We develop a methodology for constructing confidence sets for parameters of statistical models via a reduction to sequential prediction. Our key observation is that for any generalized linear model (GLM), one can construct an associated game of sequential probability assignment such that achieving low regret in the game implies a high-probability upper bound on the excess likelihood of the true parameter of the GLM. This allows us to develop a scheme that we call online-to-confidence-set conversions, which effectively reduces the problem of proving the desired statistical claim to an algorithmic question. We study two varieties of this conversion scheme: 1) analytical conversions that only require proving the existence of algorithms with low regret and provide confidence sets centered at the maximum-likelihood estimator 2) algorithmic conversions that actively leverage the output of the online algorithm to construct confidence sets (and may be centered at other, adaptively constructed point estimators). The resulting methodology recovers all state-of-the-art confidence set constructions within a single framework, and also provides several new types of confidence sets that were previously unknown in the literature.

We propose a new framework for Bayesian estimation of differential privacy, incorporating evidence from multiple membership inference attacks (MIA). Bayesian estimation is carried out via a Markov chain Monte Carlo (MCMC) algorithm, named MCMC-DP-Est, which provides an estimate of the full posterior distribution of the privacy parameter (e.g., instead of just credible intervals). Critically, the proposed method does not assume that privacy auditing is performed with the most powerful attack on the worst-case (dataset, challenge point) pair, which is typically unrealistic. Instead, MCMC-DP-Est jointly estimates the strengths of MIAs used and the privacy of the training algorithm, yielding a more cautious privacy analysis. We also present an economical way to generate measurements for the performance of an MIA that is to be used by the MCMC method to estimate privacy. We present the use of the methods with numerical examples with both artificial and real data.

This paper presents a fault-tolerant control for the trajectory tracking of autonomous underwater vehicles (AUVs) against thruster failures. We formulate faults in AUV thrusters as discrete switching events during a UAV mission, and develop a soft-switching approach in facilitating shift of control strategies across fault scenarios. We mathematically define AUV thruster fault scenarios, and develop the fault-tolerant control that captures the fault scenario via Bayesian approach. Particularly, when the AUV fault type switches from one to another, the developed control captures the fault states and maintains the control by a linear quadratic tracking controller. With the captured fault states by Bayesian approach, we derive the control law by aggregating the control outputs for individual fault scenarios weighted by their Bayesian posterior probability. The developed fault-tolerant control works in an adaptive way and guarantees soft-switching across fault scenarios, and requires no complicated fault detection dedicated to different type of faults. The entailed soft-switching ensures stable AUV trajectory tracking when fault type shifts, which otherwise leads to reduced control under hard-switching control strategies. We conduct numerical simulations with diverse AUV thruster fault settings. The results demonstrate that the proposed control can provide smooth transition across thruster failures, and effectively sustain AUV trajectory tracking control in case of thruster failures and failure shifts.

We present a control framework for robot-assisted dressing that augments low-level hazard response with runtime monitoring and formal verification. A parametric discrete-time Markov chain (pDTMC) models the dressing process, while Bayesian inference dynamically updates this pDTMC's transition probabilities based on sensory and user feedback. Safety constraints from hazard analysis are expressed in probabilistic computation tree logic, and symbolically verified using a probabilistic model checker. We evaluate reachability, cost, and reward trade-offs for garment-snag mitigation and escalation, enabling real-time adaptation. Our approach provides a formal yet lightweight foundation for safety-aware, explainable robotic assistance.

Recent advances in large pre-trained models showed promising results in few-shot learning. However, their generalization ability on two-dimensional Out-of-Distribution (OoD) data, i.e., correlation shift and diversity shift, has not been thoroughly investigated. Researches have shown that even with a significant amount of training data, few methods can achieve better performance than the standard empirical risk minimization method (ERM) in OoD generalization. This few-shot OoD generalization dilemma emerges as a challenging direction in deep neural network generalization research, where the performance suffers from overfitting on few-shot examples and OoD generalization errors. In this paper, leveraging a broader supervision source, we explore a novel Bayesian cross-modal image-text alignment learning method (Bayes-CAL) to address this issue. Specifically, the model is designed as only text representations are fine-tuned via a Bayesian modelling approach with gradient orthogonalization loss and invariant risk minimization (IRM) loss. The Bayesian approach is essentially introduced to avoid overfitting the base classes observed during training and improve generalization to broader unseen classes. The dedicated loss is introduced to achieve better image-text alignment by disentangling the causal and non-casual parts of image features. Numerical experiments demonstrate that Bayes-CAL achieved state-of-the-art OoD generalization performances on two-dimensional distribution shifts. Moreover, compared with CLIP-like models, Bayes-CAL yields more stable generalization performances on unseen classes. Our code is available at https://github.com/LinLLLL/BayesCAL.

