This is my guess for the number of parameters (in the covariance matrix alone) at 38:16: Full - p^2 (There are p*p distinct elements) Diagonal - p (There are only p distinct elements along diagonal, all else is 0) Spehrical - 1 (Same as diagonal but equal variance in all dimensions, so only one number to compute) If the model is separate, multiply the number above by 2, otherwise 1. Add 2p to account for the mean vectors as well. (There are p distinct means to calculate for each of the two classes)
Thanks for posting - very helpful video. I did get a bit confused with some of the notation. Looking at the slide titled estimating gaussian parameters (25:49) - the covariance matrix we're estimating is indexing over Ck which is the subset of the design matrix for which Y=k? are X and mu_k both matrixes or is mu_k a vector?
3 года назад
Thanks. Let me see... x_i is a vector (sample number i). mu_k is a vector (average over all samples belonging to class k, so with Y=k). Sigma_k is a matrix (covariance matrix over all samples belonging to class k). I usually use lowercase bold for vectors and uppercase bold for matrices.
