Neural Inference Functions for Margins for Time Series Copula Models

2026-03-22

AI Summary

This work addresses the high computational cost and limited scalability of Bayesian inference in high-dimensional time series Copula models. To overcome these challenges, the authors propose the Neural Inference for Marginal Functions (N-IFM) framework, which integrates neural networks into the classical Inference Functions for Margins (IFM) approach for the first time. N-IFM enables efficient estimation of Copula parameters, sequence forecasting, and model comparison. The method achieves inference accuracy comparable to Hamiltonian Monte Carlo while substantially improving computational efficiency. Its scalability and practical utility are demonstrated through both simulated and real-world datasets.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Copula models are widely employed in multivariate time series analysis because they permit flexible modelling of marginal distributions independently of the dependence structure, which is fully characterised by the copula function. However, Bayesian inference with these models becomes computationally demanding as the number of variables in the time series increases. Motivated by the classical inference functions for margins (IFM) approach, we propose a new neural-network based inference framework for estimating parameters in copula models, termed the neural inference functions for margins (N-IFM). N-IFM enables rapid parameter estimation for new data, fast sequential prediction, and efficient model comparison via time-series validation. We assess the performance of N-IFM using both simulated and real datasets and compare it to Hamiltonian Monte Carlo, demonstrating substantial computational gains with comparable inferential accuracy.

Problem

• copula models
• Bayesian inference
• time series
• computational efficiency
• multivariate analysis

Innovation

• neural inference functions
• copula models
• time series
• Bayesian inference
• computational efficiency