Trustworthy multi-view classification (TMVC) addresses the challenge of achieving reliable decision-making in complex scenarios where multi-source information is heterogeneous, inconsistent, or even conflicting. Existing TMVC approaches predominantly rely on globally dense neighbor relationships to model intra-view dependencies, leading to high computational costs and an inability to directly ensure consistency across inter-view relationships. Furthermore, these methods typically aggregate evidence from different views through manually assigned weights, lacking guarantees that the learned multi-view neighbor structures are consistent within the class space, thus undermining the trustworthiness of classification outcomes. To overcome these limitations, we propose a novel TMVC framework that introduces prototypes to represent the neighbor structures of each view. By simplifying the learning of intra-view neighbor relations and enabling dynamic alignment of intra- and inter-view structure, our approach facilitates more efficient and consistent discovery of cross-view consensus. Extensive experiments on multiple public multi-view datasets demonstrate that our method achieves competitive downstream performance and robustness compared to prevalent TMVC methods.

The increasing availability of data and advancements in computational intelligence have accelerated the adoption of data-driven methods (DDMs) in product development. However, their integration into product development remains fragmented. This fragmentation stems from uncertainty, particularly the lack of clarity on what types of DDMs to use and when to employ them across the product development lifecycle. To address this, a necessary first step is to investigate the usage of DDM in engineering design by identifying which methods are being used, at which development stages, and for what application. This paper presents a PRISMA systematic literature review. The V-model as a product development framework was adopted and simplified into four stages: system design, system implementation, system integration, and validation. A structured search across Scopus, Web of Science, and IEEE Xplore (2014--2024) retrieved 1{,}689 records. After screening, 114 publications underwent full-text analysis. Findings show that machine learning (ML) and statistical methods dominate current practice, whereas deep learning (DL), though still less common, exhibits a clear upward trend in adoption. Additionally, supervised learning, clustering, regression analysis, and surrogate modeling are prevalent in design, implementation, and integration system stages but contributions to validation remain limited. Key challenges in existing applications include limited model interpretability, poor cross-stage traceability, and insufficient validation under real-world conditions. Additionally, it highlights key limitations and opportunities such as the need for interpretable hybrid models. This review is a first step toward design-stage guidelines; a follow-up synthesis should map computer science algorithms to engineering design problems and activities.

Deep actor-critic algorithms have reached a level where they influence everyday life. They are a driving force behind continual improvement of large language models through user feedback. However, their deployment in physical systems is not yet widely adopted, mainly because no validation scheme fully quantifies their risk of malfunction. We demonstrate that it is possible to develop tight risk certificates for deep actor-critic algorithms that predict generalization performance from validation-time observations. Our key insight centers on the effectiveness of minimal evaluation data. A small feasible set of evaluation roll-outs collected from a pretrained policy suffices to produce accurate risk certificates when combined with a simple adaptation of PAC-Bayes theory. Specifically, we adopt a recently introduced recursive PAC-Bayes approach, which splits validation data into portions and recursively builds PAC-Bayes bounds on the excess loss of each portion's predictor, using the predictor from the previous portion as a data-informed prior. Our empirical results across multiple locomotion tasks, actor-critic methods, and policy expertise levels demonstrate risk certificates tight enough to be considered for practical use.

Variational Bayes methods are popular due to their computational efficiency and adaptability to diverse applications. In specifying the variational family, mean-field classes are commonly used, which enables efficient algorithms such as coordinate ascent variational inference (CAVI) but fails to capture parameter dependence and typically underestimates uncertainty. In this work, we introduce a variational bagging approach that integrates a bagging procedure with variational Bayes, resulting in a bagged variational posterior for improved inference. We establish strong theoretical guarantees, including posterior contraction rates for general models and a Bernstein-von Mises (BVM) type theorem that ensures valid uncertainty quantification. Notably, our results show that even when using a mean-field variational family, our approach can recover off-diagonal elements of the limiting covariance structure and provide proper uncertainty quantification. In addition, variational bagging is robust to model misspecification, with covariance structures matching those of the target covariance. We illustrate our variational bagging method in numerical studies through applications to parametric models, finite mixture models, deep neural networks, and variational autoencoders (VAEs).

Modeling nonlinear systems with Volterra series is challenging because the number of kernel coefficients grows exponentially with the model order. This work introduces Bayesian Tensor Network Volterra kernel machines (BTN-V), extending the Bayesian Tensor Network framework to Volterra system identification. BTN-V represents Volterra kernels using canonical polyadic decomposition, reducing model complexity from O(I^D) to O(DIR). By treating all tensor components and hyperparameters as random variables, BTN-V provides predictive uncertainty estimation at no additional computational cost. Sparsity-inducing hierarchical priors enable automatic rank determination and the learning of fading-memory behavior directly from data, improving interpretability and preventing overfitting. Empirical results demonstrate competitive accuracy, enhanced uncertainty quantification, and reduced computational cost.

