index.md (2667B)
1 +++ 2 title = 'Classification 2' 3 template = 'page-math.html' 4 +++ 5 # Classification 2 6 uncertainty is everywhere. probabilistic models look at learning as process of reducing uncertainty. 7 8 probability can be for single variables, but also conditional/posterior — how existing beliefs change in light of new evidence 9 10 ## Naive Bayes classifier 11 12 given a set of classes, use Bayes rule to get posterior probabilities that object with features belongs to class. 13 14 the class with highest posterior probability is most likely class. 15 naive — assuming that elements in feature vector are conditionally independent 16 17 $P(C_{i} | X) = \frac{P(X | C_{i}) \times P(C_{i})}{P(X)}$ 18 19 ## Hidden Markov Model Classifier 20 works on a set of temporal data (when time is important) 21 each clock tick, the system moves to new state (can be the previous one) 22 we do not know these states (hidden), but we see observations 23 steps: 24 25 - Train by calculating: 26 - probability that person is in state x 27 - transition probability P(xj | xi) 28 - observation probability P(yi | xi) 29 - Use HMM as classifier 30 - given observation y, use Bayes to calculate P(xi | y) 31 - class with highest P wins 32 33 ## Unsupervised learning 34 35 do not have training sets, explore data and search for naturally occurring patterns and clusters 36 37 once clusters are found we make decisions 38 39 two inputs cluster if their vectors are similar (they are close to each other in feature space) 40 41  42 43 ## Evaluating classifiers 44 45 predictive accuracy — proportion of new, unseen instances that classifies correctly 46 47 classification error — correctly classified or not 48 error rate — # of classification errors / # of classifications attempted 49 50 true positives/negatives VS false positives/negatives — false negatives can be most dangerous! 51 52 true positive rate (hit rate) — proportion of positive instances that are correctly classified as positive (TP/(TP+FN)) 53 54 false positive rate — negative instances that are erroneously classified as positive (FP/(FP+TN)) 55 56 accuracy — percent of correct classifications 57 58 confusion matrix gives info on how frequently instances were correctly/incorrectly classified. the diagonal is what’s important. 59 60 when writing a report, it’s best to explicitly give the confusion matrix 61  62 63 receiver operating characteristics (ROC) graphs 64 useful for organising classifiers and visualising their performance 65 depict tradeoff between hit rates and false alarm rates over noisy channel 66 67 