Poisson Classifier for Multiclass Classification. Let X ER be a univariate random variable representing input data. And Y be the random variable representing the output data. In binary classification with logistic regression, the conditional distribution of a binary output Y (assuming no intercept terms for simplicity) is assumed to be: 1 P(Y = 1|X) = exp-(BX) Now consider we are required to multi-class classification where the output Y can take any non-negative integer value 0, 1, 2, ... (for example, the number of daily hits on a web server). A standard model for Y is the Poisson. Recalling the probability mass function of the Poisson distribution, we now assume the conditional distribution of the ouput Y given X as: (BX) P(Y = k|X) = PA -(BX), for k = 0, 1, 2, ... (a) is the above approach for multi-class classification, a generative or discriminative ap- proach ?
(b) Given n training samples (21, yı),..., (In, Yn), how will you estimate the parameter B via MLE.
(c) Given a new sample z, how will you decide which class it belongs to?