The field of probabilistic modeling and uncertainty quantification is witnessing significant advancements, driven by the development of novel techniques and the refinement of existing ones. A key direction is the integration of probabilistic methods with deep learning, enabling the estimation of uncertainty in complex models. This is evident in the proliferation of Bayesian neural networks and variational inference methods. Another area of focus is the development of more efficient and scalable algorithms for probabilistic modeling, such as stochastic variance reduced gradient methods and likelihood-weighted normalizing flows. Furthermore, there is a growing interest in applying probabilistic models to real-world problems, including structural health monitoring, cardiac electrophysiology, and digital image correlation. Noteworthy papers in this area include the introduction of Polynomial Neural Sheaf Diffusion, which achieves state-of-the-art results on graph benchmarks, and the proposal of Uncertainty Reasoning with Photonic Bayesian Machines, which enables high-speed trustworthy AI systems. Additionally, the development of Physics-informed self-supervised learning for predictive modeling of coronary artery digital twins demonstrates the potential of probabilistic models in clinical applications.
Emerging Trends in Probabilistic Modeling and Uncertainty Quantification
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KAN-SAs: Efficient Acceleration of Kolmogorov-Arnold Networks on Systolic Arrays
We Still Don't Understand High-Dimensional Bayesian Optimization
Compositional Inference for Bayesian Networks and Causality
Polynomial Neural Sheaf Diffusion: A Spectral Filtering Approach on Cellular Sheaves
Scalable and Interpretable Scientific Discovery via Sparse Variational Gaussian Process Kolmogorov-Arnold Networks (SVGP KAN)
Walking on the Fiber: A Simple Geometric Approximation for Bayesian Neural Networks
A unified framework for geometry-independent operator learning in cardiac electrophysiology simulations
Graph Distance as Surprise: Free Energy Minimization in Knowledge Graph Reasoning
SVRG and Beyond via Posterior Correction
Uncertainty Reasoning with Photonic Bayesian Machines
Embedding networks with the random walk first return time distribution
Adversarial Jamming for Autoencoder Distribution Matching
Physics-informed self-supervised learning for predictive modeling of coronary artery digital twins
Approximate Bayesian Inference on Mechanisms of Network Growth and Evolution
Real-Time Structural Health Monitoring with Bayesian Neural Networks: Distinguishing Aleatoric and Epistemic Uncertainty for Digital Twin Frameworks
Probabilistic Foundations of Fuzzy Simplicial Sets for Nonlinear Dimensionality Reduction
Density-Informed VAE (DiVAE): Reliable Log-Prior Probability via Density Alignment Regularization
Bayes-DIC Net: Estimating Digital Image Correlation Uncertainty with Bayesian Neural Networks
Score Matching for Estimating Finite Point Processes
Amortized Inference of Multi-Modal Posteriors using Likelihood-Weighted Normalizing Flows