Counterfactual Forecasting For Panel Data

2025-11-09

AI Summary

This paper addresses counterfactual prediction in panel data with missing observations and time-varying latent factors. We propose FOCUS—a unified framework integrating matrix completion with autoregressive modeling of latent factors, explicitly distinguishing stochastic and deterministic temporal dynamics. Built upon a PCA-based estimator, FOCUS supports finite-sample error bounds and asymptotic normality under stationarity assumptions. Theoretically and empirically, FOCUS outperforms existing benchmarks—particularly in settings with autoregressive latent factors. In application to the HeartSteps mobile health study, FOCUS accurately predicts individual-level step-count trajectories under interventions, demonstrating its validity and practical utility for real-world causal inference tasks.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We address the challenge of forecasting counterfactual outcomes in a panel data with missing entries and temporally dependent latent factors -- a common scenario in causal inference, where estimating unobserved potential outcomes ahead of time is essential. We propose Forecasting Counterfactuals under Stochastic Dynamics (FOCUS), a method that extends traditional matrix completion methods by leveraging time series dynamics of the factors, thereby enhancing the prediction accuracy of future counterfactuals. Building upon a PCA estimator, our method accommodates both stochastic and deterministic components within the factors, and provides a flexible framework for various applications. In case of stationary autoregressive factors and under standard conditions, we derive error bounds and establish asymptotic normality of our estimator. Empirical evaluations demonstrate that our method outperforms existing benchmarks when the latent factors have an autoregressive component. We illustrate FOCUS results on HeartSteps, a mobile health study, illustrating its effectiveness in forecasting step counts for users receiving activity prompts, thereby leveraging temporal patterns in user behavior.

Problem

• Forecasting counterfactual outcomes with missing panel data entries
• Modeling temporally dependent latent factors in causal inference
• Enhancing prediction accuracy using time series dynamics

Innovation

• Extends matrix completion with time series dynamics
• Accommodates stochastic and deterministic latent factors
• Provides error bounds and asymptotic normality guarantees