Density regression models allow a comprehensive understanding of data by modeling the complete conditional probability distribution. While flexible estimation approaches such as normalizing flows (NF) work particularly well in multiple dimensions, interpreting the input-output relationship of such models is often difficult, due to the black-box character of deep learning models. In contrast, existing statistical methods for multivariate outcomes such as multivariate conditional transformation models (MCTM) are restricted in flexibility and are often not expressive enough to represent complex multivariate probability distributions. In this paper, we combine MCTM with state-of-the-art and autoregressive NF to leverage the transparency of MCTM for modeling interpretable feature effects on the marginal distributions in the first step and the flexibility of neural-network-based NF techniques to account for complex and non-linear relationships in the joint data distribution. We demonstrate our method's versatility in various numerical experiments and compare it with MCTM and other NF models on both simulated and real-world data.

Diffusion bridges are a promising class of deep-learning methods for sampling from unnormalized distributions. Recent works show that the Log Variance (LV) loss consistently outperforms the reverse Kullback-Leibler (rKL) loss when using the reparametrization trick to compute rKL-gradients. While the on-policy LV loss yields identical gradients to the rKL loss when combined with the log-derivative trick for diffusion samplers with non-learnable forward processes, this equivalence does not hold for diffusion bridges or when diffusion coefficients are learned. Based on this insight we argue that for diffusion bridges the LV loss does not represent an optimization objective that can be motivated like the rKL loss via the data processing inequality. Our analysis shows that employing the rKL loss with the log-derivative trick (rKL-LD) does not only avoid these conceptual problems but also consistently outperforms the LV loss. Experimental results with different types of diffusion bridges on challenging benchmarks show that samplers trained with the rKL-LD loss achieve better performance. From a practical perspective we find that rKL-LD requires significantly less hyperparameter optimization and yields more stable training behavior.

Although large language models (LLMs) are becoming increasingly capable of solving challenging real-world tasks, accurately quantifying their uncertainty remains a critical open problem, which limits their applicability in high-stakes domains. This challenge is further compounded by the closed-source, black-box nature of many state-of-the-art LLMs. Moreover, LLM-based systems can be highly sensitive to the prompts that bind them together, which often require significant manual tuning (i.e., prompt engineering). In this work, we address these challenges by viewing LLM-based systems through a Bayesian lens. We interpret prompts as textual parameters in a statistical model, allowing us to use a small training dataset to perform Bayesian inference over these prompts. This novel perspective enables principled uncertainty quantification over both the model's textual parameters and its downstream predictions, while also incorporating prior beliefs about these parameters expressed in free-form text. To perform Bayesian inference, a difficult problem even for well-studied data modalities, we introduce Metropolis-Hastings through LLM Proposals (MHLP), a novel Markov chain Monte Carlo (MCMC) algorithm that combines prompt optimization techniques with standard MCMC methods. MHLP is a turnkey modification to existing LLM pipelines, including those that rely exclusively on closed-source models. Empirically, we demonstrate that our method yields improvements in both predictive accuracy and uncertainty quantification (UQ) on a range of LLM benchmarks and UQ tasks. More broadly, our work demonstrates a viable path for incorporating methods from the rich Bayesian literature into the era of LLMs, paving the way for more reliable and calibrated LLM-based systems.

It is well known that semantic and structural features of the generated images emerge at different times during the reverse dynamics of diffusion, a phenomenon that has been connected to physical phase transitions in magnets and other materials. In this paper, we introduce a general information-theoretic approach to measure when these class-semantic "decisions" are made during the generative process. By using an online formula for the optimal Bayesian classifier, we estimate the conditional entropy of the class label given the noisy state. We then determine the time intervals corresponding to the highest information transfer between noisy states and class labels using the time derivative of the conditional entropy. We demonstrate our method on one-dimensional Gaussian mixture models and on DDPM models trained on the CIFAR10 dataset. As expected, we find that the semantic information transfer is highest in the intermediate stages of diffusion while vanishing during the final stages. However, we found sizable differences between the entropy rate profiles of different classes, suggesting that different "semantic decisions" are located at different intermediate times.

Off-policy learning serves as the primary framework for learning optimal policies from logged interactions collected under a static behavior policy. In this work, we investigate the more practical and flexible setting of adaptive off-policy learning, where policies are iteratively refined and re-deployed to collect higher-quality data. Building on the success of PAC-Bayesian learning with Logarithmic Smoothing (LS) in static settings, we extend this framework to the adaptive scenario using tools from online PAC-Bayesian theory. Furthermore, we demonstrate that a principled adjustment to the LS estimator naturally accommodates multiple rounds of deployment and yields faster convergence rates under mild conditions. Our method matches the performance of leading offline approaches in static settings, and significantly outperforms them when intermediate policy deployments are allowed. Empirical evaluations across diverse scenarios highlight both the advantages of adaptive data collection and the strength of the PAC-Bayesian formulation.

-- In many nations, diabetes is becoming a significant health problem, and early identi - fication and control are crucial. Using machine learning algorithms to predict diabetes has yielded encouraging results. Using the Pima Indians Dia - betes dataset, this study attempts to evaluate the efficacy of several machine - learning methods for diabetes prediction. The collection includes infor - mation on 768 patients, such as their ages, BMIs, and glucose levels. The techniques assessed are Logistic Regression, Decision Tree, Random Forest, k - Nearest Neighbors, Naive Bayes, Support Vector Machine, Gradient Boosting, and Neural Network. The findings indicate that the Neural Network algorithm performed the best, with an accuracy of 78.57 The study implies that machine learning algorithms can aid diabetes prediction and be an efficient early detection tool. Diabetes is a chronic metabolic disease af - fecting millions worldwide and is a significant cause of morbidity and death [1]. High blood glucose levels characterize the disorder and can result in some complications, including cardiovascular disease, stroke, blindness, and amputations. To prevent or postpone com - plications, diabetes must be recognized and treated as soon as feasible; however, this can be challenging because symptoms may be mild or absent [2]. Machine learning (ML) is a subfield of artificial intelligence that comprises the de - velopment of algorithms that can learn from data and generate inferences or predictions without being explicitly programmed. ML algorithms are beneficial in several fields, in - cluding healthcare.

