Learning from Interval Targets

TL;DR

This paper addresses regression problems with interval targets, proposing new loss functions and a min-max formulation to handle uncertainty, backed by theoretical bounds and extensive experiments demonstrating state-of-the-art results.

Contribution

It introduces a novel min-max learning approach for interval targets and establishes non-asymptotic generalization bounds under relaxed assumptions.

Findings

Proposed loss functions are compatible with interval targets.

The min-max formulation achieves competitive performance.

Experimental results outperform existing methods on real datasets.

Abstract

We study the problem of regression with interval targets, where only upper and lower bounds on target values are available in the form of intervals. This problem arises when the exact target label is expensive or impossible to obtain, due to inherent uncertainties. In the absence of exact targets, traditional regression loss functions cannot be used. First, we study the methodology of using a loss functions compatible with interval targets, for which we establish non-asymptotic generalization bounds based on smoothness of the hypothesis class that significantly relaxing prior assumptions of realizability and small ambiguity degree. Second, we propose a novel min-max learning formulation: minimize against the worst-case (maximized) target labels within the provided intervals. The maximization problem in the latter is non-convex, but we show that good performance can be achieved with the incorporation of smoothness constraints. Finally, we perform extensive experiments on real-world datasets and show that our methods achieve state-of-the-art performance.