Divide-and-Conquer Predictive Coding: a structured Bayesian inference algorithm
This work addresses a bottleneck in applying predictive coding to machine learning tasks, offering a biologically plausible method for structured Bayesian inference, though it appears incremental as it builds on existing predictive coding frameworks.
The paper tackles the problem of predictive coding algorithms underperforming in high-dimensional, structured inference tasks compared to other variational methods, and introduces a novel algorithm called divide-and-conquer predictive coding (DCPC) that achieves better numerical performance and accurate inference in previously unaddressed problems.
Unexpected stimuli induce "error" or "surprise" signals in the brain. The theory of predictive coding promises to explain these observations in terms of Bayesian inference by suggesting that the cortex implements variational inference in a probabilistic graphical model. However, when applied to machine learning tasks, this family of algorithms has yet to perform on par with other variational approaches in high-dimensional, structured inference problems. To address this, we introduce a novel predictive coding algorithm for structured generative models, that we call divide-and-conquer predictive coding (DCPC). DCPC differs from other formulations of predictive coding, as it respects the correlation structure of the generative model and provably performs maximum-likelihood updates of model parameters, all without sacrificing biological plausibility. Empirically, DCPC achieves better numerical performance than competing algorithms and provides accurate inference in a number of problems not previously addressed with predictive coding. We provide an open implementation of DCPC in Pyro on Github.