# Causal Inference in Non-linear Time-series using Deep Networks and Knockoff Counterfactuals

arXiv: https://arxiv.org/abs/2109.10817 · HTML: https://mlsanity.com/paper/2109.10817/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 41 references that are in the map.
- First posted on arXiv 22 Sep 2021.

## Builds on (most cited first, 13 of 13)

- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Generating Sequences With Recurrent Neural Networks](https://mlsanity.com/paper/1308.0850/) (2013)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [Controlling the false discovery rate via knockoffs](https://mlsanity.com/paper/1404.5609/) (2014)
- [High-recall causal discovery for autocorrelated time series with latent confounders](https://mlsanity.com/paper/2007.01884/) (2020)
- [Instance-based Counterfactual Explanations for Time Series Classification](https://mlsanity.com/paper/2009.13211/) (2020)
- [Deep Knockoffs](https://mlsanity.com/paper/1811.06687/) (2018)
- [Data Generating Process to Evaluate Causal Discovery Techniques for Time Series Data](https://mlsanity.com/paper/2104.08043/) (2021)
- [Neural Granger Causality](https://mlsanity.com/paper/1802.05842/) (2018)
- [Robust inference with knockoffs](https://mlsanity.com/paper/1801.03896/) (2018)
- [Knockoffs for the mass: new feature importance statistics with false discovery guarantees](https://mlsanity.com/paper/1807.06214/) (2018)
- [Counterfactual Generation with Knockoffs](https://mlsanity.com/paper/2102.00951/) (2021)

## Built on by (most cited first, 3 of 3)

- [Time Series Causal Link Estimation under Hidden Confounding using Knockoff Interventions](https://mlsanity.com/paper/2209.11497/) (2022)
- [Causal Discovery using Model Invariance through Knockoff Interventions](https://mlsanity.com/paper/2207.04055/) (2022)
- [Group Interventions on Deep Networks for Causal Discovery in Subsystems](https://mlsanity.com/paper/2510.23906/) (2025)

## Abstract (arXiv)

Estimating causal relations is vital in understanding the complex interactions in multivariate time series. Non-linear coupling of variables is one of the major challenges inaccurate estimation of cause-effect relations. In this paper, we propose to use deep autoregressive networks (DeepAR) in tandem with counterfactual analysis to infer nonlinear causal relations in multivariate time series. We extend the concept of Granger causality using probabilistic forecasting with DeepAR. Since deep networks can neither handle missing input nor out-of-distribution intervention, we propose to use the Knockoffs framework (Barberand Cand`es, 2015) for generating intervention variables and consequently counterfactual probabilistic forecasting. Knockoff samples are independent of their output given the observed variables and exchangeable with their counterpart variables without changing the underlying distribution of the data. We test our method on synthetic as well as real-world time series datasets. Overall our method outperforms the widely used vector autoregressive Granger causality and PCMCI in detecting nonlinear causal dependency in multivariate time series.