The predict-then-optimize paradigm bridges online learning and contextual optimization in dynamic environments. Previous works have investigated the sequential updating of predictors using feedback from downstream decisions to minimize regret in the full-information settings. However, existing approaches are predominantly frequentist, rely heavily on gradient-based strategies, and employ deterministic predictors that could yield high variance in practice despite their asymptotic guarantees. This work introduces, to the best of our knowledge, the first Bayesian online contextual optimization framework. Grounded in PAC-Bayes theory and general Bayesian updating principles, our framework achieves $\mathcal{O}(\sqrt{T})$ regret for bounded and mixable losses via a Gibbs posterior, eliminates the dependence on gradients through sequential Monte Carlo samplers, and thereby accommodates nondifferentiable problems. Theoretical developments and numerical experiments substantiate our claims.

We derive a new theoretical interpretation of the reweighted losses that are widely used for training diffusion models. Our method is based on constructing a cascade of time-dependent variational lower bounds on the data log-likelihood, that provably improves upon the standard evidence lower bound and results in reduced data-model KL-divergences. Combining such bounds gives rise to reweighted objectives that can be applied to any generative diffusion model including both continuous Gaussian diffusion and masked (discrete) diffusion models. Then, we showcase this framework in masked diffusion and report significant improvements over previous training losses in pixel-space image modeling, approaching sample quality comparable to continuous diffusion models. Our results also provide a theoretical justification for the simple weighting scheme widely used in masked image models.

This study investigates the limitations of applying Markov Chain Monte Carlo (MCMC) methods to arbitrary objective functions, focusing on a two-block MCMC framework which alternates between Metropolis-Hastings and Gibbs sampling. While such approaches are often considered advantageous for enabling data-driven regularization, we show that their performance critically depends on the sharpness of the employed likelihood form. By introducing a sharpness parameter and exploring alternative likelihood formulations proportional to the target objective function, we demonstrate how likelihood curvature governs both in-sample performance and the degree of regularization inferred by the training data. Empirical applications are conducted on reinforcement learning tasks: including a navigation problem and the game of tic-tac-toe. The study concludes with a separate analysis examining the implications of extreme likelihood sharpness on arbitrary objective functions stemming from the classic game of blackjack, where the first block of the two-block MCMC framework is replaced with an iterative optimization step. The resulting hybrid approach achieves performance nearly identical to the original MCMC framework, indicating that excessive likelihood sharpness effectively collapses posterior mass onto a single dominant mode.

The Heckman selection model is one of the most well-renounced econometric models in the analysis of data with sample selection. This model is designed to rectify sample selection biases based on the assumption of bivariate normal error terms. However, real data diverge from this assumption in the presence of heavy tails and/or atypical observations. Recently, this assumption has been relaxed via a more flexible Student's t-distribution, which has appealing statistical properties. This paper introduces a novel Heckman selection model using a bivariate contaminated normal distribution for the error terms. We present an efficient ECM algorithm for parameter estimation with closed-form expressions at the E-step based on truncated multinormal distribution formulas. The identifiability of the proposed model is also discussed, and its properties have been examined. Through simulation studies, we compare our proposed model with the normal and Student's t counterparts and investigate the finite-sample properties and the variation in missing rate. Results obtained from two real data analyses showcase the usefulness and effectiveness of our model. The proposed algorithms are implemented in the R package HeckmanEM.

We address the challenge of efficient exploration in model-based reinforcement learning (MBRL), where the system dynamics are unknown and the RL agent must learn directly from online interactions. We propose Scalable and Optimistic MBRL (SOMBRL), an approach based on the principle of optimism in the face of uncertainty. SOMBRL learns an uncertainty-aware dynamics model and greedily maximizes a weighted sum of the extrinsic reward and the agent's epistemic uncertainty. SOMBRL is compatible with any policy optimizers or planners, and under common regularity assumptions on the system, we show that SOMBRL has sublinear regret for nonlinear dynamics in the (i) finite-horizon, (ii) discounted infinite-horizon, and (iii) non-episodic settings. Additionally, SOMBRL offers a flexible and scalable solution for principled exploration. We evaluate SOMBRL on state-based and visual-control environments, where it displays strong performance across all tasks and baselines. We also evaluate SOMBRL on a dynamic RC car hardware and show SOMBRL outperforms the state-of-the-art, illustrating the benefits of principled exploration for MBRL.