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Poisson Classifier for Multiclass Classification. Let X ∈ R 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: P(Y = 1|X) = 1 / (1 + exp(-βX)) Now consider we are required to perform 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 distribution. Recalling the probability mass function of the Poisson distribution, we now assume the conditional distribution of the output Y given X as: P(Y = k|X) = (βX)^k e^{-βX} / k!, for k = 0, 1, 2, ... Is the above approach for multi-class classification generative or discriminative? Given n training samples (x1, y1), (x2, y2), ..., (xn, yn), how will you estimate the parameter β via MLE? Given a new sample x, how will you decide which class it belongs to?

          Poisson Classifier for Multiclass Classification. Let X ∈ R 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:
P(Y = 1|X) = 1 / (1 + exp(-βX))

Now consider we are required to perform 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 distribution. Recalling the probability mass function of the Poisson distribution, we now assume the conditional distribution of the output Y given X as:
P(Y = k|X) = (βX)^k e^{-βX} / k!,  for k = 0, 1, 2, ...

Is the above approach for multi-class classification generative or discriminative? Given n training samples (x1, y1), (x2, y2), ..., (xn, yn), how will you estimate the parameter β via MLE? Given a new sample x, how will you decide which class it belongs to?

poisson classifier for multiclass classification let x r be uivariate random variable representing input data and y be the random variable representing the output data binary classification 74544

Added by Lisa M.

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