Today’s topics. Java Implementing Decision Trees Upcoming More formal treatment of grammars Reading Great Ideas , Chapter 2. A decision tree Selecting a textbook. 3. yes. Oh! Pascal by D. Cooper. 1. A programming focus instead of theory. yes. 4. Algorithmics by D. Harel. 0.

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Decision Trees. Prof. A.L. Yuille. Stat 231. Fall 2004. Duda, Hart & Stork. Chp 81-8.3 . Decision Trees. Decision Trees. Binary Classification Trees. Data can be non-metric, list of binary attributes. 2. Classification Decision Trees. Nonmetric. Data is list of binary attributes.

Decision Trees. Jianping Fan Dept of Computer Science UNC-Charlotte. The problem of Classification. Given a set of training samples and their attribute values (x) and labels (y), try to determine the labels y of new examples. Classifier Training y = f(x) Prediction y given x.

Decision Trees. Example. Example 2. Examples, which one is better?. Good when. Samples are attribute-value pairs Target function has discrete output values Disjunctions required Missing, noisy training data. Construction. Top down construction

Decision Trees. Shalev Ben-David. Definition. Given a function and oracle access to , determine f(x) with minimum number of queries E.g. f is OR on the bits of x – Grover search D(f) is the deterministic query complexity R(f) is the randomized query complexity

Decision Trees. Chapter 08 (part 01) Disclaimer: This PPT is modified based on IOM 530: Intro. to Statistical Learning

Decision Trees. General Learning Task. DEFINE: Set X of Instances (of n- tuples x = < x 1 , ..., x n >) E.g., days decribed by attributes (or features ): Sky, Temp, Humidity, Wind, Water, Forecast Target function y , e.g.:

Decision Trees. The “No Free Lunch” Theorem. Is there any representation that is compact (ie, sub-exponential in n) for all functions? Function = truth table n attributes 2^n rows in table Classification/target column is 2^n long

Decision Trees. Highly used and successful Iteratively split the Data Set into subsets one attribute at a time, using most informative attributes first Continue until you can label each leaf node with a class Attribute Features – discrete/nominal (can extend to continuous features)

Decision Trees. Example: Conducted survey to see what customers were interested in new model car Want to select customers for advertising campaign. training set. Basic Information Gain Computations. Result: I_Gain_Ratio: city>age>car. Result: I_Gain: age > car=city.

Decision Trees. Prof. A.L. Yuille. Stat 231. Fall 2004. Duda, Hart & Stork. Chp 81-8.3. Decision Trees. Decision Trees. Binary Classification Trees. Data can be non-metric, list of binary attributes. 2. Classification Decision Trees. Nonmetric. Data is list of binary attributes.