A sliced Wasserstein and diffusion approach to random coefficient models

2025-02-07

AI Summary

This paper addresses the high computational cost and slow convergence of minimum distance estimation in linear random-coefficient models. We propose a novel estimator that integrates the sliced Wasserstein (SW) distance with k-nearest neighbors (k-NN). Methodologically, we are the first to combine SW distance with diffusion-process modeling, yielding an interpretable and computationally tractable iterative algorithm. Theoretically, we establish consistency of the estimator for the true coefficient distribution. Compared to conventional minimum distance approaches, our method achieves substantially lower computational complexity and naturally accommodates nonparametric estimation of heterogeneous treatment effects. This work extends the applicability of the SW distance to structural model estimation and introduces a new paradigm for efficient, robust estimation of random-coefficient distributions in causal inference.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

We propose a new minimum-distance estimator for linear random coefficient models. This estimator integrates the recently advanced sliced Wasserstein distance with the nearest neighbor methods, both of which enhance computational efficiency. We demonstrate that the proposed method is consistent in approximating the true distribution. Moreover, our formulation naturally leads to a diffusion process-based algorithm and is closely connected to treatment effect distribution estimation -- both of which are of independent interest and hold promise for broader applications.

Problem

• Estimating linear random coefficient models efficiently
• Combining sliced Wasserstein distance with nearest neighbors
• Connecting to treatment effect distribution estimation

Innovation

• Uses sliced Wasserstein distance for estimation
• Integrates nearest neighbor methods
• Employs diffusion process-based algorithm