Like visual processing, language processing is susceptible to illusions in which people systematically misperceive stimuli. In one such case--the comparative illusion (CI), e.g., More students have been to Russia than I have--comprehenders tend to judge the sentence as acceptable despite its underlying nonsensical comparison. Prior research has argued that this phenomenon can be explained as Bayesian inference over a noisy channel: the posterior probability of an interpretation of a sentence is proportional to both the prior probability of that interpretation and the likelihood of corruption into the observed (CI) sentence. Initial behavioral work has supported this claim by evaluating a narrow set of alternative interpretations of CI sentences and showing that comprehenders favor interpretations that are more likely to have been corrupted into the illusory sentence. In this study, we replicate and go substantially beyond this earlier work by directly predicting the strength of illusion with a quantitative model of the posterior probability of plausible interpretations, which we derive through a novel synthesis of statistical language models with human behavioral data. Our model explains not only the fine gradations in the strength of CI effects, but also a previously unexplained effect caused by pronominal vs. full noun phrase than-clause subjects. These findings support a noisy-channel theory of sentence comprehension by demonstrating that the theory makes novel predictions about the comparative illusion that bear out empirically. This outcome joins related evidence of noisy channel processing in both illusory and non-illusory contexts to support noisy channel inference as a unified computational-level theory of diverse language processing phenomena.

Bayesian networks (BNs) are a widely used class of probabilistic graphical models employed in numerous application domains. However, inferring the network's graphical structure from data remains challenging. Bayesian structure learners approach this problem by inferring a posterior distribution over the possible directed acyclic graphs underlying the BN. The inference process often requires marginalizing over probability distributions, which is typically done using dynamic programming methods that restrict the set of possible parents for each node. Instead, we present a novel method that utilizes tractable probabilistic circuits to circumvent this restriction. This method utilizes a new learning routine that trains these circuits on both the original distribution and marginal queries. The architecture of probabilistic circuits then inherently allows for fast and exact marginalization on the learned distribution. We then show empirically that utilizing our method to answer marginals allows Bayesian structure learners to improve their performance compared to current methods.

Failures are the norm in highly complex and heterogeneous devices spanning the distributed computing continuum (DCC), from resource-constrained IoT and edge nodes to high-performance computing systems. Ensuring reliability and global consistency across these layers remains a major challenge, especially for AI-driven workloads requiring real-time, adaptive coordination. This work-in-progress paper introduces a Probabilistic Active Inference Resilience Agent (PAIR-Agent) to achieve resilience in DCC systems. PAIR-Agent performs three core operations: (i) constructing a causal fault graph from device logs, (ii) identifying faults while managing certainties and uncertainties using Markov blankets and the free energy principle, and (iii) autonomously healing issues through active inference. Through continuous monitoring and adaptive reconfiguration, the agent maintains service continuity and stability under diverse failure conditions. Theoretical validations confirm the reliability and effectiveness of the proposed framework.

Diffusion models (DMs) have emerged as powerful image priors in Bayesian computational imaging. Two primary strategies have been proposed for leveraging DMs in this context: Plug-and-Play methods, which are zero-shot and highly flexible but rely on approximations; and specialized conditional DMs, which achieve higher accuracy and faster inference for specific tasks through supervised training. In this work, we introduce a novel framework that integrates deep unfolding and model distillation to transform a DM image prior into a few-step conditional model for posterior sampling. A central innovation of our approach is the unfolding of a Markov chain Monte Carlo (MCMC) algorithm - specifically, the recently proposed LATINO Langevin sampler (Spagnoletti et al., 2025) - representing the first known instance of deep unfolding applied to a Monte Carlo sampling scheme. We demonstrate our proposed unfolded and distilled samplers through extensive experiments and comparisons with the state of the art, where they achieve excellent accuracy and computational efficiency, while retaining the flexibility to adapt to variations in the forward model at inference time.

To distinguish Markov equivalent graphs in causal discovery, it is necessary to restrict the structural causal model. Crucially, we need to be able to distinguish cause $X$ from effect $Y$ in bivariate models, that is, distinguish the two graphs $X \to Y$ and $Y \to X$. Location-scale noise models (LSNMs), in which the effect $Y$ is modeled based on the cause $X$ as $Y = f(X) + g(X)N$, form a flexible class of models that is general and identifiable in most cases. Estimating these models for arbitrary noise terms $N$, however, is challenging. Therefore, practical estimators are typically restricted to symmetric distributions, such as the normal distribution. As we showcase in this paper, when $N$ is a skewed random variable, which is likely in real-world domains, the reliability of these approaches decreases. To approach this limitation, we propose SkewD, a likelihood-based algorithm for bivariate causal discovery under LSNMs with skewed noise distributions. SkewD extends the usual normal-distribution framework to the skew-normal setting, enabling reliable inference under symmetric and skewed noise. For parameter estimation, we employ a combination of a heuristic search and an expectation conditional maximization algorithm. We evaluate SkewD on novel synthetically generated datasets with skewed noise as well as established benchmark datasets. Throughout our experiments, SkewD exhibits a strong performance and, in comparison to prior work, remains robust under high skewness.

