Low-Rank Constraints for Fast Inference in Structured Models
This addresses scalability bottlenecks for researchers and practitioners using structured probabilistic models in domains like NLP and multimedia, though it is incremental as it builds on existing matrix-vector product methods.
The paper tackled the high computational and memory complexity in scaling structured models like HMMs and PCFGs by introducing a low-rank constraint to reduce inference time and space requirements, achieving practical speedups while matching accuracy in tasks such as language modeling and video modeling.
Structured distributions, i.e. distributions over combinatorial spaces, are commonly used to learn latent probabilistic representations from observed data. However, scaling these models is bottlenecked by the high computational and memory complexity with respect to the size of the latent representations. Common models such as Hidden Markov Models (HMMs) and Probabilistic Context-Free Grammars (PCFGs) require time and space quadratic and cubic in the number of hidden states respectively. This work demonstrates a simple approach to reduce the computational and memory complexity of a large class of structured models. We show that by viewing the central inference step as a matrix-vector product and using a low-rank constraint, we can trade off model expressivity and speed via the rank. Experiments with neural parameterized structured models for language modeling, polyphonic music modeling, unsupervised grammar induction, and video modeling show that our approach matches the accuracy of standard models at large state spaces while providing practical speedups.