belief-state estimation

This study addresses the challenge of inefficient inference in Gaussian processes for sequential signal processing by moving beyond the conventional machine learning reliance on independent and identically distributed assumptions. It proposes a unified sequential inference framework for Gaussian processes, systematically integrating techniques from sequential Bayesian inference, incremental learning, streaming computation, and state-space modeling, with signal processing as the central organizing principle. This work not only bridges the longstanding gap between modern machine learning and classical signal processing but also delivers scalable and efficient practical solutions—along with a clear deployment roadmap—for time-series forecasting, anomaly detection, adaptive sensing, and real-time Bayesian optimization.

To address particle degeneracy—caused by iterative resampling in recursive Bayesian inference—this paper proposes a novel method for constructing proposal distributions via smoothed empirical distributions. At each recursion step, the method leverages the empirical distribution of historical particles, applies kernel smoothing to yield a high-quality proposal, and then employs accept-reject sampling for efficient importance weighting and resampling, thereby balancing computational efficiency and particle diversity. Its key innovation lies in embedding empirical distribution smoothing directly into the recursive framework, mitigating rapid degeneration inherent in conventional sequential importance sampling (SIS) and particle filtering (PF). Empirical evaluation on simulated data from logistic regression and a hierarchical forest vegetation model for New Mexico demonstrates that the method significantly improves posterior approximation accuracy and stability. It is particularly effective for streaming data and large-scale block-wise analysis.

Distributed Bayesian estimation in sensor networks—specifically, collaborative density estimation over continuous-variable function spaces using only local subset observations—lacks provably convergent algorithms. Method: We propose the first distributed algorithmic framework with rigorous convergence guarantees, integrating distributed consensus optimization and variational inference. Our approach incorporates nonlinear likelihood modeling, Gaussian approximations, and marginal density projection, yielding a memory-aware marginal distribution estimator adaptable to heterogeneous observation structures. Contribution/Results: We establish the first theoretical proof of almost-sure convergence of each node’s density estimate to the global posterior marginal density in the function space. Experiments on LiDAR mapping demonstrate substantial reductions in communication and storage overhead. The framework provides a provably correct, scalable paradigm for distributed Bayesian estimation in subset-observation settings—including cooperative localization and federated learning—where data decentralization and structural heterogeneity are inherent.

This work addresses the challenge of event localization in communication-denied environments, where path-integral sensors provide only binary path observations, thereby hindering precise event detection and limiting information fusion and path planning. The paper proposes a Bayesian network–based belief map updating method that, for the first time, enables principled Bayesian inference over path observations by explicitly modeling false alarms and missed detections. By integrating Shannon information theory, the approach plans trajectories that maximize information gain. In contrast to existing methods relying on posterior mean approximations, the proposed technique significantly accelerates belief map convergence and substantially improves both accuracy and efficiency in static hazard detection, demonstrating consistent advantages in both single-robot and multi-robot scenarios.

Accurately quantifying predictive uncertainty under model misspecification remains challenging. Method: We propose Prediction-oriented Posterior (PrO), a unified framework that integrates the strengths of parameter inference and density estimation, constructing the posterior distribution explicitly to optimize predictive performance. PrO converges at rate $n^{-1/2}$ to the true parameter under correct specification, while automatically collapsing to the optimal predictive distribution under misspecification—thereby explicitly disentangling irreducible uncertainty from model inadequacy. Efficient sampling is achieved via mean-field Langevin dynamics. Contribution/Results: We establish asymptotic superiority of PrO over both classical and generalized Bayesian methods. Extensive numerical experiments demonstrate its robust predictive gains and practical utility across regression, classification, and generative modeling tasks.

This work addresses the lack of explicit confidence modeling for various sources of uncertainty in Bayesian inference by proposing a general extension framework that, for the first time, explicitly incorporates confidence in key uncertainty components—such as the prior and likelihood—into Bayesian modeling. The framework not only introduces a novel regularization mechanism but also provides a unified approach to inducing model sparsity. Without compromising theoretical rigor, the method achieves controllable sparsity across diverse models, including linear regression, logistic regression, and Bayesian neural networks, thereby significantly enhancing both interpretability and generalization performance.

This study addresses the lack of convergence guarantees for belief propagation (BP) algorithms in multi-path data association (MPDA), where a single target generates multiple measurements via distinct paths, resulting in a tripartite association among targets, paths, and measurements. For the first time, this work establishes a rigorous convergence theory for BP in this setting. By leveraging graphical model inference and fixed-point analysis, it proves that the message update rules converge to a unique fixed point. Simulation results demonstrate that the proposed approach outperforms both single-scan and two-scan multiple hypothesis trackers in balancing accuracy and computational efficiency, thereby filling a critical gap in the theoretical understanding of BP algorithms under tripartite associations.

In Bayesian sequential inference, the marginal likelihood is often treated as a static constant, overlooking its role in modulating the pace of belief updates. This work reveals that the marginal likelihood not only governs the magnitude of individual updates but also encodes frequency patterns embedded in historical data, which the authors reformulate as a dynamic regularizer. By introducing three diagnostic metrics to control online estimation gain and integrating prior and posterior distributions into a hybrid probabilistic mechanism, the proposed approach adaptively adjusts to distributional drift. The resulting framework unifies Bayesian updating with frequentist characteristics within a two-layer probabilistic architecture, substantially enhancing the robustness of sequential estimation and offering a novel paradigm for online risk quantification.

This study addresses the limitation of traditional statistical process control, which emphasizes detecting historical shifts while neglecting the acceptability of the current process state. To overcome this, the authors propose a Bayesian sequential monitoring framework tailored for recoverable processes subject to parameter drift. By recursively computing the posterior probability that the process is in-control at the current time, the method shifts the monitoring focus toward real-time state assessment. The framework integrates time-to-failure modeling, Gaussian and binomial tracking, and multivariate data analysis within a unified Bayesian formulation. Demonstrated through simulation studies and an application to white wine quality data, the approach effectively identifies the current operational status of dynamic recoverable processes, significantly enhancing both monitoring accuracy and practical applicability.