Likelihood

[!def] What is Likelihood?
Likelihood is the probability of a distribution given the data, $p(distribution | data)$
$$
\text{Likelihood of a sequence} = \prod^i P(x_i|x_{<i})
$$
$$
\text{Likelihood for categorical values} = \prod^i P(x_i)^{y_i} (1 - P(x_i))^{(1-y_i)}
$$