Model-free Estimation of Latent Structure via Multiscale Nonparametric Maximum Likelihood

2024-10-29

AI Summary

Identifying latent discrete structures in multivariate distributions is challenging due to their unknown existence, form, and lack of prior assumptions. Method: We propose a model-free, multiscale nonparametric maximum likelihood estimation framework that jointly models the joint density across scales and introduces a novel prior-free existence test for latent structures. Without presupposing the presence or parametric form of latent structure, it adaptively discovers and integrates discrete patterns—from coarse- to fine-grained—through data-driven density estimation. Contribution/Results: Theoretically, we establish the asymptotic distribution of the estimator. Methodologically, the framework unifies interpretable discrete representation learning with data-driven model selection. Experiments on diverse complex distributions demonstrate substantial improvements in clustering interpretability and latent structure recovery accuracy, validating its capacity to effectively capture underlying data-generating mechanisms.

Technology Category

• Machine Learning: Structured Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Multivariate distributions often carry latent structures that are difficult to identify and estimate, and which better reflect the data generating mechanism than extrinsic structures exhibited simply by the raw data. In this paper, we propose a model-free approach for estimating such latent structures whenever they are present, without assuming they exist a priori. Given an arbitrary density $p_0$, we construct a multiscale representation of the density and propose data-driven methods for selecting representative models that capture meaningful discrete structure. Our approach uses a nonparametric maximum likelihood estimator to estimate the latent structure at different scales and we further characterize their asymptotic limits. By carrying out such a multiscale analysis, we obtain coarseto-fine structures inherent in the original distribution, which are integrated via a model selection procedure to yield an interpretable discrete representation of it. As an application, we design a clustering algorithm based on the proposed procedure and demonstrate its effectiveness in capturing a wide range of latent structures.

Problem

• Estimating latent structures in multivariate distributions without models
• Selecting representative models to capture meaningful discrete structures
• Designing clustering algorithms to identify diverse latent structures

Innovation

• Model-free multiscale nonparametric maximum likelihood estimation
• Data-driven selection of representative discrete structures
• Multiscale analysis for interpretable latent structure representation