Previous research has shown the benefit Bayesian methods can bring to certain problems within deep learning Gal et al. (2017). However, computing the exact posterior distributions of BNNs is a difficult task as traditional methods such as Markov chain Monte Carlo (MCMC) Hastings (1970) are computationally poorly suited to exploring high dimensional spaces and dealing with large amounts of data. Parametric methods such as variational inference are better suited to these difficulties, but only give an approximation to the posterior distribution. These spaces have been found to be highly complex Izmailov et al. (2021a) and therefore variational methods often give a poor approximation of the posterior. Sequential Monte Carlo (SMC) samplers Doucet et al. (2001) are an alternative to MCMC methods which also provide an empirical estimate of the posterior distribution. SMC samplers are instantly parallelisable Varsi et al. (2021b) and therefore can take advantage of the GPU resources commonly used in machine learning to speed up the training process. MCMC methods often require a warm-up period to adapt the hyperparameters, after which the chains can be parallelised. However, the hyperparameters must remain fixed after this warm-up period to obey stationarity. This means that SMC samplers can be more flexible than 1 arXiv:2505.03797v1

Model-based planning and execution systems offer a principled approach to building flexible autonomous robots that can perform diverse tasks by automatically combining a host of basic skills. This idea is almost as old as modern robotics. Yet, while diverse general-purpose reasoning architectures have been proposed since, general-purpose systems that are integrated with modern robotic platforms have emerged only recently, starting with the influential ROSPlan system. Since then, a growing number of model-based systems for robot task-level control have emerged. In this paper, we consider the diverse design choices and issues existing systems attempt to address, the different solutions proposed so far, and suggest avenues for future development.

Generating a synthetic population that is both feasible and diverse is crucial for ensuring the validity of downstream activity schedul e simulation in activity - based models (ABMs) . While deep generative models (DGMs), such as variational autoencoders and g enerative adversarial networks, have been applied to this task, they often struggle to balance the inclusion of rare but plausible combinations (i.e., sampling zeros) with the exclusion of implausible ones (i.e., structural zeros). To improve feasibility while maintaining diversity, we propose a fine - tuning method for large language models (LLMs) that explicitly controls the autoregressive generation process through topological orderings derived from a Bayesian Network (BN). Experimental result s show that our hybrid LLM - BN approach outperform s both traditional DGMs and proprietary LLMs (e.g., ChatGPT - 4o) with few - shot learning. Specifically, our approach achieves approximately 95% feasibility -- significantly higher than the ~80% observed in DGMs -- w hile maintaining comparable diversity, making it well - suited for practical applications. Importantly, the method is based on a lightweight open - source LLM, enabling fine - tuning and inference on standard personal computing environments. This makes the appro ach cost - effective and scalable for large - scale applications, such as synthesizing populations in megacities, without relying on expensive infrastructure. By initiating the ABM pipeline with high - quality synthetic populations, our method improves overall s imulation reliability and reduces downstream error propagation. The source code for these methods is available for research and practical application.

Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational problem posed by reasoning. Inspired by human reasoning, we introduce a method of first-order relational probabilistic inference that satisfies both criteria, and can handle hybrid (discrete and continuous) variables. Specifically, we extend sum-of-squares logic of expectation to relational settings, demonstrating that lifted reasoning in the bounded-degree fragment for knowledge bases of bounded quantifier rank can be performed in polynomial time, even with an a priori unknown and/or countably infinite set of objects. Crucially, our notion of tractability is framed in proof-theoretic terms, which extends beyond the syntactic properties of the language or queries. We are able to derive the tightest bounds provable by proofs of a given degree and size and establish completeness in our sum-of-squares refutations for fixed degrees.

Evaluating machine learning models is crucial not only for determining their technical accuracy but also for assessing their potential societal implications. While the potential for low-sample-size bias in algorithms is well known, we demonstrate the significance of sample-size bias induced by combi-natorics in classification metrics. This revelation challenges the efficacy of these metrics in assessing bias with high resolution, especially when comparing groups of disparate sizes, which frequently arise in social applications. We provide analyses of the bias that appears in several commonly applied metrics and propose a model-agnostic assessment and correction technique. Additionally, we analyze counts of undefined cases in metric calculations, which can lead to misleading evaluations if improperly handled. This work illuminates the previously unrecognized challenge of combinatorics and probability in standard evaluation practices and thereby advances approaches for performing fair and trustworthy classification methods.

