Likelihood

What is Likelihood?

Likelihood is the probability of a distribution given the data, $p (d i s t r i b u t i o n | d a t a)$

Likelihood of a sequence = \prod^{i} P (x_{i} | x_{< i})

Likelihood for categorical values = \prod^{i} P (x_{i})^{y_{i}} (1 - P (x_{i}))^{(1 - y_{i})}

Maximizing likelihood = minimizing Cross Entropy (negative log-likelihood). Contrast Probability vs. Likelihood.

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