This paper presents a Bayesian estimation framework for Wiener models, focusing on learning nonlinear output functions under known linear state dynamics. We derive a closed-form optimal affine estimator for the unknown parameters, characterized by the so-called "dynamic basis statistics" (DBS). Several features of the proposed estimator are studied, including Bayesian unbiasedness, closed-form posterior statistics, error monotonicity in trajectory length, and consistency condition (also known as persistent excitation). In the special case of Fourier basis functions, we demonstrate that the closed-form description is computationally available, as the Fourier DBS enjoys explicit expressions. Furthermore, we identify an inherent inconsistency in the Fourier bases for single-trajectory measurements, regardless of the input excitation. Leveraging the closed-form estimation error, we develop an active learning algorithm synthesizing input signals to minimize estimation error.

Transformers have become a standard architecture in machine learning, demonstrating strong in-context learning (ICL) abilities that allow them to learn from the prompt at inference time. However, uncertainty quantification for ICL remains an open challenge, particularly in noisy regression tasks. This paper investigates whether ICL can be leveraged for distribution-free uncertainty estimation, proposing a method based on conformal prediction to construct prediction intervals with guaranteed coverage. While traditional conformal methods are computationally expensive due to repeated model fitting, we exploit ICL to efficiently generate confidence intervals in a single forward pass. Our empirical analysis compares this approach against ridge regression-based conformal methods, showing that conformal prediction with in-context learning (CP with ICL) achieves robust and scalable uncertainty estimates. Additionally, we evaluate its performance under distribution shifts and establish scaling laws to guide model training. These findings bridge ICL and conformal prediction, providing a theoretically grounded and new framework for uncertainty quantification in transformer-based models.

The Topics over Time (ToT) model captures thematic changes in timestamped datasets by explicitly modeling publication dates jointly with word co-occurrence patterns. However, ToT was not approached in a fully Bayesian fashion, a flaw that makes it susceptible to stability problems. To address this issue, we propose a fully Bayesian Topics over Time (BToT) model via the introduction of a conjugate prior to the Beta distribution. This prior acts as a regularization that prevents the online version of the algorithm from unstable updates when a topic is poorly represented in a mini-batch. The characteristics of this prior to the Beta distribution are studied here for the first time. Still, this model suffers from a difference in scale between the single-time observations and the multiplicity of words per document. A variation of BToT, Weighted Bayesian Topics over Time (WBToT), is proposed as a solution. In WBToT, publication dates are repeated a certain number of times per document, which balances the relative influence of words and timestamps along the inference process. We have tested our models on two datasets: a collection of over 200 years of US state-of-the-union (SOTU) addresses and a large-scale COVID-19 Twitter corpus of 10 million tweets. The results show that WBToT captures events better than Latent Dirichlet Allocation and other SOTA topic models like BERTopic: the median absolute deviation of the topic presence over time is reduced by $51\%$ and $34\%$, respectively. Our experiments also demonstrate the superior coherence of WBToT over BToT, which highlights the importance of balancing the time and word modalities. Finally, we illustrate the stability of the online optimization algorithm in WBToT, which allows the application of WBToT to problems that are intractable for standard ToT.

We introduce a multiple criteria Bayesian preference learning framework incorporating behavioral cues for decision aiding. The framework integrates pairwise comparisons, response time, and attention duration to deepen insights into decision-making processes. The approach employs an additive value function model and utilizes a Bayesian framework to derive the posterior distribution of potential ranking models by defining the likelihood of observed preference data and specifying a prior on the preference structure. This distribution highlights each model's ability to reconstruct Decision-Makers' holistic pairwise comparisons. By leveraging both response time as a proxy for cognitive effort and alternative discriminability as well as attention duration as an indicator of criterion importance, the proposed model surpasses traditional methods by uncovering richer behavioral patterns. We report the results of a laboratory experiment on mobile phone contract selection involving 30 real subjects using a dedicated application with time-, eye-, and mouse-tracking components. We validate the novel method's ability to reconstruct complete preferences. The detailed ablation studies reveal time- and attention-related behavioral patterns, confirming that integrating comprehensive data leads to developing models that better align with the DM's actual preferences.

Differentially private (DP) machine learning often relies on the availability of public data for tasks like privacy-utility trade-off estimation, hyperparameter tuning, and pretraining. While public data assumptions may be reasonable in text and image domains, they are less likely to hold for tabular data due to tabular data heterogeneity across domains. We propose leveraging powerful priors to address this limitation; specifically, we synthesize realistic tabular data directly from schema-level specifications - such as variable names, types, and permissible ranges - without ever accessing sensitive records. To that end, this work introduces the notion of "surrogate" public data - datasets generated independently of sensitive data, which consume no privacy loss budget and are constructed solely from publicly available schema or metadata. Surrogate public data are intended to encode plausible statistical assumptions (informed by publicly available information) into a dataset with many downstream uses in private mechanisms. We automate the process of generating surrogate public data with large language models (LLMs); in particular, we propose two methods: direct record generation as CSV files, and automated structural causal model (SCM) construction for sampling records. Through extensive experiments, we demonstrate that surrogate public tabular data can effectively replace traditional public data when pretraining differentially private tabular classifiers. To a lesser extent, surrogate public data are also useful for hyperparameter tuning of DP synthetic data generators, and for estimating the privacy-utility tradeoff.