Related papers: Graph Metric Learning via Gershgorin Disc Alignmen…
For a given graph $\mathcal{G}$ of order $n$ with $m$ edges, and a real symmetric matrix associated to the graph, $M\left(\mathcal{G}\right)\in\mathbb{R}^{n\times n}$, the interlacing graph reduction problem is to find a graph…
This paper revisits the convergence of Stochastic Mirror Descent (SMD) in the contemporary nonconvex optimization setting. Existing results for batch-free nonconvex SMD restrict the choice of the distance generating function (DGF) to be…
The ubiquity of massive graph data sets in numerous applications requires fast algorithms for extracting knowledge from these data. We are motivated here by three electrical measures for the analysis of large small-world graphs $G = (V, E)$…
We develop faster approximation algorithms for Metric-TSP building on recent, nearly linear time approximation schemes for the LP relaxation [Chekuri and Quanrud, 2017]. We show that the LP solution can be sparsified via cut-sparsification…
We introduce a new paradigm, $\textit{measure synchronization}$, for synchronizing graphs with measure-valued edges. We formulate this problem as maximization of the cycle-consistency in the space of probability measures over relative…
We present a unified framework to analyze the global convergence of Langevin dynamics based algorithms for nonconvex finite-sum optimization with $n$ component functions. At the core of our analysis is a direct analysis of the ergodicity of…
Smooth convex minimization over the unit trace-norm ball is an important optimization problem in machine learning, signal processing, statistics and other fields, that underlies many tasks in which one wishes to recover a low-rank matrix…
We present a unified theorem for the convergence analysis of stochastic gradient algorithms for minimizing a smooth and convex loss plus a convex regularizer. We do this by extending the unified analysis of Gorbunov, Hanzely \& Richt\'arik…
As the problem of minimizing functionals on the Wasserstein space encompasses many applications in machine learning, different optimization algorithms on $\mathbb{R}^d$ have received their counterpart analog on the Wasserstein space. We…
The richness in the content of various information networks such as social networks and communication networks provides the unprecedented potential for learning high-quality expressive representations without external supervision. This…
We present a new family of min-max optimization algorithms that automatically exploit the geometry of the gradient data observed at earlier iterations to perform more informative extra-gradient steps in later ones. Thanks to this adaptation…
Motivated by the classic Generalized Assignment Problem, we consider the Graph Balancing problem in the presence of orientation costs: given an undirected multi-graph G = (V,E) equipped with edge weights and orientation costs on the edges,…
Spatiotemporal learning, which aims at extracting spatiotemporal correlations from the collected spatiotemporal data, is a research hotspot in recent years. And considering the inherent graph structure of spatiotemporal data, recent works…
We propose ALFCG (Adaptive Lipschitz-Free Conditional Gradient), the first \textit{adaptive} projection-free framework for stochastic composite nonconvex minimization that \textit{requires neither global smoothness constants nor line…
Existing machine learning literature lacks graph-based domain adaptation techniques capable of handling large distribution shifts, primarily due to the difficulty in simulating a coherent evolutionary path from source to target graph. To…
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…
A dominating set of a graph $\mathcal{G=(V, E)}$ is a subset of vertices $S\subseteq\mathcal{V}$ such that every vertex $v\in \mathcal{V} \setminus S$ outside the dominating set is adjacent to a vertex $u\in S$ within the set. The minimum…
We propose a novel weakly supervised discriminative algorithm for learning context specific registration metrics as a linear combination of conventional similarity measures. Conventional metrics have been extensively used over the past two…
Signed graphs are equipped with both positive and negative edge weights, encoding pairwise correlations as well as anti-correlations in data. A balanced signed graph is a signed graph with no cycles containing an odd number of negative…
We propose a generic framework based on a new stochastic variance-reduced gradient descent algorithm for accelerating nonconvex low-rank matrix recovery. Starting from an appropriate initial estimator, our proposed algorithm performs…