Title: Customizing Strictly Proper Scoring Rules for Specific Applications: A Case Study in Causal Inference

Abstract: Standard probabilistic models are generally optimized using general-purpose objectives, such as log-loss, a practice that can result in substantial inaccuracies during subsequent estimation tasks. This misalignment is particularly problematic in the context of Inverse Probability Weighting (IPW) for causal inference, where inaccuracies in propensity scores near the boundaries of 0 and 1 frequently cause elevated bias and variance. To address this, we introduce a rigorous framework for generating task-specific strictly proper scoring rules by aligning the local curvature of the downstream error metric with the training objective. We demonstrate the utility of this approach in estimating the Average Treatment Effect (ATE), deriving a closed-form loss function alongside its associated canonical probability mapping. This formulation is designed for seamless integration into diverse modeling architectures, including neural networks and gradient boosting algorithms. Comprehensive testing on causal inference benchmarks reveals that our customized objective consistently surpasses conventional likelihood-based methods and covariate-balancing techniques.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC