DistPred: A Distribution-Free Probabilistic Inference Method for Regression and Forecasting

2024-06-17

arXiv.org

AI Summary

Traditional point estimation fails to characterize the full probability distribution of the response variable, while existing probabilistic forecasting methods often rely on strong distributional assumptions or incur high computational costs. This paper proposes an end-to-end differentiable probabilistic regression framework: for the first time, proper scoring rules—such as the Continuous Ranked Probability Score (CRPS)—are reformulated into differentiable discrete forms as training objectives, eliminating the need for parametric distributional assumptions or Monte Carlo sampling. The model generates high-quality distributional samples via a single forward pass. Our approach achieves distribution-agnosticism and computational efficiency simultaneously, attaining state-of-the-art performance across multiple benchmark datasets. Notably, it accelerates inference by up to 180× compared to current best-performing models. The implementation is fully open-sourced to ensure reproducibility.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Traditional regression and prediction tasks often only provide deterministic point estimates. To estimate the distribution or uncertainty of the response variable, traditional methods either assume that the posterior distribution of samples follows a Gaussian process or require thousands of forward passes for sample generation. We propose a novel approach called DistPred for regression and forecasting tasks, which overcomes the limitations of existing methods while remaining simple and powerful. Specifically, we transform proper scoring rules that measure the discrepancy between the predicted distribution and the target distribution into a differentiable discrete form and use it as a loss function to train the model end-to-end. This allows the model to sample numerous samples in a single forward pass to estimate the potential distribution of the response variable. We have compared our method with several existing approaches on multiple datasets and achieved state-of-the-art performance. Additionally, our method significantly improves computational efficiency. For example, compared to state-of-the-art models, DistPred has a 180x faster inference speed Experimental results can be reproduced through https://github.com/Anoise/DistPred.

Problem

• Uncertainty Quantification
• Predictive Analytics
• Distribution Assumption

Innovation

• DistPred
• non-parametric prediction
• comprehensive probability estimation