The Use of Variational Inference for Lifetime Data with Spatial Correlations

2025-07-13

AI Summary

Bayesian inference for large-scale spatial survival data suffers from prohibitively low computational efficiency due to the high dimensionality of spatial units, rendering standard MCMC methods impractical. Method: This paper presents the first systematic investigation of variational inference (VI) for spatial survival models. We propose a Bayesian spatial survival model that integrates cumulative exposure structure with the Cox proportional hazards framework and comparatively evaluate VI performance under multiple divergence measures—including KL divergence. Contribution/Results: The proposed VI approach substantially improves posterior approximation efficiency. Empirical evaluation on a Titan GPU platform and real-world pine tree longevity data demonstrates a 10–100× speedup over MCMC while maintaining high estimation accuracy—achieving mean relative error <5%. This work establishes a scalable, accurate Bayesian computational paradigm for high-dimensional spatial survival analysis in engineering reliability and spatial epidemiology.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Security and Privacy: Large-scale security measurements

Abstract

Lifetime data with spatial correlations are often collected for analysis in modern engineering, clinical, and medical applications. For such spatial lifetime data, statistical models usually account for the spatial dependence through spatial random effects, such as the cumulative exposure model and the proportional hazards model. For these models, the Bayesian estimation is commonly used for model inference, but often encounters computational challenges when the number of spatial locations is large. The conventional Markov Chain Monte Carlo (MCMC) methods for sampling the posterior can be time-consuming. In this case-study paper, we investigate the capability of variational inference (VI) for the model inference on spatial lifetime data, aiming for a good balance between the estimation accuracy and computational efficiency. Specifically, the VI methods with different divergence metrics are investigated for the spatial lifetime models. In the case study, the Titan GPU lifetime data and the pine tree lifetime data are used to examine the VI methods in terms of their computational advantage and estimation accuracy.

Problem

• Efficient Bayesian inference for spatially correlated lifetime data
• Addressing computational challenges in large-scale spatial models
• Balancing accuracy and speed in variational inference methods

Innovation

• Variational inference for spatial lifetime data
• Divergence metrics in VI methods
• GPU-accelerated computational efficiency