Interpetable Target-Feature Aggregation for Multi-Task Learning based on Bias-Variance Analysis

TL;DR

This paper introduces an interpretable multi-task learning method that combines task clustering and feature transformation using bias-variance analysis, validated on synthetic and real-world Earth science data.

Contribution

It presents a novel two-phase MTL algorithm (NonLinCTFA) that clusters tasks and aggregates features while maintaining interpretability through mean-based aggregation.

Findings

Effective task clustering and feature aggregation demonstrated on synthetic data.

Improved interpretability of features and targets in Earth science applications.

Validation against classical and recent baselines confirms the method's utility.

Abstract

Multi-task learning (MTL) is a powerful machine learning paradigm designed to leverage shared knowledge across tasks to improve generalization and performance. Previous works have proposed approaches to MTL that can be divided into feature learning, focused on the identification of a common feature representation, and task clustering, where similar tasks are grouped together. In this paper, we propose an MTL approach at the intersection between task clustering and feature transformation based on a two-phase iterative aggregation of targets and features. First, we propose a bias-variance analysis for regression models with additive Gaussian noise, where we provide a general expression of the asymptotic bias and variance of a task, considering a linear regression trained on aggregated input features and an aggregated target. Then, we exploit this analysis to provide a two-phase MTL algorithm (NonLinCTFA). Firstly, this method partitions the tasks into clusters and aggregates each obtained group of targets with their mean. Then, for each aggregated task, it aggregates subsets of features with their mean in a dimensionality reduction fashion. In both phases, a key aspect is to preserve the interpretability of the reduced targets and features through the aggregation with the mean, which is further motivated by applications to Earth science. Finally, we validate the algorithms on synthetic data, showing the effect of different parameters and real-world datasets, exploring the validity of the proposed methodology on classical datasets, recent baselines, and Earth science applications.