Fast, Optimal, and Targeted Predictions using Parametrized Decision Analysis

TL;DR

This paper introduces a scalable, interpretable framework for targeted Bayesian prediction that optimizes specific decision-related functionals, improving prediction accuracy and interpretability in complex settings.

Contribution

It develops a class of parametrized actions for Bayesian decision analysis that produce optimal, scalable, and interpretable targeted predictions, with efficient solutions for various loss functions.

Findings

Efficient representation of optimal targeted predictions.

Development of customized predictive metrics for evaluation.

Successful application to physical activity data for improved prediction.

Abstract

Prediction is critical for decision-making under uncertainty and lends validity to statistical inference. With targeted prediction, the goal is to optimize predictions for specific decision tasks of interest, which we represent via functionals. Although classical decision analysis extracts predictions from a Bayesian model, these predictions are often difficult to interpret and slow to compute. Instead, we design a class of parametrized actions for Bayesian decision analysis that produce optimal, scalable, and simple targeted predictions. For a wide variety of action parametrizations and loss functions--including linear actions with sparsity constraints for targeted variable selection--we derive a convenient representation of the optimal targeted prediction that yields efficient and interpretable solutions. Customized out-of-sample predictive metrics are developed to evaluate and compare among targeted predictors. Through careful use of the posterior predictive distribution, we introduce a procedure that identifies a set of near-optimal, or acceptable targeted predictors, which provide unique insights into the features and level of complexity needed for accurate targeted prediction. Simulations demonstrate excellent prediction, estimation, and variable selection capabilities. Targeted predictions are constructed for physical activity data from the National Health and Nutrition Examination Survey (NHANES) to better predict and understand the characteristics of intraday physical activity.