Reinforcement-learning agents often struggle when deployed from simulation to the real-world. A dominant strategy for reducing the sim-to-real gap is domain randomization (DR) which trains the policy across many simulators produced by sampling dynamics parameters, but standard DR ignores offline data already available from the real system. We study offline domain randomization (ODR), which first fits a distribution over simulator parameters to an offline dataset. While a growing body of empirical work reports substantial gains with algorithms such as DROPO, the theoretical foundations of ODR remain largely unexplored. In this work, we (i) formalize ODR as a maximum-likelihood estimation over a parametric simulator family, (ii) prove consistency of this estimator under mild regularity and identifiability conditions, showing it converges to the true dynamics as the dataset grows, (iii) derive gap bounds demonstrating ODRs sim-to-real error is up to an O(M) factor tighter than uniform DR in the finite-simulator case (and analogous gains in the continuous setting), and (iv) introduce E-DROPO, a new version of DROPO which adds an entropy bonus to prevent variance collapse, yielding broader randomization and more robust zero-shot transfer in practice.

--Vision-and-language navigation (VLN) is a long-standing challenge in autonomous robotics, aiming to empower agents with the ability to follow human instructions while navigating complex environments. Two key bottlenecks remain in this field: generalization to out-of-distribution environments and reliance on fixed discrete action spaces. To address these challenges, we propose Vision-Language Fly (VLFly), a framework tailored for Unmanned Aerial Vehicles (UAVs) to execute language-guided flight. Without the requirement for localization or active ranging sensors, VLFly outputs continuous velocity commands purely from egocentric observations captured by an onboard monocular camera. The VLFly integrates three modules: an instruction encoder based on a large language model (LLM) that reformulates high-level language into structured prompts, a goal retriever powered by a vision-language model (VLM) that matches these prompts to goal images via vision-language similarity, and a waypoint planner that generates executable trajectories for real-time UAV control. VLFly is evaluated across diverse simulation environments without additional fine-tuning and consistently outperforms all baselines. Moreover, real-world VLN tasks in indoor and outdoor environments under direct and indirect instructions demonstrate that VLFly achieves robust open-vocabulary goal understanding and generalized navigation capabilities, even in the presence of abstract language input. The capability of robots to execute complex tasks based on natural language instructions has long been a compelling objective in robotics and artificial intelligence (AI). Particularly within the field of autonomous navigation, this capability enables applications spanning home assistance [1], urban inspection [2], and environmental exploration [3]. Y uhang Zhang and Haosheng Y u are co-first authors.

The safety validation of Advanced Driver Assistance Systems (ADAS) and Automated Driving Systems (ADS) increasingly demands efficient and reliable methods to quantify residual risk while adhering to international standards such as ISO 21448. Traditionally, Field Operational Testing (FOT) has been pivotal for macroscopic safety validation of automotive driving functions up to SAE automation level 2. However, state-of-the-art derivations for empirical safety demonstrations using FOT often result in impractical testing efforts, particularly at higher automation levels. Even at lower automation levels, this limitation - coupled with the substantial costs associated with FOT - motivates the exploration of approaches to enhance the efficiency of FOT-based macroscopic safety validation. Therefore, this publication systematically identifies and evaluates state-of-the-art Reduction Approaches (RAs) for FOT, including novel methods reported in the literature. Based on an analysis of ISO 21448, two models are derived: a generic model capturing the argumentation components of the standard, and a base model, exemplarily applied to Automatic Emergency Braking (AEB) systems, establishing a baseline for the real-world driving requirement for a Quantitative Safety Validation of Residual Risk (QSVRR). Subsequently, the RAs are assessed using four criteria: quantifiability, threats to validity, missing links, and black box compatibility, highlighting potential benefits, inherent limitations, and identifying key areas for further research. Our evaluation reveals that, while several approaches offer potential, none are free from missing links or other substantial shortcomings. Moreover, no identified alternative can fully replace FOT, reflecting its crucial role in the safety validation of ADAS and ADS.

Language models are essentially probability distributions over token sequences. Auto-regressive models generate sentences by iteratively computing and sampling from the distribution of the next token. This iterative sampling introduces stochasticity, leading to the assumption that language models make probabilistic decisions, similar to sampling from unknown distributions. Building on this assumption, prior research has used simulated Gibbs sampling, inspired by experiments designed to elicit human priors, to infer the priors of language models. In this paper, we revisit a critical question: Do language models possess Bayesian brains? Our findings show that under certain conditions, language models can exhibit near-deterministic decision-making, such as producing maximum likelihood estimations, even with a non-zero sampling temperature. This challenges the sampling assumption and undermines previous methods for eliciting human-like priors. Furthermore, we demonstrate that without proper scrutiny, a system with deterministic behavior undergoing simulated Gibbs sampling can converge to a "false prior." To address this, we propose a straightforward approach to distinguish between stochastic and deterministic decision patterns in Gibbs sampling, helping to prevent the inference of misleading language model priors. We experiment on a variety of large language models to identify their decision patterns under various circumstances. Our results provide key insights in understanding decision making of large language models.