1 Machine Learning 10-601 Tom M. Mitchell Machine Learning Department Carnegie Mellon University September 13, 2011 Today: • What is machine learning? • Decision tree learning • Course logistics Readings: • “The Discipline of ML” • Mitchell, Chapter 3 • Bishop, Chapter 14.4 Machine Learning: Study of algorithms that • improve their performance P • at some task T • with experience E well-defined learning task: <P,T,E>2 Learning to Predict Emergency C-Sections 9714 patient records, each with 215 features [Sims et al., 2000] Learning to detect objects in images Example training images for each orientation (Prof. H. Schneiderman)3 Learning to classify text documents Company home page vs Personal home page vs University home page vs … Reading a noun (vs verb) [Rustandi et al., 2005]4 Machine Learning - Practice Object recognition Mining Databases Speech Recognition Control learning • Supervised learning • Bayesian networks • Hidden Markov models • Unsupervised clustering • Reinforcement learning • .... Text analysis Machine Learning - Theory PAC Learning Theory # examples (m) representational complexity (H) error rate (ε) failure probability (δ) Other theories for • Reinforcement skill learning • Semi-supervised learning • Active student querying • … … also relating: • # of mistakes during learning • learnerʼs query strategy • convergence rate • asymptotic performance • bias, variance (supervised concept learning)5 Animal learning (Cognitive science, Psychology, Neuroscience) Machine learning Statistics Computer science Adaptive Control Theory Evolution Economics and Organizational Behavior Machine Learning in Computer Science • Machine learning already the preferred approach to – Speech recognition, Natural language processing – Computer vision – Medical outcomes analysis – Robot control – … • This ML niche is growing (why?) All software apps. ML apps.6 • Machine learning already the preferred approach to – Speech recognition, Natural language processing – Computer vision – Medical outcomes analysis – Robot control – … • This ML niche is growing – Improved machine learning algorithms – Increased data capture, networking, new sensors – Software too complex to write by hand – Demand for self-customization to user, environment All software apps. ML apps. Machine Learning in Computer Science Function Approximation and Decision tree learning7 Function approximation Problem Setting: • Set of possible instances X!• Unknown target function f : XàY!• Set of function hypotheses H={ h | h : XàY }!Input: • Training examples {<x(i),y(i)>} of unknown target function f !Output: • Hypothesis h ∈ H that best approximates target function f!superscript: ith training example!Each internal node: test one discrete-valued attribute Xi Each branch from a node: selects one value for Xi Each leaf node: predict Y (or P(Y|X ∈ leaf)) A Decision tree for F: <Outlook, Humidity, Wind, Temp> à PlayTennis?8 Problem Setting: • Set of possible instances X – each instance x in X is a feature vector – e.g., <Humidity=low, Wind=weak, Outlook=rain, Temp=hot> • Unknown target function f : XàY!– Y is discrete valued • Set of function hypotheses H={ h | h : XàY }!– each hypothesis h is a decision tree – trees sorts x to leaf, which assigns y Decision Tree Learning Decision Tree Learning Problem Setting: • Set of possible instances X – each instance x in X is a feature vector x = < x1, x2 … xn> • Unknown target function f : XàY!– Y is discrete valued • Set of function hypotheses H={ h | h : XàY }!– each hypothesis h is a decision tree Input: • Training examples {<x(i),y(i)>} of unknown target function f!Output: • Hypothesis h ∈ H that best approximates target function f!9 Decision Trees Suppose X = <X1,… Xn> where Xi are boolean variables How would you represent Y = X2 X5 ? Y = X2 ∨ X5 !!!!!How would you represent X2 X5 ∨ X3X4(¬X1) !!! !10 node = Root [ID3, C4.5, Quinlan] Sample Entropy11 Entropy Entropy H(X) of a random variable X H(X) is the expected number of bits needed to encode a randomly drawn value of X (under most efficient code) Why? Information theory: • Most efficient code assigns -log2P(X=i) bits to encode the message X=i • So, expected number of bits to code one random X is: # of possible values for X!Entropy Entropy H(X) of a random variable X Specific conditional entropy H(X|Y=v) of X given Y=v : Conditional entropy H(X|Y) of X given Y : Mututal information (aka Information Gain) of X and Y :12 Information Gain is the mutual information between input attribute A and target variable Y Information Gain is the expected reduction in entropy of target variable Y for data sample S, due to sorting on variable A1314 Decision Tree Learning Applet • http://www.cs.ualberta.ca/%7Eaixplore/learning/DecisionTrees/Applet/DecisionTreeApplet.html Which Tree Should We Output? • ID3 performs heuristic search through space of decision trees • It stops at smallest acceptable tree. Why? Occamʼs razor: prefer the simplest hypothesis that fits the data15 Why Prefer Short Hypotheses? (Occamʼs Razor) Arguments in favor: Arguments opposed: Why Prefer Short Hypotheses? (Occamʼs Razor) Argument in favor: • Fewer short hypotheses than long ones à a short hypothesis that fits the data is less likely to be a statistical coincidence à highly probable that a sufficiently complex hypothesis will fit the data Argument opposed: • Also fewer hypotheses with prime number of nodes and attributes beginning with “Z” • What’s so special about “short” hypotheses?16 Overfitting Consider a hypothesis h and its • Error rate over training data: • True error rate over all data: We say h overfits the training data if Amount of overfitting =1718 Split data into training and validation set!Create tree that classifies training set correctly!1920 What you should know: • Well posed function approximation problems: – Instance space, X – Sample of labeled training data { <x(i), y(i)>} – Hypothesis space, H = { f: XàY } • Learning is a search/optimization
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