Exact Decoding on Latent Variable Conditional Models is NP-Hard

TL;DR

This paper proves that exact decoding in latent variable conditional models is NP-hard and introduces methods for approximate inference that can achieve near-exact results efficiently.

Contribution

The paper establishes the NP-hardness of exact decoding in latent conditional models and proposes new inference algorithms that approximate exact inference.

Findings

Decoding in latent conditional models is NP-hard.

Proposed LDI-Naive and LDI-Bounded methods perform near-exact inference.

Algorithms leverage top-n search and dynamic programming for efficiency.

Abstract

Latent variable conditional models, including the latent conditional random fields as a special case, are popular models for many natural language processing and vision processing tasks. The computational complexity of the exact decoding/inference in latent conditional random fields is unclear. In this paper, we try to clarify the computational complexity of the exact decoding. We analyze the complexity and demonstrate that it is an NP-hard problem even on a sequential labeling setting. Furthermore, we propose the latent-dynamic inference (LDI-Naive) method and its bounded version (LDI-Bounded), which are able to perform exact-inference or almost-exact-inference by using top-$n$ search and dynamic programming.