The asymptotic properties of Bayesian Neural Networks (BNNs) have been extensively studied, particularly regarding their approximations by Gaussian processes in the infinite-width limit. We extend these results by showing that posterior BNNs can be approximated by Student-t processes, which offer greater flexibility in modeling uncertainty. Specifically, we show that, if the parameters of a BNN follow a Gaussian prior distribution, and the variance of both the last hidden layer and the Gaussian likelihood function follows an Inverse-Gamma prior distribution, then the resulting posterior BNN converges to a Student-t process in the infinite-width limit. Our proof leverages the Wasserstein metric to establish control over the convergence rate of the Student-t process approximation.

Synthetic data generation for tabular datasets must balance fidelity, efficiency, and versatility to meet the demands of real-world applications. We introduce the Tabular Auto-Regressive Generative Network (TabularARGN), a flexible framework designed to handle mixed-type, multivariate, and sequential datasets. By training on all possible conditional probabilities, TabularARGN supports advanced features such as fairness-aware generation, imputation, and conditional generation on any subset of columns. The framework achieves state-of-the-art synthetic data quality while significantly reducing training and inference times, making it ideal for large-scale datasets with diverse structures. Evaluated across established benchmarks, including realistic datasets with complex relationships, TabularARGN demonstrates its capability to synthesize high-quality data efficiently. By unifying flexibility and performance, this framework paves the way for practical synthetic data generation across industries.

Availability of datasets is a strong driver for research on 3D semantic understanding, and whilst obtaining unlabeled 3D point cloud data is straightforward, manually annotating this data with semantic labels is time-consuming and costly. Recently, Vision Foundation Models (VFMs) enable open-set semantic segmentation on camera images, potentially aiding automatic labeling. However,VFMs for 3D data have been limited to adaptations of 2D models, which can introduce inconsistencies to 3D labels. This work introduces Label Any Pointcloud (LeAP), leveraging 2D VFMs to automatically label 3D data with any set of classes in any kind of application whilst ensuring label consistency. Using a Bayesian update, point labels are combined into voxels to improve spatio-temporal consistency. A novel 3D Consistency Network (3D-CN) exploits 3D information to further improve label quality. Through various experiments, we show that our method can generate high-quality 3D semantic labels across diverse fields without any manual labeling. Further, models adapted to new domains using our labels show up to a 34.2 mIoU increase in semantic segmentation tasks.

The estimation of uncertainties associated with predictions from quantitative structure-activity relationship (QSAR) models can accelerate the drug discovery process by identifying promising experiments and allowing an efficient allocation of resources. Several computational tools exist that estimate the predictive uncertainty in machine learning models. However, deviations from the i.i.d. setting have been shown to impair the performance of these uncertainty quantification methods. We use a real-world pharmaceutical dataset to address the pressing need for a comprehensive, large-scale evaluation of uncertainty estimation methods in the context of realistic distribution shifts over time. We investigate the performance of several uncertainty estimation methods, including ensemble-based and Bayesian approaches. Furthermore, we use this real-world setting to systematically assess the distribution shifts in label and descriptor space and their impact on the capability of the uncertainty estimation methods. Our study reveals significant shifts over time in both label and descriptor space and a clear connection between the magnitude of the shift and the nature of the assay. Moreover, we show that pronounced distribution shifts impair the performance of popular uncertainty estimation methods used in QSAR models. This work highlights the challenges of identifying uncertainty quantification methods that remain reliable under distribution shifts introduced by real-world data.

The successful application of modern machine learning for time series classification is often hampered by limitations in quality and quantity of available training data. To overcome these limitations, available domain expert knowledge in the form of parametrised mechanistic dynamical models can be used whenever it is available and time series observations may be represented as an element from a given class of parametrised dynamical models. This makes the learning process interpretable and allows the modeller to deal with sparsely and irregularly sampled data in a natural way. However, the internal processes of a dynamical model are often only partially observed. This can lead to ambiguity regarding which particular model realization best explains a given time series observation. This problem is well-known in the literature, and a dynamical model with this issue is referred to as structurally unidentifiable. Training a classifier that incorporates knowledge about a structurally unidentifiable dynamical model can negatively influence classification performance. To address this issue, we employ structural identifiability analysis to explicitly relate parameter configurations that are associated with identical system outputs. Using the derived relations in classifier training, we demonstrate that this method significantly improves the classifier's ability to generalize to unseen data on a number of example models from the biomedical domain. This effect is especially pronounced when the number of training instances is limited. Our results demonstrate the importance of accounting for structural identifiability, a topic that has received relatively little attention from the machine learning community.

