Learning from Imprecise and Fuzzy Observations: Data Disambiguation through Generalized Loss Minimization

TL;DR

This paper introduces a novel approach for learning from fuzzy data by generalizing loss functions in empirical risk minimization, enabling simultaneous model identification and data disambiguation, and demonstrating its effectiveness in classification tasks.

Contribution

It proposes a new method that generalizes loss functions to better handle fuzzy data, addressing limitations of existing ad-hoc fuzzy extensions in machine learning.

Findings

The method effectively disambiguates fuzzy data during model training.

Connections established between generalized loss functions and traditional regression/classification losses.

Illustrated application in logistic regression for binary classification.

Abstract

Methods for analyzing or learning from "fuzzy data" have attracted increasing attention in recent years. In many cases, however, existing methods (for precise, non-fuzzy data) are extended to the fuzzy case in an ad-hoc manner, and without carefully considering the interpretation of a fuzzy set when being used for modeling data. Distinguishing between an ontic and an epistemic interpretation of fuzzy set-valued data, and focusing on the latter, we argue that a "fuzzification" of learning algorithms based on an application of the generic extension principle is not appropriate. In fact, the extension principle fails to properly exploit the inductive bias underlying statistical and machine learning methods, although this bias, at least in principle, offers a means for "disambiguating" the fuzzy data. Alternatively, we therefore propose a method which is based on the generalization of loss functions in empirical risk minimization, and which performs model identification and data disambiguation simultaneously. Elaborating on the fuzzification of specific types of losses, we establish connections to well-known loss functions in regression and classification. We compare our approach with related methods and illustrate its use in logistic regression for binary classification.