing different types of information.\n", "\n", "* Construction and study of systems that can learn from data." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Adaptation\n", "* The environment/real world is in constant change.\n", "* The capacity to adapt implies to be able to modify what has been learn in order to cope with those modifications.\n", "* There are many real-world cases:\n", " * Changes in economy\n", " * Wear of mechanic parts of a robot\n", "* In many instances the capacity to adapt is essential to solve the problem $\\rightarrow$ *continuous learning*.\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Flexibility and robustness\n", "* It is required to have a robust and consistent system.\n", " * Similar inputs should generate consistent outputs.\n", "* Self-organization\n", "* 'Classical' approaches based on Boolean algebra and logic have limited flexibility." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Explanations\n", "\n", "* Explanations are necessary to validate and find directions for improvement.\n", "* It is not enough to automate the decision making process.\n", " * In many context explanations are necessary: medicine, credit evaluation, etc.\n", "* They are important if a human expert takes part of the decission loop.\n", "* Machine learning can become a research tool." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Discovery/creativity\n", "\n", "* Capacity of discovering processes and/or relations previously unknown.\n", "* Creation of solution and artifacts.\n", "\n", "Example: Evolving cars with genetic algorithms: http://www.boxcar2d.com/." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "More formally, the machine learning can be described as:\n", "$\\renewcommand{\\vec}[1]{\\mathbf{#1}}$\n", "\n", "* Having a **process** $\\mathbf{F}:\\mathcal{D}\\rightarrow\\mathcal{I}$ that **transforms** a given $\\vec{x}\\in\\mathcal{D}$ in a $\\vec{y}$. \n", "* Construct on a dataset $\\Psi=\\left\\{\\left<\\vec{x}_i,\\vec{y}_i\\right>\\right\\}$ with $i=1,\\ldots,N$.\n", "* Each $\\left<\\vec{x}_i,\\vec{y}_i\\right>$ represents an **input** and its corresponding **expected output**: $\\vec{y}_i=\\mathbf{F}\\left(\\vec{x}_i\\right)$.\n", "* **Optimize** a **model** $\\mathbf{M}(\\vec{x};\\vec{\\theta})$ by adjusting its parameters $\\vec{\\theta}$.\n", " * Make $\\mathbf{M}()$ to be as similar as possible to $\\mathbf{F}()$ by optimizing one or more error (loss) functions.\n", "\n", "*Note*: Generally, $\\mathcal{D}\\subseteq\\mathbb{R}^n$; the definition of $\\mathcal{I}$ depends on the problem." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Classes of machine learning problems \n", "\n", "* *Classification*: $\\mathbf{F}: \\mathcal{D}\\rightarrow\\left\\{1,\\ldots, k\\right\\}$; $\\mathbf{F}(\\cdot)$ defines 'categories' or 'classes' labels.\n", "* *Regression*: $\\mathbf{F}: \\mathbb{R}^n\\rightarrow\\mathbb{R}$; it is necessary to predict a real-valued output instead of categories.\n", "* *Density estimation*: predicit a function $p_\\mathrm{model}: \\mathbb{R}^n\\rightarrow\\mathbb{R}$, where $p_\\mathrm{model}(\\vec{x})$ can be interpreted as a [probability density function](https://en.wikipedia.org/wiki/Probability_density_function) on the set that the examples were drawn from.\n", "* *Clustering*: group a set of objects in such a way that objects in the same group (*cluster*) are more *similar* to each other than to those in other groups (clusters).\n", "* *Synthesis*: generate new examples that are similar to those in the training data.\n", "\n", "> Many more: [times-series](https://en.wikipedia.org/wiki/Time_series) analysis, [anomaly detection](https://en.wikipedia.org/wiki/Anomaly_detection), [imputation](https://en.wikipedia.org/wiki/Imputation), transcription, etc." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Supervised learning\n", "\n", "* Sometimes we can observe the pairs $\\left<\\vec{x}_i,\\vec{y}_i\\right>$:\n", " * We can use the $\\vec{y}_i$'s to provide a *scalar feedback* on how good is the model $\\mathbf{M}(\\vec{x};\\vec{\\theta})$.\n", " * That feed back is known as the *loss function*.\n", " * Modify parameters $\\vec{\\theta}$ as to improve $\\mathbf{M}(\\vec{x};\\vec{\\theta})$ $\\rightarrow$ *learning*." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "An example of a supervised problem (regression)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import random\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "plt.rc('text', usetex=True); plt.rc('font', family='serif')\n", "plt.rc('text.latex', preamble='\\\\usepackage{libertine}\\n\\\\usepackage[utf8]{inputenc}')\n", "\n", "# numpy - pretty matrix \n", "np.set_printoptions(precision=3, threshold=1000, edgeitems=5, linewidth=80, suppress=True)\n", "\n", "import seaborn\n", "seaborn.set(style='whitegrid'); seaborn.set_context('talk')\n", "\n", "%matplotlib inline\n", "%config InlineBackend.figure_format = 'retina'" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# Fixed seed to make the results replicable - remove in real life!