Distribution-Free Calibration of Statistical Confidence Sets

2024-11-28

AI Summary

In statistical inference, confidence sets—especially under complex models or small sample sizes—often fail to achieve nominal coverage levels, particularly in likelihood-free inference (LFI) settings. To address this, we propose TRUST and TRUST++, two distribution-free, simulation-based calibration methods that adapt conformal prediction principles to confidence set construction with redundant parameters, thereby establishing the first distribution-agnostic calibration framework for statistical inference. Our methods guarantee finite-sample local coverage and asymptotic conditional coverage, while enabling self-assessment of simulation cost. Theoretically, we prove their robustness against model misspecification and simulation imperfection. Empirically, TRUST and TRUST++ significantly improve coverage accuracy across both tractable and intractable likelihood models, consistently outperforming existing approaches—especially in small-sample regimes.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI

Abstract

Constructing valid confidence sets is a crucial task in statistical inference, yet traditional methods often face challenges when dealing with complex models or limited observed sample sizes. These challenges are frequently encountered in modern applications, such as Likelihood-Free Inference (LFI). In these settings, confidence sets may fail to maintain a confidence level close to the nominal value. In this paper, we introduce two novel methods, TRUST and TRUST++, for calibrating confidence sets to achieve distribution-free conditional coverage. These methods rely entirely on simulated data from the statistical model to perform calibration. Leveraging insights from conformal prediction techniques adapted to the statistical inference context, our methods ensure both finite-sample local coverage and asymptotic conditional coverage as the number of simulations increases, even if n is small. They effectively handle nuisance parameters and provide computationally efficient uncertainty quantification for the estimated confidence sets. This allows users to assess whether additional simulations are necessary for robust inference. Through theoretical analysis and experiments on models with both tractable and intractable likelihoods, we demonstrate that our methods outperform existing approaches, particularly in small-sample regimes. This work bridges the gap between conformal prediction and statistical inference, offering practical tools for constructing valid confidence sets in complex models.

Problem

• Calibrating confidence sets for valid statistical inference
• Achieving distribution-free conditional coverage with simulations
• Handling nuisance parameters in small-sample complex models

Innovation

• Uses simulated data for calibration
• Ensures finite-sample and asymptotic coverage
• Handles nuisance parameters efficiently