Related papers: Learning Graphical Factor Models with Riemannian O…

Factor graph, as a bipartite graphical model, offers a structured representation by revealing local connections among graph nodes. This study explores the utilization of factor graphs in modeling the autonomous racecar planning problem,…

We present and analyze an algorithm designed for addressing vector-valued regression problems involving possibly infinite-dimensional input and output spaces. The algorithm is a randomized adaptation of reduced rank regression, a technique…

Functional Gaussian graphical models (GGM) used for analyzing multivariate functional data customarily estimate an unknown graphical model representing the conditional relationships between the functional variables. However, in many…

Geometric optimisation algorithms are developed that efficiently find the nearest low-rank correlation matrix. We show, in numerical tests, that our methods compare favourably to the existing methods in the literature. The connection with…

This work proposes an algorithmic framework to learn time-varying graphs from online data. The generality offered by the framework renders it model-independent, i.e., it can be theoretically analyzed in its abstract formulation and then…

The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over…

Graphical models are a powerful tool to estimate a high-dimensional inverse covariance (precision) matrix, which has been applied for a portfolio allocation problem. The assumption made by these models is a sparsity of the precision matrix.…

Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, existing approaches…

Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…

The low-rank matrix completion problem can be solved by Riemannian optimization on a fixed-rank manifold. However, a drawback of the known approaches is that the rank parameter has to be fixed a priori. In this paper, we consider the…

Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. It is well known that structured graph learning from observed samples is an NP-hard combinatorial problem. In…

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…

In this paper, we develop a novel weighted Laplacian method, which is partially inspired by the theory of graph Laplacian, to study recent popular graph problems, such as multilevel graph partitioning and balanced minimum cut problem, in a…

The aim of this paper is to propose a novel framework to infer the sheaf Laplacian, including the topology of a graph and the restriction maps, from a set of data observed over the nodes of a graph. The proposed method is based on sheaf…

Graphical models have been popularly used for capturing conditional independence structure in multivariate data, which are often built upon independent and identically distributed observations, limiting their applicability to complex…

This paper presents a novel factor graph-based approach to solve the discrete-time finite-horizon Linear Quadratic Regulator problem subject to auxiliary linear equality constraints within and across time steps. We represent such optimal…

Laplacian regularized stratified models (LRSM) are models that utilize the explicit or implicit network structure of the sub-problems as defined by the categorical features called strata (e.g., age, region, time, forecast horizon, etc.),…

We consider the problem of learning low-rank tensors from partial observations with structural constraints, and propose a novel factorization of such tensors, which leads to a simpler optimization problem. The resulting problem is an…

Graph coarsening is a widely used dimensionality reduction technique for approaching large-scale graph machine learning problems. Given a large graph, graph coarsening aims to learn a smaller-tractable graph while preserving the properties…

We propose a novel method to optimize the structure of factor graphs for graph-based inference. As an example inference task, we consider symbol detection on linear inter-symbol interference channels. The factor graph framework has the…