Bayesian Model Averaging

Prior-data fitted networks (PFNs) are trained to approximate the Bayesian posterior predictive distribution (PPD) of a synthetic prior, yet results about the approximation quality are surprisingly thin. Taking an empirical risk minimization perspective, we decompose the deployment error of PFNs into prior, context, and amortization error, and measure the latter against a reference PPD under a realistic prior. Results show that PFNs generally recover the targeted PPD very well. Nevertheless, we find that parts of the residual amortization error persist, especially in rare settings under the prior pretraining distribution, even when scaling the model size, which manifests in disagreement between independently pretrained PFNs and leaves uncertainty about the predictor at inference time. As a remedy, we study multiple types of Bayesian model averages and find that these can consistently reduce this uncertainty and improve predictions up to full-size TabICLv2 models.

Masked Diffusion Language Models (MDLMs) generate sequences by iteratively replacing masked tokens with model predictions. At each denoising step, the decoder chooses which positions are sufficiently confident to commit. Existing decoding methods typically rely on softmax confidence, which can be miscalibrated. We introduce BayesER (BAYESian Entropy-based Reordering), a post-hoc Bayesian decoding framework that uses predictive uncertainty to guide token commitment. In BayesER, we construct a lightweight approximate posterior centered at the pretrained checkpoint, similar to Laplace-LoRA but without training LoRA adapters. We average predictions over posterior samples and use predictive entropy to prioritize reliable positions. We examine how posterior predictions affect position ordering and token selection across benchmarks spanning code generation, mathematical reasoning, planning, and molecular generation. We show that BayesER reduces sequence-level calibration error while preserving or improving accuracy relative to common decoding schemes, including confidence-threshold decoding. Additionally, a posterior fitted on one code-generation dataset reduces calibration error on another without refitting, suggesting that Bayesian uncertainty may provide a transferable signal for more reliable MDLM decoding.

Counterfactual explanations (CEs) enhance the interpretability of machine learning models by identifying the smallest change to an input required to obtain a desired output. Although CEs are conventionally formulated as a distance-minimization problem, the theoretical basis of this formulation has received limited attention. We show that a distance-minimization-based CE is mathematically equivalent to the maximum a posteriori (MAP) estimate of a Gibbs posterior within the generalized Bayes framework, specifically when a distance-based prior is used. We call this formulation the Distance-Prior Generalized Bayes CE (DP-GBCE). Building on this posterior perspective, we introduce two decision rules beyond MAP within a unified framework: a Bayes decision that minimizes expected decision loss and CVaR-CE, a risk-averse decision rule. We also propose an extension that uses Bayesian model weights to mix the posterior distributions of multiple models, thereby accounting for model multiplicity, where several models have comparable predictive performance. Finally, we define metrics for evaluating both individual CEs and the posterior distribution as a whole, and use experiments on simulated data and Google Trends data to quantify the trade-offs among the decision rules.

Bayesian posterior uncertainty can be spread across many models that share the same substantive pattern. Lists of individual models can obscure this structure, while marginal summaries do not describe which configurations are jointly supported. We study how to represent joint model uncertainty through a compact collection of interpretable regions, each grouping models that share a specified pattern. We formulate this task as minimizing representation complexity subject to retaining a prescribed posterior mass within an analyst-supplied family. To address unknown regional probabilities, we develop Adaptive Regional Selection (ARS), which combines adaptive exploration and regional weight estimation with conservative and optimistic selection. These complementary problems identify a summary meeting the mass target and bound how much further its complexity could improve. Under valid regional bounds, we establish guarantees for retained mass, total-variation error, and suboptimality, together with conditions for certifying optimality. We also show that, under bounded within-region weight variation, sufficient sample counts for regional estimation need not grow with the number of represented models, and construct bounds that remain valid under adaptive sampling and stopping. Empirical studies illustrate regional summaries in Bayesian model averaging and Bayesian networks, examining retained mass, representation complexity, and certification.

