Generative vs Discriminative Classifier

In Generative classifier we have to find joint probability of the instance and its class
P(XY) = P(Y)P(X|Y). Assume some functional form for P(Y) and P(X|Y). Once we get this, we can use Bayes Rule to get P(Y|X). Here for P(Y), we assume some class distribution. And we can empirically find P(X|Y) from the data available.

Discriminative Classifier: we have to estimate class conditional probaility. P(Y|X) = we have assumed some distribution for P(Y|X) and then estimate the parameters from the data.

1. Pros for Generative classifier:
   Thus finding distributions for generative classifier is easier than discriminative classifiers.
   We can generate data.
2. Cons for Generative Classifier:
3. Pros for Discriminative classifier:
   When the data is insufficient, can better estimate the conditional distribution.
   
   It makes no assumption about data in terms of distribution
4. Cons for Discriminative classifier:
   Cannot sample data.

Why should we use generative classifier ? When our only concern is to get P(Y|X) !!

Curse of Dimensionality


Bias-Variance Trade off


Poisson Distribution

The Poisson distribution is a useful discrete distribution which can be used to model the number of occurrences of something per unit time. For example, in networking, packet arrival density is often modeled with the Poisson distribution. That is, if we sit at a computer, count the number of packets arriving in each time interval (say every minute, for 30 minutes) and plot the histogram of how many time intervals had X number of packets, we expect to see something like the Poisson probability mass function.

The Poisson PMF is defined as,...


Beta Distribution
Simplex