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We present a novel framework based on optimal transport for the challenging problem of comparing graphs. Specifically, we exploit the probabilistic distribution of smooth graph signals defined with respect to the graph topology. This allows…
We propose a new nonlinear factorization model for graphs that are with topological structures, and optionally, node attributes. This model is based on a pseudometric called Gromov-Wasserstein (GW) discrepancy, which compares graphs in a…
We propose a new self-adaptive, double-loop smoothing algorithm to solve composite, nonsmooth, and constrained convex optimization problems. Our algorithm is based on Nesterov's smoothing technique via general Bregman distance functions. It…
We consider the problem of minimizing a convex separable objective (as a separable sum of two proper closed convex functions $f$ and $g$) over a linear coupling constraint. We assume that $f$ can be decomposed as the sum of a smooth part…
This paper proposes a new easy-to-implement parameter-free gradient-based optimizer: DoWG (Distance over Weighted Gradients). We prove that DoWG is efficient -- matching the convergence rate of optimally tuned gradient descent in convex…
We establish the convergence of the forward-backward splitting algorithm based on Bregman distances for the sum of two monotone operators in reflexive Banach spaces. Even in Euclidean spaces, the convergence of this algorithm has so far…
In this work, we investigate the convergence properties of the backward regularized Wasserstein proximal (BRWP) method for sampling a target distribution. The BRWP approach can be shown as a semi-implicit time discretization for a…
In this paper, we address variational inequalities (VI) with a finite-sum structure. We introduce a novel single-loop stochastic variance-reduced algorithm, incorporating the Bregman distance function, and establish an optimal convergence…
Gromov-Wasserstein distance has found many applications in machine learning due to its ability to compare measures across metric spaces and its invariance to isometric transformations. However, in certain applications, this invariance…
Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key…
Wasserstein Generative Adversarial Networks (WGANs) provide a versatile class of models, which have attracted great attention in various applications. However, this framework has two main drawbacks: (i) Wasserstein-1 (or Earth-Mover)…
Given a complete edge-weighted graph G, we present a polynomial time algorithm to compute a degree-four-bounded spanning Eulerian subgraph of 2G that has at most 1.5 times the weight of an optimal TSP solution of G. Based on this algorithm…
Recently, a new distance has been introduced for the graphs of two point-to-set operators, one of which is maximally monotone. When both operators are the subdifferential of a proper lower semicontinuous convex function, this distance…
In this paper, we study nonconvex constrained stochastic zeroth-order optimization problems, for which we have access to exact information of constraints and noisy function values of the objective. We propose a Bregman linearized augmented…
The classical convergence analysis of quasi-Newton methods assumes that the function and gradients employed at each iteration are exact. In this paper, we consider the case when there are (bounded) errors in both computations and establish…
The Gromov-Wasserstein (GW) problem is an extension of the classical optimal transport problem to settings where the source and target distributions reside in incomparable spaces, and for which a cost function that attributes the price of…
We consider the general problem of finding the minimum weight $\bm$-matching on arbitrary graphs. We prove that, whenever the linear programming (LP) relaxation of the problem has no fractional solutions, then the belief propagation (BP)…
Motivated by approximation Bayesian computation using mean-field variational approximation and the computation of equilibrium in multi-species systems with cross-interaction, this paper investigates the composite geodesically convex…
We consider the problem of estimating the inverse covariance matrix by maximizing the likelihood function with a penalty added to encourage the sparsity of the resulting matrix. We propose a new approach based on the split Bregman method to…
The Sliced Gromov-Wasserstein (SGW) distance, aiming to relieve the computational cost of solving a non-convex quadratic program that is the Gromov-Wasserstein distance, utilizes projecting directions sampled uniformly from unit…