\n", "random.seed(42)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "x = np.arange(100)\n", "y_real = np.sin(x/100*2*np.pi)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "y_measured = y_real + (np.random.rand(100) - 0.5)/1 # simulating noise" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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pn/2sKYg4kkCkrQ327x8IopNJ83Nbm6q5S+WJRqM1s3KYyHAyOWNBKbPLg/Jg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\nlVB++cJOHZR6ncGIJElqq0ZLAZf1MkKTxD8AZqbsnyCUl10C3EPdS7f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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 270, "width": 401 } }, "output_type": "display_data" } ], "source": [ "plt.scatter(x,y_measured, marker='.', color='b', label='measured')\n", "plt.plot(x,y_real, color='magenta', label='real')\n", "plt.xlabel('x'); plt.ylabel('y'); plt.legend(frameon=True);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "We can now learn from the dataset $\\Psi=\\left\\{x, y_\\text{measured}\\right\\}$.\n", "* We are going to use a [support vector regressor](https://en.wikipedia.org/wiki/Support_vector_machine) from [`scikit-learn`](http://scikit-learn.org/).\n", "* Don't get too excited, you will have to program things 'by hand'." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Training (adjusting) SVR" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "from sklearn.svm import SVR" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "SVR(C=1.0, cache_size=200, coef0=0.0, degree=3, epsilon=0.1, gamma='auto',\n", " kernel='rbf', max_iter=-1, shrinking=True, tol=0.001, verbose=False)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "clf = SVR() # using default parameters\n", "clf.fit(x.reshape(-1, 1), y_measured)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "We can now see how our SVR models the data." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "y_pred = clf.predict(x.reshape(-1, 1))" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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MJShGCEkTRiqzlILjskO1faLtBLz9yUsnNdKCoKYGWL9eDpJXXLasVnl7/Xqm9SWEXJ0E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\nzt6Ry40HHUsB+4WRt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DRnjlU/Zf58axEEOlbhVhZhxDCMbbJqeeRij2ma/r918sgwjJYs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\nlSSZpskQLQAAAFQUwkie2BPQN0ja6goWz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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 270, "width": 401 } }, "output_type": "display_data" } ], "source": [ "plt.scatter(x, y_measured, marker='.', color='blue', label='measured')\n", "plt.plot(x, y_pred, color='green', label='predicted')\n", "plt.xlabel('x'); plt.ylabel('y'); plt.legend(frameon=True);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We observe for the first time an important negative phenomenon: *overfitting*." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## What if... we don't have a label?\n", "\n", "
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" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## [Unsupervised learning](http://en.wikipedia.org/wiki/Unsupervised_learning)\n", "\n", "In some cases we can just observe a series of items or values, e.g., $\\Psi=\\left\\{\\vec{x}_i\\right\\}$:\n", "* It is necessary to find the *hidden structure* of *unlabeled data*.\n", "* We need a measure of correctness of the model that does not requires an expected outcome.\n", "* Although, at first glance, it may look a bit awkward, this type of problem is very common.\n", " \n", " * Related to anomaly detection, clustering, etc.\n", " \n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### An unsupervised learning example: Clustering\n", "\n", "Let's generate a dataset that is composed by three groups or clusters of elements, $\\vec{x}\\in\\mathbb{R}^2$. " ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "x_1 = np.random.randn(30,2) + (5,5)\n", "x_2 = np.random.randn(30,2) + (10,0)\n", "x_3 = np.random.randn(30,2) + (0,2)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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EbPh34sQJuN1ubN68OeL1lExHMt2+Ham1WvINDg7i0qVLKC0tDX6vqqoqGND1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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 287, "width": 398 } }, "output_type": "display_data" } ], "source": [ "plt.scatter(x_1[:,0], x_1[:,1], c='red', label='Cluster 1')\n", "plt.scatter(x_2[:,0], x_2[:,1], c='blue', label='Cluster 2')\n", "plt.scatter(x_3[:,0], x_3[:,1], c='green', label='Cluster 3')\n", "plt.legend(frameon=True); plt.xlabel('$x_1$'); plt.ylabel('$x_2$'); \n", "plt.title('Three datasets');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Preparing the training dataset." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(90, 2)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = np.concatenate(( x_1, x_2, x_3), axis=0)\n", "x.shape" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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dfWxEw1+mdjeiafiRYS08s6BivujrOIw+QyPHR7SqVV/HAQDdhugGkVdeL2vu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\nug4AIBiIXtD1yutlzT0+p+V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gdKokld8oq892eeX5V6TV313deoWyWbukgX844NnfSN8X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\nflFq9KyzQCreL2rq9alE6oWdEfADAABgW6XFkhY+WmjqZGM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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 269, "width": 382 } }, "output_type": "display_data" } ], "source": [ "plt.scatter(x[:,0], x[:,1], c='m')\n", "plt.title('Training dataset');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "We can now try to learn what clusters are in the dataset. We are going to use the [$k$-means clustering algorithm](https://en.wikipedia.org/wiki/K-means_clustering)." