On Maximum Entropy Linear Feature Inversion

TL;DR

This paper introduces a unified MaxEnt-based method for inverting linear dimension reduction mappings, addressing inconsistencies and extending applicability to data constrained within [0, 1], with implications for machine learning.

Contribution

A new unified MaxEnt approach that generalizes existing methods and handles data constraints, enabling broader applications in machine learning.

Findings

Provides a consistent MaxEnt inversion framework

Extends solutions to data constrained in [0, 1]

Offers potential for new machine learning applications

Abstract

We revisit the classical problem of inverting dimension-reducing linear mappings using the maximum entropy (MaxEnt) criterion. In the literature, solutions are problem-dependent, inconsistent, and use different entropy measures. We propose a new unified approach that not only specializes to the existing approaches, but offers solutions to new cases, such as when data values are constrained to [0, 1], which has new applications in machine learning.