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.

-- This paper introduces COR-MCTS (Conservation of Resources - Monte Carlo Tree Search), a novel tactical decision-making approach for automated driving focusing on maneuver planning over extended horizons. Traditional decision-making algorithms are often constrained by fixed planning horizons, typically up to 6 seconds for classical approaches and 3 seconds for learning-based methods limiting their adaptability in particular dynamic driving scenarios. However, planning must be done well in advance in environments such as highways, roundabouts, and exits to ensure safe and efficient maneuvers. T o address this challenge, we propose a hybrid method integrating Monte Carlo Tree Search (MCTS) with our prior utility-based framework, COR-MP (Conservation of Resources Model for Maneuver Planning). This combination enables long-term, real-time decision-making, significantly enhancing the ability to plan a sequence of maneuvers over extended horizons. Through simulations across diverse driving scenarios, we demonstrate that COR-MCTS effectively improves planning robustness and decision efficiency over extended horizons. The deployment of self-driving cars offers numerous benefits, such as improved transportation mobility, enhanced vehicle efficiency in terms of fuel consumption, and better traffic flow management [1], [2]. However, significant challenges remain before fully autonomous vehicles can be integrated into daily life.

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.

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.

Causal inference aids researchers in discovering cause-and-effect relationships, leading to scientific insights. Accurate causal estimation requires identifying confounding variables to avoid false discoveries. Pearl's causal model uses causal DAGs to identify confounding variables, but incorrect DAGs can lead to unreliable causal conclusions. However, for high dimensional data, the causal DAGs are often complex beyond human verifiability. Graph summarization is a logical next step, but current methods for general-purpose graph summarization are inadequate for causal DAG summarization. This paper addresses these challenges by proposing a causal graph summarization objective that balances graph simplification for better understanding while retaining essential causal information for reliable inference. We develop an efficient greedy algorithm and show that summary causal DAGs can be directly used for inference and are more robust to misspecification of assumptions, enhancing robustness for causal inference. Experimenting with six real-life datasets, we compared our algorithm to three existing solutions, showing its effectiveness in handling high-dimensional data and its ability to generate summary DAGs that ensure both reliable causal inference and robustness against misspecifications.

For peg-in-hole tasks, humans rely on binocular visual perception to locate the peg above the hole surface and then proceed with insertion. This paper draws insights from this behavior to enable agents to learn efficient assembly strategies through visual reinforcement learning. Hence, we propose a Separate Primitive Policy (S2P) to simultaneously learn how to derive location and insertion actions. S2P is compatible with model-free reinforcement learning algorithms. Ten insertion tasks featuring different polygons are developed as benchmarks for evaluations. Simulation experiments show that S2P can boost the sample efficiency and success rate even with force constraints. Real-world experiments are also performed to verify the feasibility of S2P. Ablations are finally given to discuss the generalizability of S2P and some factors that affect its performance.

In the field of natural language processing (NLP), the capability to infer and reason about causality is increasingly recognized as a critical component of intelligent systems. Despite the recent advancement of large language models (LLMs) (Radford et al., 2019; Devlin et al., 2019; Brown et al., 2020; Zhang et al., 2022; OpenAI, 2023; Ignat et al., 2024, inter alia), a key question still remains: Can these models understand and reason about causality? This is a critical skill before we can trust AI agents to be integrated into decision-making systems. Moreover, even if LLMs succeed at some extent of reasoning, they still lack transparency of how their decisions are made, forming a strong need for interpretabil-ity (Luo and Specia, 2024; Räuker et al., 2023; Zou et al., 2023). T o bridge the gap, this thesis explores various facets of causal reasoning in LLMs. W e present a series of studies that collectively advance the knowledge of how well these models perform causal reasoning (Part I), how their decisions are made (Part II), how causality among learning variables influences NLP tasks (Part III), and how causality and NLP can together analyze social problems (Part IV). Below we introduce an overview of the four parts and their corresponding chapters.