🤖 AI Summary
Traditional Bayesian changepoint and segmentation models struggle with non-uniform designs, multi-sample hierarchies, and grouped (or latent-grouped) structures, limiting accurate inference. This work proposes a modular offline Bayesian segmentation framework that decouples candidate segment marginal likelihoods from global dynamic programming, enabling—for the first time—exact sum-product inference for segmentation models under weighted exponential-family likelihoods. The approach unifies support for irregularly sampled, multi-level, and grouped data, efficiently computing the posterior distribution over the number of segments \(P(k|y)\), marginal boundary probabilities, and Bayesian regression curves, while distinguishing full posterior inference from joint MAP segmentation. Key innovations include closed-form segment evidence via conjugate priors, cumulative sufficient statistics, and max-sum backtracking, balancing computational efficiency with principled uncertainty quantification.
📝 Abstract
Bayesian change-point and segmentation models provide uncertainty-aware piecewise-constant representations of ordered data, but exact inference is often tied to narrow likelihood classes, single-sequence settings, or index-uniform designs. We present \texttt{BayesBreak}, a modular offline Bayesian segmentation framework built around a simple separation: each candidate block contributes a marginal likelihood and any required moment numerators, and a global dynamic program combines those block scores into posterior quantities over segment counts, boundary locations, and latent signals. For weighted exponential-family likelihoods with conjugate priors, block evidences and posterior moments are available in closed form from cumulative sufficient statistics, yielding exact sum-product inference for $P(y\mid k)$, $P(k\mid y)$, boundary marginals, and Bayes regression curves. We also distinguish these quantities from the \emph{joint} MAP segmentation, which is recovered by a separate max-sum backtracking recursion.