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sklearn.cluster import KMeans" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "KMeans(algorithm='auto', copy_x=True, init='k-means++', max_iter=300,\n", " n_clusters=3, n_init=10, n_jobs=1, precompute_distances='auto',\n", " random_state=None, tol=0.0001, verbose=0)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "clus = KMeans(n_clusters=3)\n", "clus.fit(x)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1\n", " 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n", " 0 0 0 0 0 0 0 0 0 0]\n" ] } ], "source": [ "labels_pred = clus.predict(x)\n", "print(labels_pred)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "scrolled": true, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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ipYQBDCIiShmXywVRFNHd3Q2PxwO/3w+lUgmfz4eMjAyoVCoolUpkZGSgvLw8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\nL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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 287, "width": 536 } }, "output_type": "display_data" } ], "source": [ "cm=iter(plt.cm.Set1(np.linspace(0,1,len(np.unique(labels_pred)))))\n", "for label in np.unique(labels_pred):\n", " plt.scatter(x[labels_pred==label][:,0], x[labels_pred==label][:,1],\n", " c=next(cm), label='Pred. cluster ' +str(label+1))\n", "plt.legend(loc='upper right', bbox_to_anchor=(1.45,1), frameon=True);\n", "plt.xlabel('$x_1$'); plt.ylabel('$x_2$'); plt.title('Clusters predicted');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Needing to set the number of clusters can lead to problems." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clus = KMeans(n_clusters=10)\n", "clus.fit(x)\n", "labels_pred = clus.predict(x)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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y+b9LyaVRiSgwTiEhIqK4UygUeOqpp/Dggw9CoVAELOwpk8mgUCjw4IMP4qmn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\nx7N8w4YNi6wL20Tq6+vnbNiwYZHH41nu8XiWb9myperixYu2H8zWcohVq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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 287, "width": 536 } }, "output_type": "display_data" } ], "source": [ "cm=iter(plt.cm.Set1(np.linspace(0,1,len(np.unique(labels_pred)))))\n", "for label in np.unique(labels_pred):\n", " plt.scatter(x[labels_pred==label][:,0], x[labels_pred==label][:,1],\n", " c=next(cm), label='Pred. cluster ' + str(label+1))\n", "plt.legend(loc='upper right', bbox_to_anchor=(1.45,1), frameon=True)\n", "plt.xlabel('$x_1$'); plt.ylabel('$x_2$'); plt.title('Ten clusters predicted');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## [Semi-supervised learning](http://en.wikipedia.org/wiki/Semi-supervised_learning):\n", "* Obtaining a supervised learning dataset can be expensive.\n", "* Some times it can be complemented with a \"cheaper\" unsupervised learning dataset.\n", "* What if we first learn as much as possible from unlabeled data and then use the labeled dataset. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Reinforcement learning\n", "\n", "* Inspired by behaviorist psychology;\n", "* How to take actions in an environment so as to maximize some notion of cumulative reward?\n", "* Differs from standard supervised learning in that correct input/output pairs are never presented, \n", "* ...nor sub-optimal actions explicitly corrected. \n", "* Involves finding a balance between exploration (of uncharted territory) and exploitation (of current knowledge). " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Problems types vs learning\n", "\n", "
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" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Components of a machine learning problem/solution\n", "\n", "- *A parametrized family of functions* $\\mathbf{M}(\\vec{x};\\theta)$ describing how the learner will behave on new examples.\n", " * What output $\\mathbf{M}(\\vec{x};\\theta)$ will produce given some input $\\vec{x}$?\n", "- *A loss function* $\\ell()$ describing what scalar loss $\\ell(\\hat{\\vec{y}}, \\vec{y})$ is associated with each supervised example $(x, y)$, as a function of the learner's output $\\hat{\\vec{y}} = f_\\theta(\\vec{x})$ and the target output $\\vec{y}$.\n", "- Training consists in choosing the parameters $\\theta$ given some training examples $\\Psi=\\left\\{\\left<\\vec{x}_i,\\vec{y}_i\\right>\\right\\}$ sampled from an unknown data generating distribution $P(X, Y)$." ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "slideshow": { "slide_type": "slide" } }, "source": [ "## Components of a machine learning problem/solution (II)\n", "\n", "- Define a *training criterion*. \n", " - *Ideally*: to minimize the expected loss sampled from the unknown data generating distribution.\n", " - This is not possible because the expectation makes use of the true underlying $P()$...