Filtering Variational Objectives
This work addresses the challenge of improving variational inference for sequential data, offering a novel method that enhances training efficiency and model performance in domains like time-series analysis.
The paper tackles the problem of training latent variable models on sequential data by introducing Filtering Variational Objectives (FIVOs), which extend the evidence lower bound (ELBO) to form tighter bounds, resulting in substantial improvements over ELBO training.
When used as a surrogate objective for maximum likelihood estimation in latent variable models, the evidence lower bound (ELBO) produces state-of-the-art results. Inspired by this, we consider the extension of the ELBO to a family of lower bounds defined by a particle filter's estimator of the marginal likelihood, the filtering variational objectives (FIVOs). FIVOs take the same arguments as the ELBO, but can exploit a model's sequential structure to form tighter bounds. We present results that relate the tightness of FIVO's bound to the variance of the particle filter's estimator by considering the generic case of bounds defined as log-transformed likelihood estimators. Experimentally, we show that training with FIVO results in substantial improvements over training the same model architecture with the ELBO on sequential data.