https://grdm.io/tags/predictive-bayes/Recent content in Predictive-Bayes on Gerardo Duran-MartinHugoen-usFri, 10 Apr 2026 00:00:00 +0000https://grdm.io/articles/streaming-hmm2026/Fri, 10 Apr 2026 00:00:00 +0000https://grdm.io/articles/streaming-hmm2026/<h2 id="abstract">Abstract</h2> <p>We develop a predictive-first optimisation framework for streaming hidden Markov models. Unlike classical approaches that prioritise full posterior recovery under a fully specified generative model, we assume access to regime-specific predictive models whose parameters are learned online while maintaining a fixed transition prior over regimes. Our objective is to sequentially identify latent regimes while maintaining accurate step-ahead predictive distributions. Because the number of possible regime paths grows exponentially, exact filtering is infeasible. We therefore formulate streaming inference as a constrained projection problem in predictive-distribution space: under a fixed hypothesis budget, we approximate the full posterior predictive by the forward-KL optimal mixture supported on S paths. The solution is the renormalised top-S posterior-weighted mixture, providing a principled derivation of beam search for HMMs. The resulting algorithm is fully recursive and deterministic, performing beam-style truncation with closed-form predictive updates and requiring neither EM nor sampling. Empirical comparisons against Online EM and Sequential Monte Carlo under matched computational budgets demonstrate competitive prequential performance.</p>https://grdm.io/articles/mpnn2025/Fri, 13 Jun 2025 00:00:00 +0000https://grdm.io/articles/mpnn2025/<h2 id="abstract">Abstract</h2> <p>We introduce scalable algorithms for online learning of neural network parameters and Bayesian sequential decision making. Unlike classical Bayesian neural networks, which induce predictive uncertainty through a posterior over model parameters, our methods adopt a predictive-first perspective based on martingale posteriors. In particular, we work directly with the one-step-ahead posterior predictive, which we parameterize with a neural network and update sequentially with incoming observations.</p> <p>This decouples Bayesian decision-making from parameter-space inference: we sample from the posterior predictive for decision making, and update the parameters of the posterior predictive via fast, frequentist Kalman-filter-like recursions. Our algorithms operate in a fully online, replay-free setting, providing principled uncertainty quantification without costly posterior sampling. Empirically, they achieve competitive performance-speed trade-offs in non-stationary contextual bandits and Bayesian optimization, offering 10-100 times faster inference than classical Thompson sampling while maintaining comparable or superior decision performance.</p>