Sparse dynamics identification is an essential tool for discovering interpretable physical models and enabling efficient control in engineering systems. However, existing methods rely on batch learning with full historical data, limiting their applicability to real-time scenarios involving sequential and partially observable data. To overcome this limitation, this paper proposes an online Sparse Kalman Identification (SKI) method by integrating the Augmented Kalman Filter (AKF) and Automatic Relevance Determination (ARD). The main contributions are: (1) a theoretically grounded Bayesian sparsification scheme that is seamlessly integrated into the AKF framework and adapted to sequentially collected data in online scenarios; (2) an update mechanism that adapts the Kalman posterior to reflect the updated selection of the basis functions that define the model structure; (3) an explicit gradient-descent formulation that enhances computational efficiency. Consequently, the SKI method achieves accurate model structure selection with millisecond-level efficiency and higher identification accuracy, as demonstrated by extensive simulations and real-world experiments (showing an 84.21\% improvement in accuracy over the baseline AKF).

Robots must learn from both what people do and what they say, but either modality alone is often incomplete: physical corrections are grounded but ambiguous in intent, while language expresses high-level goals but lacks physical grounding. We introduce QuickLAP: Quick Language-Action Preference learning, a Bayesian framework that fuses physical and language feedback to infer reward functions in real time. Our key insight is to treat language as a probabilistic observation over the user's latent preferences, clarifying which reward features matter and how physical corrections should be interpreted. QuickLAP uses Large Language Models (LLMs) to extract reward feature attention masks and preference shifts from free-form utterances, which it integrates with physical feedback in a closed-form update rule. This enables fast, real-time, and robust reward learning that handles ambiguous feedback. In a semi-autonomous driving simulator, QuickLAP reduces reward learning error by over 70% compared to physical-only and heuristic multimodal baselines. A 15-participant user study further validates our approach: participants found QuickLAP significantly more understandable and collaborative, and preferred its learned behavior over baselines. Code is available at https://github.com/MIT-CLEAR-Lab/QuickLAP.

Large language models (LLMs) solve complex problems yet fail on simpler variants, suggesting they achieve correct outputs through mechanisms fundamentally different from human reasoning. To understand this gap, we synthesize cognitive science research into a taxonomy of 28 cognitive elements spanning reasoning invariants, meta-cognitive controls, representations for organizing reasoning & knowledge, and transformation operations. We introduce a fine-grained evaluation framework and conduct the first large-scale empirical analysis of 192K traces from 18 models across text, vision, and audio, complemented by 54 human think-aloud traces, which we make publicly available. We find that models under-utilize cognitive elements correlated with success, narrowing to rigid sequential processing on ill-structured problems where diverse representations and meta-cognitive monitoring are critical. Human traces show more abstraction and conceptual processing, while models default to surface-level enumeration. Meta-analysis of 1.6K LLM reasoning papers reveals the research community concentrates on easily quantifiable elements (sequential organization: 55%, decomposition: 60%) but neglecting meta-cognitive controls (self-awareness: 16%) that correlate with success. Models possess behavioral repertoires associated with success but fail to deploy them spontaneously. Leveraging these patterns, we develop test-time reasoning guidance that automatically scaffold successful structures, improving performance by up to 66.7% on complex problems. By establishing a shared vocabulary between cognitive science and LLM research, our framework enables systematic diagnosis of reasoning failures and principled development of models that reason through robust cognitive mechanisms rather than spurious shortcuts, while providing tools to test theories of human cognition at scale.

Many sequential decision settings in healthcare feature funnel structures characterized by a series of stages, such as screenings or evaluations, where the number of patients who advance to each stage progressively decreases and decisions become increasingly costly. For example, an oncologist may first conduct a breast exam, followed by a mammogram for patients with concerning exams, followed by a biopsy for patients with concerning mammograms. A key challenge is that the ground truth outcome, such as the biopsy result, is only revealed at the end of this funnel. The selective censoring of the ground truth can introduce statistical biases in risk estimation, especially in underserved patient groups, whose outcomes are more frequently censored. We develop a Bayesian model for funnel decision structures, drawing from prior work on selective labels and censoring. We first show in synthetic settings that our model is able to recover the true parameters and predict outcomes for censored patients more accurately than baselines. We then apply our model to a dataset of emergency department visits, where in-hospital mortality is observed only for those who are admitted to either the hospital or ICU. We find that there are gender-based differences in hospital and ICU admissions. In particular, our model estimates that the mortality risk threshold to admit women to the ICU is higher for women (5.1%) than for men (4.5%).

Non-invasive electroencephalography (EEG)-based brain-computer interfaces (BCIs) offer an intuitive means for individuals with severe motor impairments to independently operate assistive robotic wheelchairs and navigate built environments. Despite considerable progress in BCI research, most current motion control systems are limited to discrete commands, rather than supporting continuous pursuit, where users can freely adjust speed and direction in real time. Such natural mobility control is, however, essential for wheelchair users to navigate complex public spaces, such as transit stations, airports, hospitals, and indoor corridors, to interact socially with the dynamic populations with agility, and to move flexibly and comfortably as autonomous driving is refined to allow movement at will. In this study, we address the gap of continuous pursuit motion control in BCIs by proposing and validating a brain-inspired Bayesian inference framework, where embodied dynamics in acceleration-based motor representations are decoded. This approach contrasts with conventional kinematics-level decoding and deep learning-based methods. Using a public dataset with sixteen hours of EEG from four subjects performing motor imagery-based target-following, we demonstrate that our method, utilizing Automatic Relevance Determination for feature selection and continual online learning, reduces the normalized mean squared error between predicted and true velocities by 72% compared to autoregressive and EEGNet-based methods in a session-accumulative transfer learning setting. Theoretically, these findings empirically support embodied cognition theory and reveal the brain's intrinsic motor control dynamics in an embodied and predictive nature. Practically, grounding EEG decoding in the same dynamical principles that govern biological motion offers a promising path toward more stable and intuitive BCI control.