Probabilistic survival analysis models seek to estimate the distribution of the future occurrence (time) of an event given a set of covariates. In recent years, these models have preferred nonparametric specifications that avoid directly estimating survival distributions via discretization. Specifically, they estimate the probability of an individual event at fixed times or the time of an event at fixed probabilities (quantiles), using supervised learning. Borrowing ideas from the quantile regression literature, we propose a parametric survival analysis method based on the Asymmetric Laplace Distribution (ALD). This distribution allows for closed-form calculation of popular event summaries such as mean, median, mode, variation, and quantiles. The model is optimized by maximum likelihood to learn, at the individual level, the parameters (location, scale, and asymmetry) of the ALD distribution. Extensive results on synthetic and real-world data demonstrate that the proposed method outperforms parametric and nonparametric approaches in terms of accuracy, discrimination and calibration.

Neurofeedback training (NFT) aims to teach self-regulation of brain activity through real-time feedback, but suffers from highly variable outcomes and poorly understood mechanisms, hampering its validation. To address these issues, we propose a formal computational model of the NFT closed loop. Using Active Inference, a Bayesian framework modelling perception, action, and learning, we simulate agents interacting with an NFT environment. This enables us to test the impact of design choices (e.g., feedback quality, biomarker validity) and subject factors (e.g., prior beliefs) on training. Simulations show that training effectiveness is sensitive to feedback noise or bias, and to prior beliefs (highlighting the importance of guiding instructions), but also reveal that perfect feedback is insufficient to guarantee high performance. This approach provides a tool for assessing and predicting NFT variability, interpret empirical data, and potentially develop personalized training protocols.

Human education transcends mere knowledge transfer, it relies on co-adaptation dynamics -- the mutual adjustment of teaching and learning strategies between agents. Despite its centrality, computational models of co-adaptive teacher-student interactions (T-SI) remain underdeveloped. We argue that this gap impedes Educational Science in testing and scaling contextual insights across diverse settings, and limits the potential of Machine Learning systems, which struggle to emulate and adaptively support human learning processes. To address this, we present a computational T-SI model that integrates contextual insights on human education into a testable framework. We use the model to evaluate diverse T-SI strategies in a realistic synthetic classroom setting, simulating student groups with unequal access to sensory information. Results show that strategies incorporating co-adaptation principles (e.g., bidirectional agency) outperform unilateral approaches (i.e., where only the teacher or the student is active), improving the learning outcomes for all learning types. Beyond the testing and scaling of context-dependent educational insights, our model enables hypothesis generation in controlled yet adaptable environments. This work bridges non-computational theories of human education with scalable, inclusive AI in Education systems, providing a foundation for equitable technologies that dynamically adapt to learner needs.

Data derived from remote sensing or numerical simulations often have a regular gridded structure and are large in volume, making it challenging to find accurate spatial models that can fill in missing grid cells or simulate the process effectively, especially in the presence of spatial heterogeneity and heavy-tailed marginal distributions. To overcome this issue, we present a spatial autoregressive modeling framework, which maps observations at a location and its neighbors to independent random variables. This is a highly flexible modeling approach and well-suited for non-Gaussian fields, providing simpler interpretability. In particular, we consider the SAR model with Generalized Extreme Value distribution innovations to combine the observation at a central grid location with its neighbors, capturing extreme spatial behavior based on the heavy-tailed innovations. While these models are fast to simulate by exploiting the sparsity of the key matrices in the computations, the maximum likelihood estimation of the parameters is prohibitive due to the intractability of the likelihood, making optimization challenging. To overcome this, we train a convolutional neural network on a large training set that covers a useful parameter space, and then use the trained network for fast parameter estimation. Finally, we apply this model to analyze annual maximum precipitation data from ERA-Interim-driven Weather Research and Forecasting (WRF) simulations, allowing us to explore its spatial extreme behavior across North America.

We propose a novel nonparametric approach for linking covariates to Continuous Time Markov Chains (CTMCs) using the mathematical framework of Reproducing Kernel Hilbert Spaces (RKHS). CTMCs provide a robust framework for modeling transitions across clinical or behavioral states, but traditional multistate models often rely on linear relationships. In contrast, we use a generalized Representer Theorem to enable tractable inference in functional space. For the Frequen-tist version, we apply normed square penalties, while for the Bayesian version, we explore sparsity inducing spike and slab priors. Due to the computational challenges posed by high-dimensional spaces, we successfully adapt the Expectation Maximization Variable Selection (EMVS) algorithm to efficiently identify the posterior mode. We demonstrate the effectiveness of our method through extensive simulation studies and an application to follicular cell lymphoma data. Our performance metrics include the normalized difference between estimated and true nonlinear transition functions, as well as the difference in the probability of getting absorbed in one the final states, capturing the ability of our approach to predict long-term behaviors.