Semiparametric Nonlinear Bipartite Graph Representation Learning with Provable Guarantees

TL;DR

This paper introduces a novel semiparametric approach for bipartite graph representation learning, leveraging neural networks and statistical estimation to achieve provable guarantees and robustness.

Contribution

It develops a new estimation framework for bipartite graphs using semiparametric exponential family models with neural network embeddings, providing convergence guarantees.

Findings

Gradient descent achieves linear convergence near the ground truth.

Sample complexity is linear in dimensions, up to logarithmic factors.

Method is robust to model misspecification within the exponential family.

Abstract

Graph representation learning is a ubiquitous task in machine learning where the goal is to embed each vertex into a low-dimensional vector space. We consider the bipartite graph and formalize its representation learning problem as a statistical estimation problem of parameters in a semiparametric exponential family distribution. The bipartite graph is assumed to be generated by a semiparametric exponential family distribution, whose parametric component is given by the proximity of outputs of two one-layer neural networks, while nonparametric (nuisance) component is the base measure. Neural networks take high-dimensional features as inputs and output embedding vectors. In this setting, the representation learning problem is equivalent to recovering the weight matrices. The main challenges of estimation arise from the nonlinearity of activation functions and the nonparametric nuisance component of the distribution. To overcome these challenges, we propose a pseudo-likelihood objective based on the rank-order decomposition technique and focus on its local geometry. We show that the proposed objective is strongly convex in a neighborhood around the ground truth, so that a gradient descent-based method achieves linear convergence rate. Moreover, we prove that the sample complexity of the problem is linear in dimensions (up to logarithmic factors), which is consistent with parametric Gaussian models. However, our estimator is robust to any model misspecification within the exponential family, which is validated in extensive experiments.