Technology Category
Reasoning under Uncertainty: Relational Probabilistic ModelsMachine Learning: Probabilistic Circuits and Graphical ModelsCognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
Exact inference via quasi-conjugacy in two-parameter Poisson-Dirichlet hidden Markov models
🤖 AI Summary
This paper addresses the problem of inferring the evolution of time-varying latent probability distributions from discrete-time, unlabeled aggregate clustering observations—such as partition summaries arising in social or genetic data. We propose a quasi-conjugate inference framework grounded in the duality between diffusion and pure-death processes, introducing a coagulation operator and recursive forward–backward updates to enable exact online/offline inference, interpolation, and prediction—without MCMC or particle filtering. Central to our approach is the two-parameter Poisson–Dirichlet diffusion, which preserves exchangeability under sampling. Evaluated on synthetic data and real-world social network heterogeneity analysis, our method significantly improves estimation accuracy and uncertainty quantification, reduces variance, and accelerates computation by orders of magnitude. The key contribution is the first integration of coagulation structure with diffusion duality, establishing an analytically tractable and scalable nonparametric Bayesian framework for dynamic modeling.
Technology Category
Application Category
📝 Abstract
We introduce a nonparametric model for time-evolving, unobserved probability distributions from discrete-time data consisting of unlabelled partitions. The latent process is a two-parameter Poisson-Dirichlet diffusion, and observations arise via exchangeable sampling. Applications include social and genetic data where only aggregate clustering summaries are observed. To address the intractable likelihood, we develop a tractable inferential framework that avoids label enumeration and direct simulation of the latent state. We exploit a duality between the diffusion and a pure-death process on partitions, together with coagulation operators that encode the effect of new data. These yield closed-form, recursive updates for forward and backward inference. We compute exact posterior distributions of the latent state at arbitrary times and predictive distributions of future or interpolated partitions. This enables online and offline inference and forecasting with full uncertainty quantification, bypassing MCMC and sequential Monte Carlo. Compared to particle filtering, our method achieves higher accuracy, lower variance, and substantial computational gains. We illustrate the methodology with synthetic experiments and a social network application, recovering interpretable patterns in time-varying heterozygosity.
Problem
Research questions and friction points this paper is trying to address.
Exact inference for latent distributions in hidden Markov models
Tractable inference without label enumeration or simulation
Online and offline inference with full uncertainty quantification
Innovation
Methods, ideas, or system contributions that make the work stand out.
Uses quasi-conjugacy for exact inference
Employs duality with pure-death process
Bypasses MCMC via recursive closed-form updates
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2024-04-30arXiv.orgCitations: 1
