ML Reviews
ML Reviews

    conditional-distribution

    A [[probability-distribution]] related to the [[marginal-distribution]], as the possible values of one variable given others.

    P(x∣y)=P(x,y)P(y)P(x \vert y) = \frac{P(x,y)}{P(y)}

    The law of total probability is given as P(x)=∑yP(x∣y)P(y)P(x) = \sum_y P(x \vert y)P(y), as a re-arranged version of the conditional likelihood. This is related to [[bayes-rule]].

    Compared to marginal distributions, conditional distributions can be much more efficiently factored as [[decision trees]].

    A [[linear-gaussian-model]] is an example of a conditional distribution model.

    bayes-rule
    where $p(y)$ is the [[evidence]], $p(x)$ is the [[prior]], $p(x \vert y)$ is the [[posterior distribution]], and $p(y \vert x)$ is the [[conditional-distribution]] known as the likelihood.
    bayesian-network
    - As an expression, with variable $X_i$, each edge corresponds to the [[conditional-distribution]] likelihood $P(X_i \vert Pa(X_i))$, where $Pa(X_i)$ are the parent nodes of $X_i$, i.e. every decision made prior to arriving at $X_i$.