ece 471/571 – lecture 2 bayesian decision theory 08/25/15
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ECE471/571, Hairong Qi 2
Different Approaches - More Detail
Pattern Classification
Statistical Approach Non-Statistical Approach
Supervised Unsupervised
Basic concepts: Distance Agglomerative method
Basic concepts: Baysian decision rule (MPP, LR, Discri.)
Parametric learning (ML, BL)
Non-Parametric learning (kNN)
NN (Perceptron, BP)
k-means
Winner-take-all
Kohonen maps
Dimensionality Reduction Fisher’s linear discriminant K-L transform (PCA)
Performance Evaluation ROC curve TP, TN, FN, FP
Stochastic Methods local optimization (GD) global optimization (SA, GA)
3
Bayes formula (Bayes rule)
a-posteriori probability(posterior probability)
a-priori probability(prior probability)
Conditional probability density(pdf – probability density function)(likelihood)
normalization constant(evidence)
From domain knowledge
4
pdf examples
Gaussian distribution Bell curve Normal distribution
Uniform distributionRayleigh distribution
7
Decision regions
The effect of any decision rule is to partition the feature space into c decision regions
9
The conditional risk
Given x, the conditional risk of taking action i is:
ij is the loss when decide x belongs to class i while it should be j
ij
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Recap
Bayes decision rule maximum a-posteriori probabilityConditional risk likelihood ratioDecision regions How to calculate the overall probability of error
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