相关论文: An Information Geometry Interpretation for Approxi…

The Information Bottleneck (IB) is a conceptual method for extracting the most compact, yet informative, representation of a set of variables, with respect to the target. It generalizes the notion of minimal sufficient statistics from…

The problem of estimating a random vector x from noisy linear measurements y = A x + w with unknown parameters on the distributions of x and w, which must also be learned, arises in a wide range of statistical learning and linear inverse…

High-dimensional time series appear in many scientific setups, demanding a nuanced approach to model and analyze the underlying dependence structure. Theoretical advancements so far often rely on stringent assumptions regarding the sparsity…

This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for approximation of the solution field. The method inherits the main…

Domain generalization aims to learn invariance across multiple training domains, thereby enhancing generalization against out-of-distribution data. While gradient or representation matching algorithms have achieved remarkable success, these…

Graph neural networks (GNNs) have been widely used in graph-structured data computation, showing promising performance in various applications such as node classification, link prediction, and network recommendation. Existing works mainly…

Despite recent advances in achieving fair representations and predictions through regularization, adversarial debiasing, and contrastive learning in graph neural networks (GNNs), the working mechanism (i.e., message passing) behind GNNs…

We introduce the lifted Generalized Belief Propagation (GBP) message passing algorithm, for the computation of sum-product queries in Probabilistic Relational Models (e.g. Markov logic network). The algorithm forms a compact region graph…

We propose an orthogonal approximate message passing (OAMP) algorithm for signal estimation in the rectangular spiked matrix model with general rotationally invariant (RI) noise. We establish a rigorous state evolution that exactly…

In this paper, we extend the bilinear generalized approximate message passing (BiG-AMP) approach, originally proposed for high-dimensional generalized bilinear regression, to the multi-layer case for the handling of cascaded problem such as…

We study the compressed sensing reconstruction problem for a broad class of random, band-diagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and…

Approximate message passing algorithm enjoyed considerable attention in the last decade. In this paper we introduce a variant of the AMP algorithm that takes into account glassy nature of the system under consideration. We coin this…

We discuss the fundamental theoretical framework together with numerous results obtained by the authors and colleagues over an extended period of investigation on the Information Geometric Approach to Chaos (IGAC).

Deep learning has gained great popularity due to its widespread success on many inference problems. We consider the application of deep learning to the sparse linear inverse problem, where one seeks to recover a sparse signal from a few…

Characterizing the distribution of high-dimensional statistical estimators is a challenging task, due to the breakdown of classical asymptotic theory in high dimension. This paper makes progress towards this by developing non-asymptotic…

Message passing (MP) is a computational technique used to find approximate solutions to a variety of problems defined on networks. MP approximations are generally accurate in locally tree-like networks but require corrections to maintain…

In cosparse analysis compressive sensing (CS), one seeks to estimate a non-sparse signal vector from noisy sub-Nyquist linear measurements by exploiting the knowledge that a given linear transform of the signal is cosparse, i.e., has…

Despite enormous progress in object detection and classification, the problem of incorporating expected contextual relationships among object instances into modern recognition systems remains a key challenge. In this work we propose…

Learning on large graphs presents significant challenges, with traditional Message Passing Neural Networks suffering from computational and memory costs scaling linearly with the number of edges. We introduce the Intersecting Block Graph…

In this paper, we propose an information geometry approach (IGA) for signal detection (SD) in ultra-massive multiple-input multiple-output (MIMO) systems. We formulate the signal detection as obtaining the marginals of the a posteriori…