Spectral Algorithm for Low-rank Multitask Regression

TL;DR

This paper introduces a spectral algorithm for low-rank multitask regression that efficiently recovers shared and task-specific components, improving performance with limited data across related tasks.

Contribution

The paper proposes a non-iterative spectral method for joint recovery of shared and local low-rank components in multitask regression, with theoretical guarantees.

Findings

Effective in remote river discharge estimation with scarce data

Improves accuracy by leveraging shared low-rank structure

Demonstrates benefits in image classification tasks

Abstract

Multitask learning, i.e. taking advantage of the relatedness of individual tasks in order to improve performance on all of them, is a core challenge in the field of machine learning. We focus on matrix regression tasks where the rank of the weight matrix is constrained to reduce sample complexity. We introduce the common mechanism regression (CMR) model which assumes a shared left low-rank component across all tasks, but allows an individual per-task right low-rank component. This dramatically reduces the number of samples needed for accurate estimation. The problem of jointly recovering the common and the local components has a non-convex bi-linear structure. We overcome this hurdle and provide a provably beneficial non-iterative spectral algorithm. Appealingly, the solution has favorable behavior as a function of the number of related tasks and the small number of samples available for each one. We demonstrate the efficacy of our approach for the challenging task of remote river discharge estimation across multiple river sites, where data for each task is naturally scarce. In this scenario sharing a low-rank component between the tasks translates to a shared spectral reflection of the water, which is a true underlying physical model. We also show the benefit of the approach on the markedly different setting of image classification where the common component can be interpreted as the shared convolution filters.