Related papers: Message-Passing Algorithms and Homology
An ensemble of classical subsystems interacting with surrounding particles has been considered. In general case, a phase volume of the subsystems ensemble was shown to be a function of time. The evolutional equations of the ensemble are…
The degree heterogeneity and homophily are two typical features in network data. In this paper, we formulate a general model for undirected networks with these two features and present the moment estimation for inferring the degree and…
How can we design neural networks that allow for stable universal approximation of maps between topologically interesting manifolds? The answer is with a coordinate projection. Neural networks based on topological data analysis (TDA) use…
The sum-product or belief propagation (BP) algorithm is a widely-used message-passing algorithm for computing marginal distributions in graphical models with discrete variables. At the core of the BP message updates, when applied to a…
We address the issue of the proximity of interacting diffusion models on large graphs with a uniform degree property and a corresponding mean field model, i.e. a model on the complete graph with a suitably renormalized interaction…
In this paper we consider a network with $P$ nodes, where each node has exclusive access to a local cost function. Our contribution is a communication-efficient distributed algorithm that finds a vector $x^\star$ minimizing the sum of all…
Persistent homology is a topological feature used in a variety of applications such as generating features for data analysis and penalizing optimization problems. We develop an approach to accelerate persistent homology computations…
In this work, we introduce a novel approach based on algebraic topology to enhance graph convolution and attention modules by incorporating local topological properties of the data. To do so, we consider the framework of sheaf neural…
Incorporating social interactions is essential to an accurate modeling of epidemic spreading. This work proposes a novel local mean-field density functional theory model by using the sum-of-exponential approximation of convolution kernels…
Estimators derived from a divergence criterion such as $\varphi-$divergences are generally more robust than the maximum likelihood ones. We are interested in particular in the so-called MD$\varphi$DE, an estimator built using a dual…
Belief propagation (BP) can do exact inference in loop-free graphs, but its performance could be poor in graphs with loops, and the understanding of its solution is limited. This work gives an interpretable belief propagation rule that is…
Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…
With a view to statistical inference for discretely observed diffusion models, we propose simple methods of simulating diffusion bridges, approximately and exactly. Diffusion bridge simulation plays a fundamental role in likelihood and…
We develop numerical algorithms to approximate positive solutions of elliptic boundary value problems with superlinear subcritical nonlinearity on the boundary of the form $-\Delta u + u = 0$ in $\Omega$ with $\frac{\partial u}{\partial…
The topology and geometry of random fields - in terms of the Euler characteristic and the Minkowski functionals - has received a lot of attention in the context of the Cosmic Microwave Background (CMB), as the detection of primordial…
We provide a general framework for learning diffusion bridges that transport prior to target distributions. It includes existing diffusion models for generative modeling, but also underdamped versions with degenerate diffusion matrices,…
Gaussian Belief Propagation (BP) algorithm is one of the most important distributed algorithms in signal processing and statistical learning involving Markov networks. It is well known that the algorithm correctly computes marginal density…
We study the emergence of symmetric oscillatory behavior in multi-agent systems where each agent incorporates a continuous memory of its past states and past rates of change, modeled by distributed retarded and neutral delays. The…
Distributed parameter estimation for large-scale systems is an active research problem. The goal is to derive a distributed algorithm in which each agent obtains a local estimate of its own subset of the global parameter vector, based on…
We study Markov population processes on large graphs, with the local state transition rates of a single vertex being linear function of its neighborhood. A simple way to approximate such processes is by a system of ODEs called the…