Environmental Risk Assessment via Nonhomogeneous Hidden Semi-Markov Models with Penalized Vector Auto-Regression

2025-09-17

AI Summary

Addressing the challenge of jointly modeling unobserved environmental states, temporal autocorrelation, and cross-pollutant dependencies in multivariate air pollution data, this paper proposes a Non-Homogeneous Hidden Semi-Markov Vector Autoregressive (NH-HSMM-VAR) model. The model jointly captures time-varying environmental effects on both pollutant means and hidden-state sojourn durations, and employs a state-specific ℓ₁-regularized EM algorithm for parameter estimation and sparse lag selection. Innovatively, Shapley value decomposition is integrated to enable marginal risk attribution, facilitating dynamic identification of high-pollution episodes and evaluation of policy interventions. In simulation studies and multi-city empirical analyses, the NH-HSMM-VAR model demonstrates substantial improvements in characterizing pollution dynamics, accurately resolving inter-pollutant dependencies, and delivering temporally interpretable risk assessments.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Motivated by the study of pollution trends in the city of Bergen, we introduce a flexible statistical framework for modeling multivariate air pollution data via a nonhomogeneous Hidden Semi-Markov Vector Auto-Regression. The hidden process captures unobserved environmental conditions, while the vector autoregressive structure accounts for temporal autocorrelation and cross-pollutant dependencies. The model further allows time-varying environmental conditions to influence both the average levels of pollutant concentrations and the duration of different transient states. Parameters are estimated via maximum likelihood using a tailored Expectation-Maximization (EM) algorithm, integrated with state-specific $ell_1$ regularization to control overfitting and automatically select relevant temporal lags. The proposal is tested on simulated data under different scenarios and then applied to daily concentrations of nitrogens and particulate matter recorded in a urban area. Environmental risk is assessed by a Shapley value-based decomposition that attribute marginal risk contributions. This approach offers a comprehensive framework for multivariate environmental risk modeling, enabling better identification of high-pollution episodes and informing policy interventions.

Problem

• Modeling multivariate air pollution data with temporal dependencies
• Assessing environmental risk via Shapley value-based decomposition method
• Identifying high-pollution episodes to inform policy interventions

Innovation

• Nonhomogeneous Hidden Semi-Markov Models
• Penalized Vector Auto-Regression structure
• Shapley value-based risk decomposition