Abstract--We present a method that models the evolution of an unbounded number of time series clusters by switching among an unknown number of regimes with linear dynamics. We develop a Bayesian non-parametric approach using a hierarchical Dirichlet process as a prior on the parameters of a Switching Linear Dynamical System and a Gaussian process prior to model the statistical variations in amplitude and temporal alignment within each cluster . By modeling the evolution of time series patterns, the method avoids unnecessary proliferation of clusters in a principled manner . We perform inference by formulating a variational lower bound for off-line and on-line scenarios, enabling efficient learning through optimization. We illustrate the versatility and effectiveness of the approach through several case studies of electrocardiogram analysis using publicly available databases. Index T erms--Time series analysis, Bayesian methods, Gaussian processes, linear dynamical systems, Dirichlet processes, unsupervised learning, electrocardiogram, arrhythmia detection. IME series data analysis has come to pervade all scientific and technological domains, driven by the need to understand change over time. With the growing availability of such data, machine learning has assumed an increasingly central role in a wide variety of tasks which fall under the category of pattern recognition. Particularly, there is growing interest in identifying similar behaviors in time series data as a preliminary step towards generating insights into the dynamics of the underlying processes. Some recent methodologies can be found for characterizing sea wave conditions [1], transcriptome-wide gene expression profiling [2], selecting stocks with different share price performance [3], and discovering human motion primitives [4].

Learning from temporally-correlated data is a core facet of modern machine learning. Yet our understanding of sequential learning remains incomplete, particularly in the multi-trajectory setting where data consists of many independent realizations of a time-indexed stochastic process. This important regime both reflects modern training pipelines such as for large foundation models, and offers the potential for learning without the typical mixing assumptions made in the single-trajectory case. However, instance-optimal bounds are known only for least-squares regression with dependent covariates; for more general models or loss functions, the only broadly applicable guarantees result from a reduction to either i.i.d. learning, with effective sample size scaling only in the number of trajectories, or an existing single-trajectory result when each individual trajectory mixes, with effective sample size scaling as the full data budget deflated by the mixing-time. In this work, we significantly broaden the scope of instance-optimal rates in multi-trajectory settings via the Hellinger localization framework, a general approach for maximum likelihood estimation. Our method proceeds by first controlling the squared Hellinger distance at the path-measure level via a reduction to i.i.d. learning, followed by localization as a quadratic form in parameter space weighted by the trajectory Fisher information. This yields instance-optimal bounds that scale with the full data budget under a broad set of conditions. We instantiate our framework across four diverse case studies: a simple mixture of Markov chains, dependent linear regression under non-Gaussian noise, generalized linear models with non-monotonic activations, and linear-attention sequence models. In all cases, our bounds nearly match the instance-optimal rates from asymptotic normality, substantially improving over standard reductions.

Channel state information (CSI) acquisition is a challenging problem in massive multiple-input multiple-output (MIMO) networks. Radio maps provide a promising solution for radio resource management by reducing online CSI acquisition. However, conventional approaches for radio map construction require location-labeled CSI data, which is challenging in practice. This paper investigates unsupervised angular power map construction based on large timescale CSI data collected in a massive MIMO network without location labels. A hidden Markov model (HMM) is built to connect the hidden trajectory of a mobile with the CSI evolution of a massive MIMO channel. As a result, the mobile location can be estimated, enabling the construction of an angular power map. We show that under uniform rectilinear mobility with Poisson-distributed base stations (BSs), the Cramer-Rao Lower Bound (CRLB) for localization error can vanish at any signal-to-noise ratios (SNRs), whereas when BSs are confined to a limited region, the error remains nonzero even with infinite independent measurements. Based on reference signal received power (RSRP) data collected in a real multi-cell massive MIMO network, an average localization error of 18 meters can be achieved although measurements are mainly obtained from a single serving cell.