We propose the Modified Mahalanobis Distance Conformal Prediction (MMDCP), a unified framework for multi-class classification and outlier detection under label shift, where the training and test distributions may differ. In such settings, many existing methods construct nonconformity scores based on empirical cumulative or density functions combined with data-splitting strategies. However, these approaches are often computationally expensive due to their heavy reliance on resampling procedures and tend to produce overly conservative prediction sets with unstable coverage, especially in small samples. To address these challenges, MMDCP combines class-specific distance measures with full conformal prediction to construct a score function, thereby producing adaptive prediction sets that effectively capture both inlier and outlier structures. Under mild regularity conditions, we establish convergence rates for the resulting sets and provide the first theoretical characterization of the gap between oracle and empirical conformal $p$-values, which ensures valid coverage and effective control of the class-wise false discovery rate (CW-FDR). We further introduce the Summarized Class-Wise FDR (SCW-FDR), a novel global error metric aggregating false discoveries across classes, and show that it can be effectively controlled within the MMDCP framework. Extensive simulations and two real-data applications support our theoretical findings and demonstrate the advantages of the proposed method.

Coral bleaching is a major concern for marine ecosystems; more than half of the world's coral reefs have either bleached or died over the past three decades. Increasing sea surface temperatures, along with various spatiotemporal environmental factors, are considered the primary reasons behind coral bleaching. The statistical and machine learning communities have focused on multiple aspects of the environment in detail. However, the literature on various stochastic modeling approaches for assessing coral bleaching is extremely scarce. Data-driven strategies are crucial for effective reef management, and this review article provides an overview of existing statistical and machine learning methods for assessing coral bleaching. Statistical frameworks, including simple regression models, generalized linear models, generalized additive models, Bayesian regression models, spatiotemporal models, and resilience indicators, such as Fisher's Information and Variance Index, are commonly used to explore how different environmental stressors influence coral bleaching. On the other hand, machine learning methods, including random forests, decision trees, support vector machines, and spatial operators, are more popular for detecting nonlinear relationships, analyzing high-dimensional data, and allowing integration of heterogeneous data from diverse sources. In addition to summarizing these models, we also discuss potential data-driven future research directions, with a focus on constructing statistical and machine learning models in specific contexts related to coral bleaching.

Intermittent demand forecasting poses unique challenges due to sparse observations, cold-start items, and obsolescence. Classical models such as Croston, SBA, and the Teunter-Syntetos-Babai (TSB) method provide simple heuristics but lack a principled generative foundation. Deep learning models address these limitations but often require large datasets and sacrifice interpretability. We introduce TSB-HB, a hierarchical Bayesian extension of TSB. Demand occurrence is modeled with a Beta-Binomial distribution, while nonzero demand sizes follow a Log-Normal distribution. Crucially, hierarchical priors enable partial pooling across items, stabilizing estimates for sparse or cold-start series while preserving heterogeneity. This framework yields a fully generative and interpretable model that generalizes classical exponential smoothing. On the UCI Online Retail dataset, TSB-HB achieves lower RMSE and RMSSE than Croston, SBA, TSB, ADIDA, IMAPA, ARIMA and Theta, and on a subset of the M5 dataset it outperforms all classical baselines we evaluate. The model provides calibrated probabilistic forecasts and improved accuracy on intermittent and lumpy items by combining a generative formulation with hierarchical shrinkage, while remaining interpretable and scalable.

Adversarial robustness remains a critical challenge in deploying neural network classifiers, particularly in real-time systems where ground-truth labels are unavailable during inference. This paper investigates \textit{Volatility in Certainty} (VC), a recently proposed, label-free metric that quantifies irregularities in model confidence by measuring the dispersion of sorted softmax outputs. Specifically, VC is defined as the average squared log-ratio of adjacent certainty values, capturing local fluctuations in model output smoothness. We evaluate VC as a proxy for classification accuracy and as an indicator of adversarial drift. Experiments are conducted on artificial neural networks (ANNs) and convolutional neural networks (CNNs) trained on MNIST, as well as a regularized VGG-like model trained on CIFAR-10. Adversarial examples are generated using the Fast Gradient Sign Method (FGSM) across varying perturbation magnitudes. In addition, mixed test sets are created by gradually introducing adversarial contamination to assess VC's sensitivity under incremental distribution shifts. Our results reveal a strong negative correlation between classification accuracy and log(VC) (correlation rho < -0.90 in most cases), suggesting that VC effectively reflects performance degradation without requiring labeled data. These findings position VC as a scalable, architecture-agnostic, and real-time performance metric suitable for early-warning systems in safety-critical applications.