This work develops a probabilistic child language acquisition model to learn a range of linguistic phenonmena, most notably long-range syntactic dependencies of the sort found in object wh-questions, among other constructions. The model is trained on a corpus of real child-directed speech, where each utterance is paired with a logical form as a meaning representation. It then learns both word meanings and language-specific syntax simultaneously. After training, the model can deduce the correct parse tree and word meanings for a given utterance-meaning pair, and can infer the meaning if given only the utterance. The successful modelling of long-range dependencies is theoretically important because it exploits aspects of the model that are, in general, trans-context-free.

Quantifying model uncertainty is critical for understanding prediction reliability, yet distinguishing between aleatoric and epistemic uncertainty remains challenging. We extend recent work from classification to regression to provide a novel frequentist approach to epistemic and aleatoric uncertainty estimation. We train models to generate conditional predictions by feeding their initial output back as an additional input. This method allows for a rigorous measurement of model uncertainty by observing how prediction responses change when conditioned on the model's previous answer. We provide a complete theoretical framework to analyze epistemic uncertainty in regression in a frequentist way, and explain how it can be exploited in practice to gauge a model's uncertainty, with minimal changes to the original architecture.

Bayesian Neural Networks (BNNs) often improve model calibration and predictive uncertainty quantification compared to point estimators such as maximum-a-posteriori (MAP). Similarly, deep ensembles (DEs) are also known to improve calibration, and therefore, it is natural to hypothesize that deep ensembles of BNNs (DE-BNNs) should provide even further improvements. In this work, we systematically investigate this across a number of datasets, neural network architectures, and BNN approximation methods and surprisingly find that when the ensembles grow large enough, DEs consistently outperform DE-BNNs on in-distribution data. To shine light on this observation, we conduct several sensitivity and ablation studies. Moreover, we show that even though DE-BNNs outperform DEs on out-of-distribution metrics, this comes at the cost of decreased in-distribution performance. As a final contribution, we open-source the large pool of trained models to facilitate further research on this topic.

An important goal in cancer research is the survival prognosis of a patient based on a minimal panel of genomic and molecular markers such as genes or proteins. Purely data-driven models without any biological knowledge can produce non-interpretable results. We propose a penalized semiparametric Bayesian Cox model with graph-structured selection priors for sparse identification of multi-omics features by making use of a biologically meaningful graph via a Markov random field (MRF) prior to capturing known relationships between multi-omics features. Since the fixed graph in the MRF prior is for the prior probability distribution, it is not a hard constraint to determine variable selection, so the proposed model can verify known information and has the potential to identify new and novel biomarkers for drawing new biological knowledge. Our simulation results show that the proposed Bayesian Cox model with graph-based prior knowledge results in more trustable and stable variable selection and non-inferior survival prediction, compared to methods modeling the covariates independently without any prior knowledge. The results also indicate that the performance of the proposed model is robust to a partially correct graph in the MRF prior, meaning that in a real setting where not all the true network information between covariates is known, the graph can still be useful. The proposed model is applied to the primary invasive breast cancer patients data in The Cancer Genome Atlas project.

Effective uncertainty quantification is important for training modern predictive models with limited data, enhancing both accuracy and robustness. While Bayesian methods are effective for this purpose, they can be challenging to scale. When employing approximate Bayesian inference, ensuring the quality of samples from the posterior distribution in a computationally efficient manner is essential. This paper addresses the estimation of the Bayesian posterior to generate diverse samples by approximating the gradient flow of the Kullback-Leibler (KL) divergence and the cross entropy of the target approximation under the metric induced by the Stein Operator. It presents empirical evaluations on classification tasks to assess the method's performance and discuss its effectiveness for Model-Based Reinforcement Learning that uses uncertainty-aware network dynamics models.

This paper introduces the Heteroscedastic AddiVortes model, a Bayesian non-parametric regression framework that simultaneously models the conditional mean and variance of a response variable using adaptive Voronoi tessellations. By employing a sum-of-tessellations approach for the mean and a product-of-tessellations approach for the variance, the model provides a flexible and interpretable means to capture complex, predictor-dependent relationships and heteroscedastic patterns in data. This dual-layer representation enables precise inference, even in high-dimensional settings, while maintaining computational feasibility through efficient Markov Chain Monte Carlo (MCMC) sampling and conjugate prior structures. We illustrate the model's capability through both simulated and real-world datasets, demonstrating its ability to capture nuanced variance structures, provide reliable predictive uncertainty quantification, and highlight key predictors influencing both the mean response and its variability. Empirical results show that the Heteroscedastic AddiVortes model offers a substantial improvement in capturing distributional properties compared to both homoscedastic and heteroscedastic alternatives, making it a robust tool for complex regression problems in various applied settings.

