TTML: tensor trains for general supervised machine learning

TL;DR

This paper introduces TTML, a new supervised machine learning estimator that leverages tensor trains to efficiently model functions, offering competitive performance with lower memory requirements by optimizing discretized functions via Riemannian gradient descent.

Contribution

The paper presents a novel tensor train-based estimator for supervised learning, emphasizing the importance of initialization and demonstrating its efficiency and low memory usage.

Findings

Competitive accuracy with reduced memory footprint

Initialization significantly impacts optimization success

Faster training compared to traditional methods

Abstract

This work proposes a novel general-purpose estimator for supervised machine learning (ML) based on tensor trains (TT). The estimator uses TTs to parametrize discretized functions, which are then optimized using Riemannian gradient descent under the form of a tensor completion problem. Since this optimization is sensitive to initialization, it turns out that the use of other ML estimators for initialization is crucial. This results in a competitive, fast ML estimator with lower memory usage than many other ML estimators, like the ones used for the initialization.