Simulation-based inference via telescoping ratio estimation for trawl processes

2025-10-05

AI Summary

For stochastic processes exhibiting complex features—such as skewed marginal distributions, non-Gaussian heavy tails, and long-range dependence—parameter estimation lacks closed-form solutions and thus heavily relies on simulation-based inference (SBI). However, existing SBI methods suffer from excessive simulation requirements, architectural complexity, and severely undercalibrated credible intervals. This paper proposes a sample-efficient and robust SBI framework: it innovatively combines stepwise parameter dimensionality decomposition with Chebyshev polynomial approximation to achieve high-accuracy, low-dimensional posterior density modeling. Complementary diagnostic tools and a post-hoc calibration mechanism enable model reuse across time series of varying lengths, substantially reducing training overhead. Experiments on trawl processes demonstrate that our method maintains high inferential accuracy even under poor MCMC mixing, while yielding credible intervals that strictly attain nominal coverage.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Probabilistic Inference
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The growing availability of large and complex datasets has increased interest in temporal stochastic processes that can capture stylized facts such as marginal skewness, non-Gaussian tails, long memory, and even non-Markovian dynamics. While such models are often easy to simulate from, parameter estimation remains challenging. Simulation-based inference (SBI) offers a promising way forward, but existing methods typically require large training datasets or complex architectures and frequently yield confidence (credible) regions that fail to attain their nominal values, raising doubts on the reliability of estimates for the very features that motivate the use of these models. To address these challenges, we propose a fast and accurate, sample-efficient SBI framework for amortized posterior inference applicable to intractable stochastic processes. The proposed approach relies on two main steps: first, we learn the posterior density by decomposing it sequentially across parameter dimensions. Then, we use Chebyshev polynomial approximations to efficiently generate independent posterior samples, enabling accurate inference even when Markov chain Monte Carlo methods mix poorly. We further develop novel diagnostic tools for SBI in this context, as well as post-hoc calibration techniques; the latter not only lead to performance improvements of the learned inferential tool, but also to the ability to reuse it directly with new time series of varying lengths, thus amortizing the training cost. We demonstrate the method's effectiveness on trawl processes, a class of flexible infinitely divisible models that generalize univariate Gaussian processes, applied to energy demand data.

Problem

• Estimating parameters for complex temporal stochastic processes
• Addressing inefficiency in simulation-based inference methods
• Developing accurate posterior inference for intractable trawl processes

Innovation

• Sequential decomposition of posterior density across parameters
• Chebyshev polynomial approximations for efficient posterior sampling
• Post-hoc calibration techniques for varying time series lengths