---
title: "Doubly Robust Functional Representation Learning for Longitudinal Causal Inference with Irregular Histories"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2607.28567v1"
permalink: "https://feed.astralor.com/items/itm_ac1fabc258a6b551eeddd0e0"
published: "2026-07-30T17:33:42.000Z"
score: 77
channel: "ai"
tags: ["DR-FRL","VitalDB","Causal Inference","Representation Learning"]
---

# Doubly Robust Functional Representation Learning for Longitudinal Causal Inference with Irregular Histories

## AI commentary

> This paper offers a crucial reminder: on real medical data, fancy deep representations may not outperform simple scalar summaries. For those building clinical decision support, check whether basic features suffice before deploying complex models. For methodologists, DR-FRL's integration of EIF with functional encoders is inspiring and worth reading.

## At a glance

Longitudinal causal studies often record histories as irregular functional fragments, such as laboratory values, physiologic signals, and sensor streams. Standard doubly robust estimators usually require scalar summaries, while sequence learners optimize prediction losses that need not stabilize the efficient influence function (EIF). We propose Doubly Robust Functional Representation Learning (DR-FRL), a cross-fitted workflow that turns irregular histories into estimand-targeted states. Functional and temporal encoders map point clouds and prior histories into states, with EIF-targeted validation and diagnostics to support the estimating equation. Simulations show gains under high-dimensional functional confounding, informative measurement, weak support, or heavy-tailed pseudo-outcomes. A VitalDB audit shows that for this ICU-disposition endpoint, scalar laboratory summaries already carry much endpoint-relevant information.

## Key points

- Proposes DR-FRL, a framework combining functional encoders with EIF-targeted validation to convert irregular histories into estimand-targeted states.
- Theoretical guarantees: the mean estimator is asymptotically linear under explicit rate, overlap, calibration, and stability conditions.
- Simulations show gains over baselines under high-dimensional functional confounding, informative measurement, weak support, or heavy-tailed pseudo-outcomes.
- A VitalDB audit finds that scalar laboratory summaries already carry much endpoint-relevant information for this ICU-disposition endpoint.

## Full text

Longitudinal causal studies often record histories as irregular functional fragments: laboratory values, physiologic signals, sensor streams, and image-derived summaries measured at unequal and informative times. Standard doubly robust estimators usually require scalar summaries, whereas sequence learners optimize prediction losses that need not stabilize the efficient influence function. We propose Doubly Robust Functional Representation Learning (DR-FRL), a cross-fitted workflow that turns irregular histories into estimand-targeted states for observed-history regimes. Functional and temporal encoders map point clouds and prior histories into states; nuisance heads estimate outcome, treatment, and censoring functions; and EIF-targeted validation, calibration, overlap, tail, and ablation diagnostics assess whether the state supports the estimating equation. If the selected state preserves the nuisance information needed by the EIF, representation error enters the same second-order product remainder as ordinary nuisance error, and the mean estimator is asymptotically linear under explicit rate, overlap, calibration, and stability conditions. Catoni aggregation is treated separately as a bounded-influence point estimator, not a replacement for Wald inference. Simulations show gains when functional confounding is high-dimensional, measurement is informative, support is weak, or pseudo-outcomes are heavy-tailed. A VitalDB audit shows that DR-FRL can use irregular laboratory point clouds and deliver a useful negative finding: for this ICU-disposition endpoint, scalar laboratory summaries already carry much endpoint-relevant information.

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