Reproduce “Sampling on Discrete Spaces with Temporal Point Processes” on OpenResearch

About this paper

Cameron A. Stewart, Maneesh Sahani

Researchers at Gatsby Computational Neuroscience Unit developed a multivariate temporal point process framework for efficient sampling from discrete distributions with downward-closed support. This new sampler consistently achieved 1.4 to 2.0 times higher effective sample size and 1.9 to 3.6 times higher effective sample size per CPU second compared to traditional birth-death samplers in simulations.

Key insights

• A multivariate temporal point process can be rigorously constructed to ensure the event-count vector converges to any target discrete distribution with downward-closed support.
• The sampler inherently exhibits a "discrete momentum" property, where points remain in memory for a fixed duration, effectively suppressing random-walk behavior.
• Birth-death processes are shown to be a degenerate case of this point process framework, arising from the introduction of auxiliary randomness that discards point location information.
• The framework enables the derivation of biologically plausible recurrent stochastic neural network models that naturally incorporate relative refractory periods and can exhibit oscillatory dynamics.

Summary by alphaXiv.