Robust Estimation for Dependent Binary Network Data

2025-10-25

AI Summary

This paper addresses the poor robustness of conventional pseudo-likelihood estimation for binary network data modeled by Markov random fields (MRFs) under observation noise or contamination. We propose a robust pseudo-likelihood estimator based on the density power divergence (DPD), the first systematic integration of the DPD framework into parameter learning for dependent binary networks. Theoretically, we establish that the proposed estimator exhibits reduced asymptotic bias sensitivity and enhanced local robustness. It estimates interaction strength parameters by optimizing a DPD-based pseudo-likelihood objective function. Extensive experiments on synthetic data and real-world networks—including social, neural, and genomic networks—demonstrate that our method significantly outperforms standard maximum pseudo-likelihood (MPL) across diverse contamination scenarios: it achieves more accurate structural recovery and superior generalization performance. This work establishes a novel paradigm for network inference in high-noise settings.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

We consider the problem of learning the interaction strength between the nodes of a network based on dependent binary observations residing on these nodes, generated from a Markov Random Field (MRF). Since these observations can possibly be corrupted/noisy in larger networks in practice, it is important to robustly estimate the parameters of the underlying true MRF to account for such inherent contamination in observed data. However, it is well-known that classical likelihood and pseudolikelihood based approaches are highly sensitive to even a small amount of data contamination. So, in this paper, we propose a density power divergence (DPD) based robust generalization of the computationally efficient maximum pseudolikelihood (MPL) estimator of the interaction strength parameter, and derive its rate of consistency under the pure model. Moreover, we show that the gross error sensitivities of the proposed DPD based estimators are significantly smaller than that of the MPL estimator, thereby theoretically justifying the greater (local) robustness of the former under contaminated settings. We also demonstrate the superior (finite sample) performance of the DPD-based variants over the traditional MPL estimator in a number of synthetically generated contaminated network datasets. Finally, we apply our proposed DPD based estimators to learn the network interaction strength in several real datasets from diverse domains of social science, neurobiology and genomics.

Problem

• Robustly estimating interaction strength in noisy binary network data
• Addressing sensitivity of classical estimators to data contamination
• Proposing density power divergence for robust parameter estimation

Innovation

• Uses density power divergence for robust estimation
• Generalizes maximum pseudolikelihood estimator approach
• Reduces gross error sensitivity in contaminated data