Linear Discriminant Analysis (LDA) Questions & Accurate answers, VERIFIED.

Linear Discriminant Analysis (LDA) Questions & Accurate answers, VERIFIED. Why do we need another method from logistic regression? - LDA does not suffer from the problem of when the classes are separated, the parameter estimates for the logistic regression are surprisingly unstable. Also if n is small and the distribution of the predictors X is approximately normal in each of the classes, the LDA is more stable. Thirdly, LDA is popular when we have more than two response classes. Prior probability (pi k) - The probability that a given observation is associated with the kth category of the response variable Y If fk(x) is relatively large - there is a high probability that an observation in the kth class has X=x If fk(x) is relatively small - It is very unlikely that an observation in the kth class has X=x posterior probability - It is the probability that the observation belongs to the kth class that an observation X=x belongs to the kth class. Given the predictor value for that observation. The linear discriminant analysis method - approximates the Beyes classifier by plugging estimates for pi k and Uk and o^2 into an equation. LDA estimates pi k using the proportion of the training observations that belong to the kth class The LDA classifier - Results from assuming that the observations within each class come from a normal distribution with a class-specific mean vector and a common variance o^2, and plugging estimates for these parameters into the Beyes' classifier. Multivariate Gaussian Distribution - Assumes that each individual predictor follows a one-dimensional normal distribution, with some correlation between each pair of predictors. In the case of p1 predictors, LDA classifier assumes - That the observation in the kth class are drawn from multivariate Gaussian distribution, where uk is a class-specific mean vector, and E is a covariance matrix that is common to ALL K classes. If the Beyes' decision boundaries and LDA classifier are close - It indicates that LDA is performing well on this data Training error rate - Training error rate will usually be lower than test error rates, which are the real quantity of interest. The higher