Bayesian neural networks (BNNs), which estimate the full posterior distribution over model parameters, are well-known for their role in uncertainty quantification and its promising application in out-of-distribution detection (OoD). Amongst other uncertainty measures, BNNs provide a state-of-the art estimation of predictive entropy (total uncertainty) which can be decomposed as the sum of mutual information and expected entropy. In the context of OoD detection the estimation of predictive uncertainty in the form of the predictive entropy score confounds aleatoric and epistemic uncertainty, the latter being hypothesized to be high for OoD points. Despite these justifications, the mutual information score has been shown to perform worse than predictive entropy. Taking inspiration from Bayesian variational autoencoder (BVAE) literature, this work proposes to measure the disagreement between a corrected version of the pre-softmax quantities, otherwise known as logits, as an estimate of epistemic uncertainty for Bayesian NNs under mean field variational inference. The three proposed epistemic uncertainty scores demonstrate marked improvements over mutual information on a range of OoD experiments, with equal performance otherwise. Moreover, the epistemic uncertainty scores perform on par with the Bayesian benchmark predictive entropy on a range of MNIST and CIFAR10 experiments.

In this paper, we show a more concise and high level proof than the original one, derived by researcher Bart Jacobs, for the following theorem: in the context of Bayesian update rules for learning or updating internal states that produce predictions, the relative entropy between the observations and the predictions is reduced when applying Jeffrey's update rule to update the internal state.

Bayesian phylogenetics requires accurate and efficient approximation of posterior distributions over trees. In this work, we develop a variational Bayesian approach for ultrametric phylogenetic trees. We present a novel variational family based on coalescent times of a single-linkage clustering and derive a closed-form density of the resulting distribution over trees. Unlike existing methods for ultrametric trees, our method performs inference over all of tree space, it does not require any Markov chain Monte Carlo subroutines, and our variational family is differentiable. Through experiments on benchmark genomic datasets and an application to SARS-CoV-2, we demonstrate that our method achieves competitive accuracy while requiring significantly fewer gradient evaluations than existing state-of-the-art techniques.

Large language model (LLM)-based agents have shown promise in tackling complex tasks by interacting dynamically with the environment. Existing work primarily focuses on behavior cloning from expert demonstrations and preference learning through exploratory trajectory sampling. However, these methods often struggle in long-horizon tasks, where suboptimal actions accumulate step by step, causing agents to deviate from correct task trajectories. To address this, we highlight the importance of timely calibration and the need to automatically construct calibration trajectories for training agents. We propose Step-Level Trajectory Calibration (STeCa), a novel framework for LLM agent learning. Specifically, STeCa identifies suboptimal actions through a step-level reward comparison during exploration. It constructs calibrated trajectories using LLM-driven reflection, enabling agents to learn from improved decision-making processes. These calibrated trajectories, together with successful trajectory data, are utilized for reinforced training. Extensive experiments demonstrate that STeCa significantly outperforms existing methods. Further analysis highlights that step-level calibration enables agents to complete tasks with greater robustness. Our code and data are available at https://github.com/WangHanLinHenry/STeCa.

The performance of legged locomotion is closely tied to the accuracy and comprehensiveness of state observations. Blind policies, which rely solely on proprioception, are considered highly robust due to the reliability of proprioceptive observations. However, these policies significantly limit locomotion speed and often require collisions with the terrain to adapt. In contrast, Vision policies allows the robot to plan motions in advance and respond proactively to unstructured terrains with an online perception module. However, perception is often compromised by noisy real-world environments, potential sensor failures, and the limitations of current simulations in presenting dynamic or deformable terrains. Humanoid robots, with high degrees of freedom and inherently unstable morphology, are particularly susceptible to misguidance from deficient perception, which can result in falls or termination on challenging dynamic terrains. To leverage the advantages of both vision and blind policies, we propose VB-Com, a composite framework that enables humanoid robots to determine when to rely on the vision policy and when to switch to the blind policy under perceptual deficiency. We demonstrate that VB-Com effectively enables humanoid robots to traverse challenging terrains and obstacles despite perception deficiencies caused by dynamic terrains or perceptual noise.

