Weighted Tensor Decomposition for Learning Latent Variables with Partial Data

TL;DR

This paper introduces a weighted tensor decomposition method designed to effectively learn latent variables from incomplete data, where some dimensions are not always observed, improving accuracy over traditional unweighted methods.

Contribution

It proposes a novel weighted tensor decomposition technique that handles partial data efficiently, outperforming existing methods that ignore the varying quality of moment estimates.

Findings

Weighted tensor decomposition outperforms unweighted methods on incomplete data.

The approach is computationally as efficient as standard tensor decomposition.

It effectively leverages less-observed dimensions to improve latent variable learning.

Abstract

Tensor decomposition methods are popular tools for learning latent variables given only lower-order moments of the data. However, the standard assumption is that we have sufficient data to estimate these moments to high accuracy. In this work, we consider the case in which certain dimensions of the data are not always observed---common in applied settings, where not all measurements may be taken for all observations---resulting in moment estimates of varying quality. We derive a weighted tensor decomposition approach that is computationally as efficient as the non-weighted approach, and demonstrate that it outperforms methods that do not appropriately leverage these less-observed dimensions.