Related papers: Estimation of sparse Gaussian graphical models wit…
Gaussian graphical models are of great interest in statistical learning. Because the conditional independencies between different nodes correspond to zero entries in the inverse covariance matrix of the Gaussian distribution, one can learn…
The community detection problem for graphs asks one to partition the n vertices V of a graph G into k communities, or clusters, such that there are many intracluster edges and few intercluster edges. Of course this is equivalent to finding…
We present a probabilistic graphical model formulation for the graph clustering problem. This enables to locally represent uncertainty of image partitions by approximate marginal distributions in a mathematically substantiated way, and to…
We develop here a semiparametric Gaussian mixture model (SGMM) for unsupervised learning with valuable spatial information taken into consideration. Specifically, we assume for each instance a random location. Then, conditional on this…
Recent advances in 3D Gaussian Splatting (3DGS) have demonstrated remarkable capabilities in real-time and photorealistic novel view synthesis. However, traditional 3DGS representations often struggle with large-scale scene management and…
Gaussian graphical models are relevant tools to learn conditional independence structure between variables. In this class of models, Bayesian structure learning is often done by search algorithms over the graph space. The conjugate prior…
The Gaussian graphical model, a popular paradigm for studying relationship among variables in a wide range of applications, has attracted great attention in recent years. This paper considers a fundamental question: When is it possible to…
Gaussian mixture block models are distributions over graphs that strive to model modern networks: to generate a graph from such a model, we associate each vertex $i$ with a latent feature vector $u_i \in \mathbb{R}^d$ sampled from a mixture…
Deep latent generative models have attracted increasing attention due to the capacity of combining the strengths of deep learning and probabilistic models in an elegant way. The data representations learned with the models are often…
We address the problem of robust sparse estimation of the precision matrix for heavy-tailed distributions in high-dimensional settings. In such high-dimensional contexts, we observe that the covariance matrix can be approximated by a…
We consider the problem of calibrating an imperfect computer model using experimental data. To compensate the misspecification of the computer model and make more accurate predictions, a discrepancy function is often included and modeled…
Graphical lasso is one of the most used estimators for inferring genetic networks. Despite its diffusion, there are several fields in applied research where the limits of detection of modern measurement technologies make the use of this…
Sparse inverse covariance estimation (i.e., edge de-tection) is an important research problem in recent years, wherethe goal is to discover the direct connections between a set ofnodes in a networked system based upon the observed…
The Augmented Lagragian Method (ALM) and Alternating Direction Method of Multiplier (ADMM) have been powerful optimization methods for general convex programming subject to linear constraint. We consider the convex problem whose objective…
In this paper, we consider the Graphical Lasso (GL), a popular optimization problem for learning the sparse representations of high-dimensional datasets, which is well-known to be computationally expensive for large-scale problems.…
Spectral clustering is a powerful method for finding structure in a dataset through the eigenvectors of a similarity matrix. It often outperforms traditional clustering algorithms such as $k$-means when the structure of the individual…
The computation required for a switching Kalman Filter (SKF) increases exponentially with the number of system operation modes. In this paper, a computationally tractable graph representation is proposed for a switching linear dynamic…
We propose an efficient semi-Lagrangian method for solving the two-dimensional incompressible Euler equations with high precision on a coarse grid. The new approach evolves the flow map using the gradient-augmented level set method (GALSM).…
The problem of the definition and the estimation of generative models based on deformable templates from raw data is of particular importance for modelling non aligned data affected by various types of geometrical variability. This is…
Estimating conditional dependence graphs and precision matrices are some of the most common problems in modern statistics and machine learning. When data are fully observed, penalized maximum likelihood-type estimators have become standard…