COMP 328: Final Review Spring 2010 Nevin L. Zhang Department of Computer Science & Engineering The Hong Kong University of Science & Technology Can be used as cheat sheet

Page 2 Pre-Midterm l Algorithms for supervised learning n Decision trees n Instance-based learning n Naïve Bayes classifiers n Neural networks n Support vector machines l General issues regarding supervised learning n Classification error and confidence interval n Bias-Variance tradeoff n PAC learning theory

Post-Midterm l Clustering n Distance-Based Clustering n Model-Based Clustering l Dimension Reduction n Principal Component Analysis l Reinforcement Learning l Ensemble Learning

Clustering

Distance/Similarity Measures

Distance-Based Clustering l Partitional and Hierarchical clustering

K-Means: Partitional Clustering

l Different initial points might lead to different partitions l Solution: n Multiple runs, n Use evaluation criteria such as SSE to pick the best one

Hierarchical Clustering l Agglomerative and Divisive

Cluster Similarity

Cluster Validation l External indices n Entropy: Average purity of clusters obtained n Mutual Information between class label and cluster label

Cluster Validation l External Measure n Jaccard Index n Rand Index Measure similarity between two relationships: in-same-class & in-same-cluster # pairs in same cluster# pairs in diff cluster # pairs w/ same labelab # pairs w/ diff labelcd

Cluster Validation l Internal Measure n Dunn’s index

Cluster Validation l Internal Measure

Post-Midterm l Clustering n Distance-Based Clustering n Model-Based Clustering l Dimension Reduction n Principal Component Analysis l Reinforcement Learning l Ensemble Learning

Model-Based Clustering l Assume data generated from a mixture model with K components l Estimate parameters of the model from data l Assign objects to clusters based posterior probability: Soft Assignment

Gaussian Mixtures

Learning Gaussian Mixture Models

EM

l l(t): Log likelihood of model after t-th iteration l l(t): increases monotonically with t l But might go to infinite in case of singularity n Solution: place bound on eigen values of covariance matrix l Local maximum n Multiple restart n Use likelihood to pick best model

EM and K-Means l K-Means is hard-assignment EM

Mixture Variable for Discrete Data

Latent Class Model

Learning Latent Class Models Always converges

Post-Midterm l Clustering n Distance-Based Clustering n Model-Based Clustering l Dimension Reduction n Principal Component Analysis l Reinforcement Learning l Ensemble Learning

Dimension Reduction l Necessary because there are data sets with large numbers of attributes that are difficult to learning algorithms to handle.

Principal Component Analysis

PCA Solution

PCA Illustration

Eigenvalues and Projection Error

Post-Midterm l Clustering n Distance-Based Clustering n Model-Based Clustering l Dimension Reduction n Principal Component Analysis l Reinforcement Learning l Ensemble Learning

Reinforcement Learning

Markov Decision Process l A model of how agent interact with its environment

Markov Decision Process

Value Iteration

Reinforcement Learning

Q-Learning

l From Q-function based value iteration l Ideas n In-place/asynchronous value iteration n Approximate expectation using samples n ε-greedy policy (for exploration/exploitation) tradeoff

Time Difference Learning

Sarsa is also time difference learning

Post-Midterm l Clustering n Distance-Based Clustering n Model-Based Clustering l Dimension Reduction n Principal Component Analysis l Reinforcement Learning l Ensemble Learning

Ensemble Learning

Bagging: Reduce Variance

Boosting: Reduce Classification Error

AdaBoost: Exponential Error