Statistical parameter fitting
Consider instances x[1], x[2], …, x[M] such that
- The set of values that x can take is known
- Each is sampled from the same distribution
- Each sampled independently of the rest
The task is to find a parameter ? so that the data can be summarized by a probability P(x[j]| ? ).
- The parameters depend on the given family of probability distributions: multinomial, Gaussian, Poisson, etc.
- We will focus on multinomial distributions
- The main ideas generalize to other distribution families