# LUCID: Learning Under Confounding for Inference and Discovery in Time Series

arXiv: https://arxiv.org/abs/2609.31315 · HTML: https://mlsanity.com/paper/2609.31315/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 35 references that are in the map.
- First posted on arXiv 25 Sep 2026.

## Builds on (most cited first, 14 of 14)

- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets](https://mlsanity.com/paper/2003.03685/) (2020)
- [The Blessings of Multiple Causes](https://mlsanity.com/paper/1805.06826/) (2018)
- [High-recall causal discovery for autocorrelated time series with latent confounders](https://mlsanity.com/paper/2007.01884/) (2020)
- [CUTS+: High-dimensional Causal Discovery from Irregular Time-series](https://mlsanity.com/paper/2305.05890/) (2023)
- [NTS-NOTEARS: Learning Nonparametric DBNs With Prior Knowledge](https://mlsanity.com/paper/2109.04286/) (2021)
- [A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variables](https://mlsanity.com/paper/2312.11001/) (2023)
- [Neural Additive Vector Autoregression Models for Causal Discovery in Time Series](https://mlsanity.com/paper/2010.09429/) (2020)
- [Robust causal structure learning with some hidden variables](https://mlsanity.com/paper/1708.01151/) (2017)
- [The DeCAMFounder: Non-Linear Causal Discovery in the Presence of Hidden Variables](https://mlsanity.com/paper/2102.07921/) (2021)
- [Spectral Deconfounding via Perturbed Sparse Linear Models](https://mlsanity.com/paper/1811.05352/) (2018)
- [From Temporal to Contemporaneous Iterative Causal Discovery in the Presence of Latent Confounders](https://mlsanity.com/paper/2306.00624/) (2023)
- [Efficient Causal Discovery for Autoregressive Time Series](https://mlsanity.com/paper/2507.07898/) (2025)
- [Causal-TS: A Python Library for Causal Discovery in High-Dimensional and Nonstationary Time Series](https://mlsanity.com/paper/2607.24673/) (2026)

## Abstract (arXiv)

Unobserved common causes are pervasive in real-world time series and can induce spurious associations that causal discovery methods mistake for direct edges. We propose LUCID (Learning Under Confounding for Inference and Discovery, a regime-adaptive deconfounding layer that first estimates the confounding regime from data using a Marvcenko--Pastur spectral router, then applies a deconfounding strategy matched to that regime. When the spectrum indicates pervasive factor confounding, LUCID attenuates factor-dominated variation and recovers contemporaneous (lag-0) structure from the resulting innovations, with edge selection calibrated against a data-driven edge-free null. Rather than being tied to a particular discovery algorithm, it can wrap existing discovery engines; we demonstrate consistent improvements across three such methods. On a diverse synthetic out-of-distribution benchmark spanning changes in confounder strength and sparsity, loading density, lag structure, volatility dynamics, edge heterogeneity, persistence, intermittency, and tail behavior, LUCID achieves the best family-weighted directed, lag-resolved graph F1 (0.60), improving over the strongest baseline by 0.19 absolute (≈!46% relative). Its advantage widens relative to looser lag-collapsed scoring, and remains robust under intermittent and heavy-tailed confounding. Code reproducing the method, the benchmark generators, and every reported experiment is available at https://github.com/bloomberg/causal-ts.