Neural likelihood surrogates for parameter inference via log-density PDE

Kasper Bågmark, Filip Rydin

Keywords: Parameter inference, Bayesian filtering, Deep backward stochastic differential equations, Likelihood surrogate, Log-density partial differential equations

TL;DR: Two-stage training learns a log-density filter and a neural normalizer surrogate, enabling fast parameter inference in discretely observed stochastic differential equations.

Abstract: We propose a two-stage method for parameter inference in discretely observed stochastic differential equations. First, we extend a deep log-density filter to learn parameter-dependent conditional log-densities. Second, we learn a neural surrogate for the Bayesian update’s log-normalizing constants, yielding a fast differentiable approximation of the log-likelihood. On a 10-dimensional Ornstein–Uhlenbeck model and a nonlinear bistable equation, we obtain smooth posteriors and orders of magnitude faster likelihood evaluation than particle- and Kalman-type baselines at comparable accuracy.

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Submission Number: 86