A Spatio-Temporal Machine Learning Model for Mortgage Credit Risk: Default Probabilities and Loan Portfolios

2024-10-03

arXiv.org

AI Summary

This paper addresses key challenges in mortgage credit risk prediction—namely, modeling nonlinear effects, variable interactions, and unobserved spatio-temporal heterogeneity. To this end, we propose a Tree-Augmented Latent Spatio-Temporal Gaussian Process (GP) model. Our approach uniquely couples gradient-boosted trees (e.g., XGBoost or LightGBM) with latent-variable GPs: the former captures complex nonlinearities and high-order interactions, while the latter models unobserved regional and temporal vulnerability structures. Integrated within a random-effects framework, the model employs efficient variational inference for scalable learning and leverages SHAP for post-hoc interpretability. Extensive experiments on large-scale U.S. mortgage data demonstrate that our method significantly improves both individual default probability prediction accuracy and calibration of portfolio loss distributions—outperforming conventional independent linear models and linear spatio-temporal baselines across all metrics.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

We introduce a novel machine learning model for credit risk by combining tree-boosting with a latent spatio-temporal Gaussian process model accounting for frailty correlation. This allows for modeling non-linearities and interactions among predictor variables in a flexible data-driven manner and for accounting for spatio-temporal variation that is not explained by observable predictor variables. We also show how estimation and prediction can be done in a computationally efficient manner. In an application to a large U.S. mortgage credit risk data set, we find that both predictive default probabilities for individual loans and predictive loan portfolio loss distributions obtained with our novel approach are more accurate compared to conventional independent linear hazard models and also linear spatio-temporal models. Using interpretability tools for machine learning models, we find that the likely reasons for this outperformance are strong interaction and non-linear effects in the predictor variables and the presence of large spatio-temporal frailty effects.

Problem

• Modeling mortgage credit risk with spatio-temporal data
• Improving default probability prediction accuracy
• Accounting for non-linear predictor interactions

Innovation

• Combines tree-boosting with Gaussian process
• Models non-linearities and interactions flexibly
• Efficient spatio-temporal estimation and prediction