arXiv Machine Learning
4d ago

Averaged Mirror Descent and Dual Gradient Methods: Convergent Algorithms for Entropic Gromov-Wasserstein Problems

The paper studies algorithms for computing the Entropic Gromov-Wasserstein (EGW) distance, a measure of discrepancy between metric measure spaces. It introduces Averaged Mirror Descent (AMD), which averages successive Mirror Descent steps and is proven to converge for any cost function, and shows that a dual gradient method with a fixed step size also converges for arbitrary costs, even when iterations are inexact. Empirical comparisons demonstrate that both AMD and the dual gradient method succeed on cases where classical Mirror Descent fails.

By Joanna Marks, Gabriel Rioux, Riccardo Passeggeri
arXiv Machine Learning
Sep 11

Generalized Score Matching for Parameter Estimation on Convex Domains

The paper introduces a generalized score matching objective for parameter estimation on convex subsets of ρ^d, derived from Minimum Probability Flow learning. It shows that this objective is a proper local scoring rule of second order, ensuring recovery of the true density when minimized, and proves convexity and consistency for exponential family models under standard conditions. Experiments demonstrate the method’s effectiveness on constrained domains where the partition function is intractable, including a generative modeling use‑case.

By Nishanth Shetty, Saisuchith Mahajan, Chandra Sekhar Seelamantula
arXiv Statistics ML
Sep 4

Discrete Gromov-Wasserstein Duality: Algorithms and Isomorphism Testing

The paper presents a new duality formulation for the Gromov‑Wasserstein distance that applies to all finitely supported metric‑measure spaces, with and without entropic regularization. Using this duality, the authors derive sample‑complexity bounds and limit distributions for empirical GW distances, and introduce algorithms with formal convergence guarantees. These results enable a principled, efficient method for testing isomorphism between distributions on graphs with a fixed number of nodes based on samples.

By Gabriel Rioux, Joanna Marks, Riccardo Passeggeri, Ziv Goldfeld