We ask: when do Bayesian model averaging (BMA) weights over decision trees carry sufficient epistemic information to justify committed exploitation of the averaging distribution? We answer this question in closed form for Bayesian decision trees (BDTs) with Dirichlet-Multinomial leaf models and a Catalan-exponential tree-size prior (Schetinin&Jakaite, 2025), establishing a complete non-asymptotic theory of rational commitment thresholds.

While parameter-efficient fine-tuning methods like low-rank adaptation (LoRA) are standard for large language models, principled estimation of epistemic uncertainty remains challenging. Recent results in the LoRA regime suggest that discrete multi-mode approaches such as deep ensembles offer little benefit over single-mode methods. This contradicts broader observations in deep learning, where ensembling independent optima typically improves generalization, and linking these modes through continuous low-loss valleys further enhances Bayesian model averaging (BMA). Whether such structure exists in the LoRA space and whether it yields functional diversity missed by local or discrete methods has not been studied. We introduce LoRA-Curve, a segmented Bézier curve parameterization in the LoRA space, with two variants: a free configuration that jointly optimizes all control points, and an anchored configuration that connects independently fine-tuned LoRA optima. We prove pathwise continuity and Lipschitz regularity of the loss along the curve and empirically show, across reasoning and classification benchmarks with Qwen2.5 7B, that linear interpolation encounters loss barriers, while our anchored multi-segment curves connect independent optima through continuous low-loss valleys. Combined with flat-minima perturbations and a Jensen-Shannon divergence regularizer, LoRA-Curve yields measurably higher mutual information of the predictive distribution without sacrificing performance, and links continuous parameter-space traversal to functional diversity.

Multimodal 3D vision-language models show strong generalization across diverse 3D tasks, but their performance still degrades notably under domain shifts. This has motivated recent studies on test-time adaptation (TTA), which enables models to adapt online using test-time data. Among existing TTA methods, cache-based mechanisms are widely adopted for leveraging previously observed samples in online prediction refinement. However, they store only limited historical information, leading to progressive information loss as the test stream evolves. In addition, their prediction logits are fused heuristically, making adaptation unstable. To address these limitations, we propose BayesMM, a Multimodal Bayesian Distribution Learning framework for test-time point cloud analysis. BayesMM models textual priors and streaming visual features of each class as Gaussian distributions: textual parameters are derived from semantic prompts, while visual parameters are updated online with arriving samples. The two modalities are fused via Bayesian model averaging, which automatically adjusts their contributions based on posterior evidence, yielding a unified prediction that adapts continually to evolving test-time data without training. Extensive experiments on multiple point cloud benchmarks demonstrate that BayesMM maintains robustness under distributional shifts, yielding over 4% average improvement.

Accurate prediction of surgical duration is pivotal for hospital resource management. Although recent supervised learning approaches-from machine learning (ML) to fine-tuned large language models (LLMs)-have shown strong performance, they remain constrained by the need for high-quality labeled data and computationally intensive training. In contrast, zero-shot LLM inference offers a promising training-free alternative but it lacks grounding in institution-specific clinical context (e.g., local demographics and case-mix distributions), making its predictions clinically misaligned and prone to instability. To address these limitations, we present PREBA, a retrieval-augmented framework that integrates PCA-weighted retrieval and Bayesian averaging aggregation to ground LLM predictions in institution-specific clinical evidence and statistical priors. The core of PREBA is to construct an evidence-based prompt for the LLM, comprising (1) the most clinically similar historical surgical cases and (2) clinical statistical priors. To achieve this, PREBA first encodes heterogeneous clinical features into a unified representation space enabling systematic retrieval. It then performs PCA-weighted retrieval to identify clinically relevant historical cases, which form the evidence context supplied to the LLM. Finally, PREBA applies Bayesian averaging to fuse multi-round LLM predictions with population-level statistical priors, yielding calibrated and clinically plausible duration estimates. We evaluate PREBA on two real-world clinical datasets using three state-of-the-art LLMs, including Qwen3, DeepSeek-R1, and HuatuoGPT-o1. PREBA significantly improves performance-for instance, reducing MAE by up to 40% and raising R^2 from -0.13 to 0.62 over zero-shot inference-and it achieves accuracy competitive with supervised ML methods, demonstrating strong effectiveness and generalization.