Solving Non-identifiable Latent Feature Models

TL;DR

This paper characterizes when latent feature models are non-identifiable and introduces a post-processing method to find appropriate solutions by navigating equivalent parameter configurations, improving estimation accuracy.

Contribution

It provides a necessary and sufficient condition for non-identifiability in LFMs and proposes a novel post-processing method to address this issue.

Findings

The condition relates to feature dependency and explains real-world non-identifiability.

The proposed method effectively finds appropriate solutions in synthetic datasets.

The method improves parameter estimation in real-world datasets.

Abstract

Latent feature models (LFM)s are widely employed for extracting latent structures of data. While offering high, parameter estimation is difficult with LFMs because of the combinational nature of latent features, and non-identifiability is a particularly difficult problem when parameter estimation is not unique and there exists equivalent solutions. In this paper, a necessary and sufficient condition for non-identifiability is shown. The condition is significantly related to dependency of features, and this implies that non-identifiability may often occur in real-world applications. A novel method for parameter estimation that solves the non-identifiability problem is also proposed. This method can be combined as a post-process with existing methods and can find an appropriate solution by hopping efficiently through equivalent solutions. We have evaluated the effectiveness of the method on both synthetic and real-world datasets.