Simulation-based calibration checking (SBC) refers to the validation of an inference algorithm and model implementation through repeated inference on data simulated from a generative model. In the original and commonly used approach, the generative model uses parameters drawn from the prior, and thus the approach is testing whether the inference works for simulated data generated with parameter values plausible under that prior. This approach is natural and desirable when we want to test whether the inference works for a wide range of datasets we might observe. However, after observing data, we are interested in answering whether the inference works conditional on that particular data. In this paper, we propose posterior SBC and demonstrate how it can be used to validate the inference conditionally on observed data. We illustrate the utility of posterior SBC in three case studies: (1) A simple multilevel model; (2) a model that is governed by differential equations; and (3) a joint integrative neuroscience model which is approximated via amortized Bayesian inference with neural networks.

In this paper, a Convolution-Based Converter (CBC) is proposed to develop a methodology for removing the strong or fixed priors in estimating the probability distribution of targets based on observations in the stochastic process. Traditional approaches, e.g., Markov-based and Gaussian process-based methods, typically leverage observations to estimate targets based on strong or fixed priors (such as Markov properties or Gaussian prior). However, the effectiveness of these methods depends on how well their prior assumptions align with the characteristics of the problem. When the assumed priors are not satisfied, these approaches may perform poorly or even become unusable. To overcome the above limitation, we introduce the Convolution-Based converter (CBC), which implicitly estimates the conditional probability distribution of targets without strong or fixed priors, and directly outputs the expected trajectory of the stochastic process that satisfies the constraints from observations. This approach reduces the dependence on priors, enhancing flexibility and adaptability in modeling stochastic processes when addressing different problems. Experimental results demonstrate that our method outperforms existing baselines across multiple metrics.

Student performance prediction is one of the most important subjects in educational data mining. As a modern technology, machine learning offers powerful capabilities in feature extraction and data modeling, providing essential support for diverse application scenarios, as evidenced by recent studies confirming its effectiveness in educational data mining. However, despite extensive prediction experiments, machine learning methods have not been effectively integrated into practical teaching strategies, hindering their application in modern education. In addition, massive features as input variables for machine learning algorithms often leads to information redundancy, which can negatively impact prediction accuracy. Therefore, how to effectively use machine learning methods to predict student performance and integrate the prediction results with actual teaching scenarios is a worthy research subject. To this end, this study integrates the results of machine learning-based student performance prediction with tiered instruction, aiming to enhance student outcomes in target course, which is significant for the application of educational data mining in contemporary teaching scenarios. Specifically, we collect original educational data and perform feature selection to reduce information redundancy. Then, the performance of five representative machine learning methods is analyzed and discussed with Random Forest showing the best performance. Furthermore, based on the results of the classification of students, tiered instruction is applied accordingly, and different teaching objectives and contents are set for all levels of students. The comparison of teaching outcomes between the control and experimental classes, along with the analysis of questionnaire results, demonstrates the effectiveness of the proposed framework.

We introduce a Bayesian framework for measuring spatio-temporal couplings (STCs) in ultra-intense lasers that reconceptualizes what constitutes a 'single-shot' measurement. Moving beyond traditional distinctions between single- and multi-shot devices, our approach provides rigorous criteria for determining when measurements can truly resolve individual laser shots rather than statistical averages. This framework shows that single-shot capability is not an intrinsic device property but emerges from the relationship between measurement precision and inherent parameter variability. Implementing this approach with a new measurement device at the ATLAS-3000 petawatt laser, we provide the first quantitative uncertainty bounds on pulse front tilt and curvature. Notably, we observe that our Bayesian method reduces uncertainty by up to 60% compared to traditional approaches. Through this analysis, we reveal how the interplay between measurement precision and intrinsic system variability defines achievable resolution -- insights that have direct implications for applications where precise control of laser-matter interaction is critical.

In this paper, we investigate the label shift quantification problem. We propose robust estimators of the label distribution which turn out to coincide with the Maximum Likelihood Estimator. We analyze the theoretical aspects and derive deviation bounds for the proposed method, providing optimal guarantees in the well-specified case, along with notable robustness properties against outliers and contamination. Our results provide theoretical validation for empirical observations on the robustness of Maximum Likelihood Label Shift.