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Within many real-world networks the links between pairs of nodes change over time. Thus, there has been a recent boom in studying temporal graphs. Recognizing patterns in temporal graphs requires a proximity measure to compare different…
We propose a new stochastic L-BFGS algorithm and prove a linear convergence rate for strongly convex and smooth functions. Our algorithm draws heavily from a recent stochastic variant of L-BFGS proposed in Byrd et al. (2014) as well as a…
In this paper, we explore a specific optimization problem that involves the combination of a differentiable nonconvex function and a nondifferentiable function. The differentiable component lacks a global Lipschitz continuous gradient,…
In this work, we propose a hybrid Bayesian approach towards clock offset and skew estimation, thereby synchronizing large scale networks. In particular, we demonstrate the advantage of Bayesian Recursive Filtering (BRF) in alleviating…
This paper studies the problem of recovering a hidden vertex correspondence between two correlated graphs when both edge weights and node features are observed. While most existing work on graph alignment relies primarily on edge…
Graph node classification is a fundamental task in graph neural networks (GNNs), aiming to assign predefined class labels to nodes. On the PubMed citation network dataset, we observe significant classification difficulty disparities, with…
Persistence diagrams (PD)s play a central role in topological data analysis. This analysis requires computing distances among such diagrams such as the $1$-Wasserstein distance. Accurate computation of these PD distances for large data sets…
We introduce a general framework for analyzing data modeled as parameterized families of networks. Building on a Gromov-Wasserstein variant of optimal transport, we define a family of parameterized Gromov-Wasserstein distances for comparing…
We develop a new variational approach on level sets aiming towards convergence rate analysis of a variable Bregman proximal gradient (VBPG) method for a broad class of nonsmooth and nonconvex optimization problems. With this new approach,…
The ability to compute similarity scores between graphs based on metrics such as Graph Edit Distance (GED) is important in many real-world applications. Computing exact GED values is typically an NP-hard problem and traditional algorithms…
The Gromov-Wasserstein (GW) distance is a powerful tool for comparing metric measure spaces which has found broad applications in data science and machine learning. Driven by the need to analyze datasets whose objects have increasingly…
This paper introduces an online approach for identifying time-varying subspaces defined by linear dynamical systems. The approach of representing linear systems by non-parametric subspace models has received significant interest in the…
The problem of learning graphons has attracted considerable attention across several scientific communities, with significant progress over the recent years in sparser regimes. Yet, the current techniques still require diverging degrees in…
Variational approximation, such as mean-field (MF) and tree-reweighted (TRW), provide a computationally efficient approximation of the log-partition function for a generic graphical model. TRW provably provides an upper bound, but the…
Gromov-Hausdorff distances measure shape difference between the objects representable as compact metric spaces, e.g. point clouds, manifolds, or graphs. Computing any Gromov-Hausdorff distance is equivalent to solving an NP-Hard…
In this paper, we present a novel interpretation of the so-called Weisfeiler-Lehman (WL) distance, introduced by Chen et al. (2022), using concepts from stochastic processes. The WL distance aims at comparing graphs with node features, has…
The Bregman-Wasserstein divergence is the optimal transport cost when the underlying cost function is given by a Bregman divergence, and arises naturally in fields such as statistics and machine learning. We establish fundamental properties…
Graph data augmentation has shown superiority in enhancing generalizability and robustness of GNNs in graph-level classifications. However, existing methods primarily focus on the augmentation in the graph signal space and the graph…
Automatic scoring of student responses enhances efficiency in education, but deploying a separate neural network for each task increases storage demands, maintenance efforts, and redundant computations. To address these challenges, this…
Training deep convolutional neural networks such as VGG and ResNet by gradient descent is an expensive exercise requiring specialized hardware such as GPUs. Recent works have examined the possibility of approximating the gradient…