The success of large generative models has driven a paradigm shift, leveraging massive multi-source data to enhance model capabilities. However, the interaction among these sources remains theoretically underexplored. This paper takes the first step toward a rigorous analysis of multi-source training in conditional generative modeling, where each condition represents a distinct data source. Specifically, we establish a general distribution estimation error bound in average total variation distance for conditional maximum likelihood estimation based on the bracketing number. Our result shows that when source distributions share certain similarities and the model is expressive enough, multi-source training guarantees a sharper bound than single-source training. We further instantiate the general theory on conditional Gaussian estimation and deep generative models including autoregressive and flexible energy-based models, by characterizing their bracketing numbers. The results highlight that the number of sources and similarity among source distributions improve the advantage of multi-source training. Simulations and real-world experiments validate our theory. Code is available at: \url{https://github.com/ML-GSAI/Multi-Source-GM}.

Because of the global need to increase power production from renewable energy resources, developments in the online monitoring of the associated infrastructure is of interest to reduce operation and maintenance costs. However, challenges exist for data-driven approaches to this problem, such as incomplete or limited histories of labelled damage-state data, operational and environmental variability, or the desire for the quantification of uncertainty to support risk management. This work first introduces a probabilistic regression model for predicting wind-turbine power, which adjusts for wake effects learnt from data. Spatial correlations in the learned model parameters for different tasks (turbines) are then leveraged in a hierarchical Bayesian model (an approach to multi-task learning) to develop a "metamodel", which can be used to make power-predictions which adjust for turbine location - including on previously unobserved turbines not included in the training data. The results show that the metamodel is able to outperform a series of benchmark models, and demonstrates a novel strategy for making efficient use of data for inference in populations of structures, in particular where correlations exist in the variable(s) of interest (such as those from wind-turbine wake-effects).

Natural Language Generation (NLG) popularity has increased owing to the progress in Large Language Models (LLMs), with zero-shot inference capabilities. However, most neural systems utilize decoder-only causal (unidirectional) transformer models, which are effective for English but may reduce the richness of languages with less strict word order, subject omission, or different relative clause attachment preferences. This is the first work that analytically addresses optimal text generation order for non-causal language models. We present a novel Viterbi algorithm-based methodology for maximum likelihood word order estimation. We analyze the non-causal most-likelihood order probability for NLG in Spanish and, then, the probability of generating the same phrases with Spanish causal NLG. This comparative analysis reveals that causal NLG prefers English-like SVO structures. We also analyze the relationship between optimal generation order and causal left-to-right generation order using Spearman's rank correlation. Our results demonstrate that the ideal order predicted by the maximum likelihood estimator is not closely related to the causal order and may be influenced by the syntactic structure of the target sentence.

We study the problem of robust information selection for a Bayesian hypothesis testing / classification task, where the goal is to identify the true state of the world from a finite set of hypotheses based on observations from the selected information sources. We introduce a novel misclassification penalty framework, which enables non-uniform treatment of different misclassification events. Extending the classical subset selection framework, we study the problem of selecting a subset of sources that minimize the maximum penalty of misclassification under a limited budget, despite deletions or failures of a subset of the selected sources. We characterize the curvature properties of the objective function and propose an efficient greedy algorithm with performance guarantees. Next, we highlight certain limitations of optimizing for the maximum penalty metric and propose a submodular surrogate metric to guide the selection of the information set. We propose a greedy algorithm with near-optimality guarantees for optimizing the surrogate metric. Finally, we empirically demonstrate the performance of our proposed algorithms in several instances of the information set selection problem.

Causal discovery aims to infer causal graphs from observational or experimental data. Methods such as the popular PC algorithm are based on conditional independence testing and utilize enabling assumptions, such as the faithfulness assumption, for their inferences. In practice, these assumptions, as well as the functional assumptions inherited from the chosen conditional independence test, are typically taken as a given and not further tested for their validity on the data. In this work, we propose internal coherency scores that allow testing for assumption violations and finite sample errors, whenever detectable without requiring ground truth or further statistical tests. We provide a complete classification of erroneous results, including a distinction between detectable and undetectable errors, and prove that the detectable erroneous results can be measured by our scores. We illustrate our coherency scores on the PC algorithm with simulated and real-world datasets, and envision that testing for internal coherency can become a standard tool in applying constraint-based methods, much like a suite of tests is used to validate the assumptions of classical regression analysis.