Bayesian causal discovery benefits from prior information elicited from domain experts, and in heterogeneous domains any prior knowledge would be badly needed. However, so far prior elicitation approaches have assumed a single causal graph and hence are not suited to heterogeneous domains. We propose a causal elicitation strategy for heterogeneous settings, based on Bayesian experimental design (BED) principles, and a variational mixture structure learning (VaMSL) method -- extending the earlier differentiable Bayesian structure learning (DiBS) method -- to iteratively infer mixtures of causal Bayesian networks (CBNs). We construct an informative graph prior incorporating elicited expert feedback in the inference of mixtures of CBNs. Our proposed method successfully produces a set of alternative causal models (mixture components or clusters), and achieves an improved structure learning performance on heterogeneous synthetic data when informed by a simulated expert. Finally, we demonstrate that our approach is capable of capturing complex distributions in a breast cancer database.

In the field of railway automation, one of the key challenges has been the development of effective computer vision systems due to the limited availability of high-quality, sequential data. Traditional datasets are restricted in scope, lacking the spatio temporal context necessary for real-time decision-making, while alternative solutions introduce issues related to realism and applicability. By focusing on route-specific, contextually relevant cues, we can generate rich, sequential datasets that align more closely with real-world operational logic. The concept of milestone determination allows for the development of targeted, rule-based models that simplify the learning process by eliminating the need for generalized recognition of dynamic components, focusing instead on the critical decision points along a route. We argue that this approach provides a practical framework for training vision agents in controlled, predictable environments, facilitating safer and more efficient machine learning systems for railway automation.

The objectives that Large Language Models (LLMs) implicitly optimize remain dangerously opaque, making trustworthy alignment and auditing a grand challenge. While Inverse Reinforcement Learning (IRL) can infer reward functions from behaviour, existing approaches either produce a single, overconfident reward estimate or fail to address the fundamental ambiguity of the task (non-identifiability). This paper introduces a principled auditing framework that re-frames reward inference from a simple estimation task to a comprehensive process for verification. Our framework leverages Bayesian IRL to not only recover a distribution over objectives but to enable three critical audit capabilities: (i) Quantifying and systematically reducing non-identifiability by demonstrating posterior contraction over sequential rounds of evidence; (ii) Providing actionable, uncertainty-aware diagnostics that expose spurious shortcuts and identify out-of-distribution prompts where the inferred objective cannot be trusted; and (iii) Validating policy-level utility by showing that the refined, low-uncertainty reward can be used directly in RLHF to achieve training dynamics and toxicity reductions comparable to the ground-truth alignment process. Empirically, our framework successfully audits a detoxified LLM, yielding a well-calibrated and interpretable objective that strengthens alignment guarantees. Overall, this work provides a practical toolkit for auditors, safety teams, and regulators to verify what LLMs are truly trying to achieve, moving us toward more trustworthy and accountable AI.

This study uses controlled simulations with known ground-truth parameters to evaluate how Distributional Latent Variable Models (DLVM) and Bayesian Distributional Active LEarning (DALE) perform in comparison to conventional Independent Maximum Likelihood Estimation (IMLE). DLVM integrates observations across multiple executive function tasks and individuals, allowing parameter estimation even under sparse or incomplete data conditions. DLVM consistently outperformed IMLE, especially under with smaller amounts of data, and converges faster to highly accurate estimates of the true distributions. In a second set of analyses, DALE adaptively guided sampling to maximize information gain, outperforming random sampling and fixed test batteries, particularly within the first 80 trials. These findings establish the advantages of combining DLVM's cross-task inference with DALE's optimal adaptive sampling, providing a principled basis for more efficient cognitive assessments.

In this paper, we introduce a novel MCMC sampler, P ARNI-DAG, for a fully-Bayesian approach to the problem of structure learning under observational data.

We establish the first mathematically rigorous link between Bayesian, variational Bayesian, and ensemble methods. A key step towards this is to reformulate the non-convex optimisation problem typically encountered in deep learning as a convex optimisation in the space of probability measures.