Accurately classifying COVID-19 pneumonia in 3D CT scans remains a significant challenge in the field of medical image analysis. Although deterministic neural networks have shown promising results in this area, they provide only point estimates outputs yielding poor diagnostic in clinical decision-making. In this paper, we explore the use of Bayesian neural networks for classifying COVID-19 pneumonia in 3D CT scans providing uncertainties in their predictions. We compare deterministic networks and their Bayesian counterpart, enhancing the decision-making accuracy under uncertainty information. Remarkably, our findings reveal that lightweight architectures achieve the highest accuracy of 96\% after developing extensive hyperparameter tuning. Furthermore, the Bayesian counterpart of these architectures via Multiplied Normalizing Flow technique kept a similar performance along with calibrated uncertainty estimates. Finally, we have developed a 3D-visualization approach to explain the neural network outcomes based on SHAP values. We conclude that explainability along with uncertainty quantification will offer better clinical decisions in medical image analysis, contributing to ongoing efforts for improving the diagnosis and treatment of COVID-19 pneumonia.

We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven learning with physical constraints, our method achieves robust and accurate solutions across diverse scenarios. Bayesian training is implemented through variational inference, allowing for comprehensive uncertainty quantification for both aleatoric and epistemic uncertainties. This ensures reliable predictions and parameter estimates even in noisy conditions or when some of the physical equations governing the problem are missing. The framework demonstrates its efficacy in solving forward and inverse problems, including the 1D unsteady heat equation and 2D reaction-diffusion equations, as well as regression tasks with sparse, noisy observations. This approach provides a computationally efficient and generalizable method for addressing uncertainty quantification in PDE surrogate modeling.

Can we use spiking neural networks (SNN) as generative models of multi-neuronal recordings, while taking into account that most neurons are unobserved? Modeling the unobserved neurons with large pools of hidden spiking neurons leads to severely underconstrained problems that are hard to tackle with maximum likelihood estimation. In this work, we use coarse-graining and mean-field approximations to derive a bottom-up, neuronally-grounded latent variable model (neuLVM), where the activity of the unobserved neurons is reduced to a low-dimensional mesoscopic description. In contrast to previous latent variable models, neuLVM can be explicitly mapped to a recurrent, multi-population SNN, giving it a transparent biological interpretation. We show, on synthetic spike trains, that a few observed neurons are sufficient for neuLVM to perform efficient model inversion of large SNNs, in the sense that it can recover connectivity parameters, infer single-trial latent population activity, reproduce ongoing metastable dynamics, and generalize when subjected to perturbations mimicking optogenetic stimulation.

We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, p(y \mid x), characterize subjective beliefs on outcomes of interest, y, conditional on predictors, x . Bayesian prediction is well-calibrated when the model is true, but the predictive intervals may exhibit poor empirical coverage when the model is misspecified, under the so called {\cal{M}} -open perspective. In contrast, conformal inference provides finite sample frequentist guarantees on predictive confidence intervals without the requirement of model fidelity. Using'add-one-in' importance sampling, we show that conformal Bayesian predictive intervals are efficiently obtained from re-weighted posterior samples of model parameters.

Coverage functions are an important class of discrete functions that capture laws of diminishing returns. In this paper, we propose a new problem of learning time-varying coverage functions which arise naturally from applications in social network analysis, machine learning, and algorithmic game theory. We develop a novel parametrization of the time-varying coverage function by illustrating the connections with counting processes. We present an efficient algorithm to learn the parameters by maximum likelihood estimation, and provide a rigorous theoretic analysis of its sample complexity. Empirical experiments from information diffusion in social network analysis demonstrate that with few assumptions about the underlying diffusion process, our method performs significantly better than existing approaches on both synthetic and real world data.

The goal of sequential event prediction is to estimate the next event based on a sequence of historical events, with applications to sequential recommendation, user behavior analysis and clinical treatment. In practice, the next-event prediction models are trained with sequential data collected at one time and need to generalize to newly arrived sequences in remote future, which requires models to handle temporal distribution shift from training to testing. In this paper, we first take a data-generating perspective to reveal a negative result that existing approaches with maximum likelihood estimation would fail for distribution shift due to the latent context confounder, i.e., the common cause for the historical events and the next event. Then we devise a new learning objective based on backdoor adjustment and further harness variational inference to make it tractable for sequence learning problems. On top of that, we propose a framework with hierarchical branching structures for learning context-specific representations.

Neural signals are typical nonstationary data where the functional mapping between neural activities and the intentions (such as the velocity of movements) can occasionally change. Existing studies mostly use a fixed neural decoder, thus suffering from an unstable performance given neural functional changes. We propose a novel evolutionary ensemble framework (EvoEnsemble) to dynamically cope with changes in neural signals by evolving the decoder model accordingly. EvoEnsemble integrates evolutionary computation algorithms in a Bayesian framework where the fitness of models can be sequentially computed with their likelihoods according to the incoming data at each time slot, which enables online tracking of time-varying functions. Two strategies of evolve-at-changes and history-model-archive are designed to further improve efficiency and stability.

This work presents novel algorithms for learning Bayesian networks of bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed integer linear programming formulations for structure learning and treewidth computation. The approximate method consists in sampling k-trees (maximal graphs of treewidth k), and subsequently selecting, exactly or approximately, the best structure whose moral graph is a subgraph of that k-tree. The approaches are empirically compared to each other and to state-of-the-art methods on a collection of public data sets with up to 100 variables.

We propose new methods for learning Bayesian networks (BNs) that reliably support fast inference. We utilize maximum state space size as a more fine-grained measure for the BN's reasoning complexity than the standard treewidth measure, thereby accommodating the possibility that variables range over domains of different sizes. Our methods combine heuristic BN structure learning algorithms with the recently introduced MaxSAT-powered local improvement method (Peruvemba Ramaswamy and Szeider, AAAI'21). Our experiments show that our new learning methods produce BNs that support significantly faster exact probabilistic inference than BNs learned with treewidth bounds.

However, training and sampling from EBMs continue to pose significant challenges. The widely-used Denoising Score Matching (DSM) method for scalable EBM training suffers from inconsistency issues, causing the energy model to learn a noisy data distribution. In this work, we propose an efficient sampling framework: (pseudo)-Gibbs sampling with moment matching, which enables effective sampling from the underlying clean model when given a noisy model that has been well-trained via DSM. We explore the benefits of our approach compared to related methods and demonstrate how to scale the method to high-dimensional datasets.