Related papers: Geometry-Aware Langevin Sampling for Matrix-Valued…

Motivated by discrete Laplacian differential operators with various accuracy orders in numerical analysis, we introduce new matrices attached to a simple graph that can be considered graph Laplacians with higher accuracy. In particular, we…

Supervised learning has recently garnered significant attention in the field of computational physics due to its ability to effectively extract complex patterns for tasks like solving partial differential equations, or predicting material…

Probabilistic Latent Variable Models (LVMs) excel at modeling complex, high-dimensional data through lower-dimensional representations. Recent advances show that equipping these latent representations with a Riemannian metric unlocks…

In decision-making systems, it is important to have classifiers that have calibrated uncertainties, with an optimisation objective that can be used for automated model selection and training. Gaussian processes (GPs) provide uncertainty…

Federated learning performed by a decentralized networks of agents is becoming increasingly important with the prevalence of embedded software on autonomous devices. Bayesian approaches to learning benefit from offering more information as…

Though Gaussian graphical models have been widely used in many scientific fields, relatively limited progress has been made to link graph structures to external covariates. We propose a Gaussian graphical regression model, which regresses…

Graph-based semi-supervised learning is a powerful paradigm in machine learning for modeling and exploiting the underlying graph structure that captures the relationship between labeled and unlabeled data. A large number of classical as…

Physics-aware recurrent convolutional networks (PARC) have demonstrated strong performance in predicting nonlinear spatiotemporal dynamics by embedding differential operators directly into the computational graph of a neural network.…

In order to solve tasks like uncertainty quantification or hypothesis tests in Bayesian imaging inverse problems, we often have to draw samples from the arising posterior distribution. For the usually log-concave but high-dimensional…

We propose a novel algorithm for the support estimation of partially known Gaussian graphical models that incorporates prior information about the underlying graph. In contrast to classical approaches that provide a point estimate based on…

The ubiquity of missing data in urban intelligence systems, attributable to adverse environmental conditions and equipment failures, poses a significant challenge to the efficacy of downstream applications, notably in the realms of traffic…

In a graph convolutional network, we assume that the graph $G$ is generated wrt some observation noise. During learning, we make small random perturbations $\Delta{}G$ of the graph and try to improve generalization. Based on quantum…

We propose a geometric latent-subspace framework for generative modeling of discrete data. Specifically, we introduce latent subspaces in the exponential parameter space of product manifolds of categorical distributions as a novel method…

A new approach in stochastic optimization via the use of stochastic gradient Langevin dynamics (SGLD) algorithms, which is a variant of stochastic gradient decent (SGD) methods, allows us to efficiently approximate global minimizers of…

We consider a network topology design problem in which an initial undirected graph underlying the network is given and the objective is to select a set of edges to add to the graph to optimize the coherence of the resulting network. We show…

Generative adversarial networks (GANs) have emerged as a powerful unsupervised method to model the statistical patterns of real-world data sets, such as natural images. These networks are trained to map random inputs in their latent space…

Most Probable Explanation (MPE) inference in Probabilistic Graphical Models (PGMs) is a fundamental yet computationally challenging problem arising in domains such as diagnosis, planning, and structured prediction. In many practical…

Representing images and videos with Symmetric Positive Definite (SPD) matrices and considering the Riemannian geometry of the resulting space has proven beneficial for many recognition tasks. Unfortunately, computation on the Riemannian…

Matrix-valued optimization tasks, including those involving symmetric positive definite (SPD) matrices, arise in a wide range of applications in machine learning, data science and statistics. Classically, such problems are solved via…

Linear discriminant analysis (LDA) is a fundamental classification and dimension reduction method that achieves Bayes optimality under Gaussian mixture, but often struggles in high-dimensional settings where the covariance matrix cannot be…