Prompt learning has emerged as an effective technique for fine-tuning large-scale foundation models for downstream tasks. However, conventional prompt tuning methods are prone to overfitting and can struggle with out-of-distribution generalization. To address these limitations, Bayesian prompt learning has been proposed, which frames prompt optimization as a Bayesian inference problem to enhance robustness. This paper introduces Repulsive Bayesian Prompt Learning (ReBaPL), a novel method for Bayesian prompt learning, designed to efficiently explore the complex and often multimodal posterior landscape of prompts. Our method integrates a cyclical step-size schedule with a stochastic gradient Hamiltonian Monte Carlo (SGHMC) algorithm, enabling alternating phases of exploration to discover new modes, and exploitation to refine existing modes. Furthermore, we introduce a repulsive force derived from a potential function over probability metrics (including Maximum Mean Discrepancy and Wasserstein distance) computed on the distributions of representations produced by different prompts. This representation-space repulsion diversifies exploration and prevents premature collapse to a single mode. Our approach allows for a more comprehensive characterization of the prompt posterior distribution, leading to improved generalization. In contrast to prior Bayesian prompt learning methods, our method provides a modular plug-and-play Bayesian extension of any existing prompt learning method based on maximum likelihood estimation. We demonstrate the efficacy of ReBaPL on several benchmark datasets, showing superior performance over state-of-the-art methods for prompt learning.

Electronic health records (EHRs) form an invaluable resource for training clinical decision support systems. To leverage the potential of such systems in high-risk applications, we need large, structured tabular datasets on which we can build transparent feature-based models. While part of the EHR already contains structured information (e.g. diagnosis codes, medications, and lab results), much of the information is contained within unstructured text (e.g. discharge summaries and nursing notes). In this work, we propose a method for multi-modal patient-level information extraction that leverages both the tabular features available in the patient's EHR (using an expert-informed Bayesian network) as well as clinical notes describing the patient's symptoms (using neural text classifiers). We propose the use of virtual evidence augmented with a consistency node to provide an interpretable, probabilistic fusion of the models' predictions. The consistency node improves the calibration of the final predictions compared to virtual evidence alone, allowing the Bayesian network to better adjust the neural classifier's output to handle missing information and resolve contradictions between the tabular and text data. We show the potential of our method on the SimSUM dataset, a simulated benchmark linking tabular EHRs with clinical notes through expert knowledge.

Bayesian Networks (BNs) are an important tool for assisting probabilistic reasoning, but despite being considered transparent models, people have trouble understanding them. Further, current User Interfaces (UIs) still do not clarify the reasoning of BNs. To address this problem, we have designed verbal and visual extensions to the standard BN UI, which can guide users through common inference patterns. We conducted a user study to compare our verbal, visual and combined UI extensions, and a baseline UI. Our main findings are: (1) users did better with all three types of extensions than with the baseline UI for questions about the impact of an observation, the paths that enable this impact, and the way in which an observation influences the impact of other observations; and (2) using verbal and visual modalities together is better than using either modality alone for some of these question types.

How do Large Language Models understand moral dimensions compared to humans? This first large-scale Bayesian evaluation of market-leading language models provides the answer. In contrast to prior work using deterministic ground truth (majority or inclusion rules), we model annotator disagreements to capture both aleatoric uncertainty (inherent human disagreement) and epistemic uncertainty (model domain sensitivity). We evaluated the best language models (Claude Sonnet 4, DeepSeek-V3, Llama 4 Maverick) across 250K+ annotations from nearly 700 annotators in 100K+ texts spanning social networks, news and forums. Our GPU-optimized Bayesian framework processed 1M+ model queries, revealing that AI models typically rank among the top 25\% of human annotators, performing much better than average balanced accuracy. Importantly, we find that AI produces far fewer false negatives than humans, highlighting their more sensitive moral detection capabilities.

In this study, a scalable online kernel learning framework is proposed for estimating bidirectional causal effects in systems characterized by mutual dependence and heteroskedasticity. Traditional causal inference often focuses on unidirectional effects, overlooking the common bidirectional relationships in real-world phenomena. Building on heteroskedasticity-based identification, the proposed method integrates a quasi-maximum likelihood estimator for simultaneous equation models with large scale online kernel learning. It employs random Fourier feature approximations to flexibly model nonlinear conditional means and variances, while an adaptive online gradient descent algorithm ensures computational efficiency for streaming and high-dimensional data. Results from extensive simulations demonstrate that the proposed method achieves superior accuracy and stability than single equation and polynomial approximation baselines, exhibiting lower bias and root mean squared error across various data-generating processes. These results confirm that the proposed approach effectively captures complex bidirectional causal effects with near-linear computational scaling. By combining econometric identification with modern machine learning techniques, the proposed framework offers a practical, scalable, and theoretically grounded solution for large scale causal inference in natural/social science, policy making, business, and industrial applications.