\n", " - ...but we only have access to a finite number of training examples, $\\Psi$. \n", " - A *training criterion* usually includes an empirical average of the loss over the training set,\n", " $$\\min_{\\theta}\\ \\mathbf{E}_{\\Psi}[\\ell(f_\\theta(\\vec{x}), \\vec{y})].$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Components of a machine learning problem/solution (III)\n", "\n", "- Some additional terms (called *regularizers*) can be added to enforce preferences over the choices of $\\vec{\\theta}$.\n", "\n", "$$\\text{min}\\ \\mathbf{E}_{\\Psi}[\\ell(f_\\theta(\\vec{x}), \\vec{y})] + R_{1}(\\theta)+\\cdots+R_{r}(\\theta).$$\n", "\n", "- *An optimization procedure* to approximately minimize the training criterion by modifying $\\theta$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Datasets and evaluation\n", "\n", "* It is clear now that we need a dataset for training (of fitting or optimizing) the model.\n", " * **Training dataset**\n", "* We need another dataset to assess progress and compute the training criterion.\n", " * **Testing dataset**\n", "* As most ML approaches are stochastic and to contrast different approaches we need to have another dataset.\n", " * **Validation dataset**\n", "\n", "This is a cornerstone issue of machine learning and we will be comming back to it." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "
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" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "The machine learning flowchart" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
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\n", " \n", " from Scikit-learn [Choosing the right estimator](http://scikit-learn.org/stable/tutorial/machine_learning_map/index.html).\n", "
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\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# *Nature-inspired* machine learning\n", "\n", "* Cellular automata\n", "* **Neural computation**\n", "* Evolutionary computation\n", "* Swarm intelligence\n", "* Artificial immune systems\n", "* Membrane computing\n", "* Amorphous computing" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Final remarks\n", "* Different classes of machine learning problems:\n", " * Classification\n", " * Regression\n", " * Clustering.\n", "* Different classes of learning scenarions:\n", " * Supervised, \n", " * unsupervised, \n", " * semi-supervised, and \n", " * reinforcement learning.\n", "* Model, dataset, loss function, optimization." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Homework\n", "\n", "* Read Chapter 2 of Hastie, Tibshirani and Friedman (2009) [The Elements of Statistical Learning (2nd edition)](http://statweb.stanford.edu/~tibs/ElemStatLearn/) Springer-Verlag." ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "slideshow": { "slide_type": "skip" } }, "source": [ "
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\n", " \"Creative\n", "
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\n", " This work is licensed under a [Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License](http://creativecommons.org/licenses/by-nc-sa/4.0/).\n", "
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" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "application/json": { "Software versions": [ { "module": "Python", "version": "3.6.1 64bit [GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)]" }, { "module": "IPython", "version": "5.3.0" }, { "module": "OS", "version": "Darwin 16.5.0 x86_64 i386 64bit" }, { "module": "scipy", "version": "0.19.0" }, { "module": "numpy", "version": "1.12.1" }, { "module": "matplotlib", "version": "2.0.0" } ] }, "text/html": [ "
SoftwareVersion
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OSDarwin 16.5.0 x86_64 i386 64bit
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Sat Apr 08 17:01:36 2017 -03
" ], "text/latex": [ "\\begin{tabular}{|l|l|}\\hline\n", "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n", "Python & 3.6.1 64bit [GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)] \\\\ \\hline\n", "IPython & 5.3.0 \\\\ \\hline\n", "OS & Darwin 16.5.0 x86\\_64 i386 64bit \\\\ \\hline\n", "scipy & 0.19.0 \\\\ \\hline\n", "numpy & 1.12.1 \\\\ \\hline\n", "matplotlib & 2.0.0 \\\\ \\hline\n", "\\hline \\multicolumn{2}{|l|}{Sat Apr 08 17:01:36 2017 -03} \\\\ \\hline\n", "\\end{tabular}\n" ], "text/plain": [ "Software versions\n", "Python 3.6.1 64bit [GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)]\n", "IPython 5.3.0\n", "OS Darwin 16.5.0 x86_64 i386 64bit\n", "scipy 0.19.0\n", "numpy 1.12.1\n", "matplotlib 2.0.0\n", "Sat Apr 08 17:01:36 2017 -03" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%load_ext version_information\n", "%version_information scipy, numpy, matplotlib" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# this code is here for cosmetic reasons\n", "from IPython.core.display import HTML\n", "from urllib.request import urlopen\n", "HTML(urlopen('https://raw.githubusercontent.com/lmarti/jupyter_custom/master/custom.include').read().decode('utf-8'))" ] }, { "cell_type": "markdown", "metadata": {}, "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" } }, "nbformat": 4, "nbformat_minor": 1 }