Variational Dual-Tree Framework for Large-Scale Transition Matrix Approximation

TL;DR

This paper introduces a dual-tree variational framework that significantly accelerates large-scale transition matrix approximation for graph-based random walks, improving efficiency in semi-supervised learning tasks.

Contribution

It presents a novel dual-tree variational approach that connects kernel density estimation and mixture modeling to efficiently approximate transition matrices.

Findings

Order of magnitude speedup over k-NN methods

Maintains accuracy in label propagation tasks

Scales efficiently to large datasets

Abstract

In recent years, non-parametric methods utilizing random walks on graphs have been used to solve a wide range of machine learning problems, but in their simplest form they do not scale well due to the quadratic complexity. In this paper, a new dual-tree based variational approach for approximating the transition matrix and efficiently performing the random walk is proposed. The approach exploits a connection between kernel density estimation, mixture modeling, and random walk on graphs in an optimization of the transition matrix for the data graph that ties together edge transitions probabilities that are similar. Compared to the de facto standard approximation method based on k-nearestneighbors, we demonstrate order of magnitudes speedup without sacrificing accuracy for Label Propagation tasks on benchmark data sets in semi-supervised learning.