In this paper, we present the amortized optimal transport filter (A-OTF) designed to mitigate the computational burden associated with the real-time training of optimal transport filters (OTFs). OTFs can perform accurate non-Gaussian Bayesian updates in the filtering procedure, but they require training at every time step, which makes them expensive. The proposed A-OTF framework exploits the similarity between OTF maps during an initial/offline training stage in order to reduce the cost of inference during online calculations. More precisely, we use clustering algorithms to select relevant subsets of pre-trained maps whose weighted average is used to compute the A-OTF model akin to a mixture of experts. A series of numerical experiments validate that A-OTF achieves substantial computational savings during online inference while preserving the inherent flexibility and accuracy of OTF.

Text-to-image latent diffusion models (LDMs) have recently emerged as powerful generative models with great potential for solving inverse problems in imaging. However, leveraging such models in a Plug & Play (PnP), zero-shot manner remains challenging because it requires identifying a suitable text prompt for the unknown image of interest. Also, existing text-to-image PnP approaches are highly computationally expensive. We herein address these challenges by proposing a novel PnP inference paradigm specifically designed for embedding generative models within stochastic inverse solvers, with special attention to Latent Consistency Models (LCMs), which distill LDMs into fast generators. We leverage our framework to propose LAtent consisTency INverse sOlver (LATINO), the first zero-shot PnP framework to solve inverse problems with priors encoded by LCMs. Our conditioning mechanism avoids automatic differentiation and reaches SOTA quality in as little as 8 neural function evaluations. As a result, LATINO delivers remarkably accurate solutions and is significantly more memory and computationally efficient than previous approaches. We then embed LATINO within an empirical Bayesian framework that automatically calibrates the text prompt from the observed measurements by marginal maximum likelihood estimation. Extensive experiments show that prompt self-calibration greatly improves estimation, allowing LATINO with PRompt Optimization to define new SOTAs in image reconstruction quality and computational efficiency.

Determining and Determining and verifying product provenance remains a critical verifying product provenance is a challenge in global supply chains, challenge in global supply chains, particularly as geopolitical conflicts as geopolitics and the lure of "don't ask, don't tell" with respect to and shifting borders create new incentives for misrepresentation the ecological and social cost creates incentives for misrepresentation of commodities, such as hiding the origin of illegally harvested of commodities, such as hiding the origin of illegally harvested timber or agriculture grown on illegally cleared land. Stable Isotope timber or agriculture grown on illegally cleared land. Ratio Analysis (SIRA), combined with Gaussian process regressionbased Product identification and provenance verification of traded natural isoscapes, has emerged as a powerful tool for geographic resources have emerged as promising research areas, with origin verification. However, the effectiveness of these models is often various combinations of methods used based on the specific natural constrained by data scarcity and suboptimal dataset selection. In resource sector and the level of granularity of species identification this work, we introduce a novel data valuation framework designed and origin-provenance determination. For example, for wood and to enhance the selection and utilization of training data for machine forest products, determining species identification and geographic learning models applied in SIRA. By prioritizing high-informative harvest provenance requires utilizing multiple testing methods and samples, our approach improves model robustness and predictive tools [5, 8, 20].

Simulation-based Bayesian inference (SBI) methods are widely used for parameter estimation in complex models where evaluating the likelihood is challenging but generating simulations is relatively straightforward. However, these methods commonly assume that the simulation model accurately reflects the true data-generating process, an assumption that is frequently violated in realistic scenarios. In this paper, we focus on the challenges faced by SBI methods under model misspecification. We consolidate recent research aimed at mitigating the effects of misspecification, highlighting three key strategies: i) robust summary statistics, ii) generalised Bayesian inference, and iii) error modelling and adjustment parameters. To illustrate both the vulnerabilities of popular SBI methods and the effectiveness of misspecification-robust alternatives, we present empirical results on an illustrative example.