PEL-CNF: Probabilistic event logic conjunctive normal form for video interpretation

This is a theoretical paper that proves that probabilistic event logic (PEL) is MAP-equivalent to its conjunctive normal form (PEL-CNF). This allows us to address the NP-hard MAP inference for PEL in a principled manner. We first map the confidence-weighted formulas from a PEL knowledge base to PEL-CNF, and then conduct MAP inference for PEL-CNF using stochastic local search. Our MAP inference leverages the spanning-interval data structure for compactly representing and manipulating entire sets of time intervals without enumerating them. For experimental evaluation, we use the specific domain of volleyball videos. Our experiments demonstrate that the MAP inference for PEL-CNF successfully detects and localizes volleyball events in the face of different types of synthetic noise introduced in the ground-truth video annotations.