In information theory, the cross-entropy from a true probability distribution $P$ to a subjective probability distribution $Q$, denoted as $H(P, Q)$, is defined as the expected surprisal of an observer who uses the subjective probabilities $Q$ when observing data that was actually generated according to the true probabilities $P$. Mathematically, this is expressed as:

$H(P, Q) \stackrel{ extrm{def}}{=} \sum_j - P(j) \log Q(j)$