# Causal State-Space Model for Causal Inference: Estimating Longitudinal Individual Treatment Effects

arXiv: https://arxiv.org/abs/2608.08288 · HTML: https://mlsanity.com/paper/2608.08288/

## 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 8 Aug 2026.

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

- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [TSMixer: An All-MLP Architecture for Time Series Forecasting](https://mlsanity.com/paper/2303.06053/) (2023)
- [Estimating Counterfactual Treatment Outcomes over Time Through Adversarially Balanced Representations](https://mlsanity.com/paper/2002.04083/) (2020)
- [Causal Transformer for Estimating Counterfactual Outcomes](https://mlsanity.com/paper/2204.07258/) (2022)
- [Generalization Bounds and Representation Learning for Estimation of Potential Outcomes and Causal Effects](https://mlsanity.com/paper/2001.07426/) (2020)
- [S4ND: Modeling Images and Videos as Multidimensional Signals Using State Spaces](https://mlsanity.com/paper/2210.06583/) (2022)
- [Bounds on Representation-Induced Confounding Bias for Treatment Effect Estimation](https://mlsanity.com/paper/2311.11321/) (2023)
- [Causal Contrastive Learning for Counterfactual Regression Over Time](https://mlsanity.com/paper/2406.00535/) (2024)
- [CAETC: Causal Autoencoding and Treatment Conditioning for Counterfactual Estimation over Time](https://mlsanity.com/paper/2603.11565/) (2026)

## Abstract (arXiv)

Estimating counterfactual outcomes over time from longitudinal observational data is central to clinical decision support. Existing methods rely on domain confusion -- adversarial training that renders representations invariant to treatment assignment -- yet this invariance creates a mutual information conflict: it suppresses treatment-correlated covariate signals necessary for accurate outcome prediction. We formalise this tension via a Jensen-Shannon divergence bound on counterfactual prediction error and develop two complementary models. CSSD (Causal State-Space model with Direct decoder) adapts selective State Space Models with a parallel multi-step decoder that eliminates accumulated rollout error by producing all prediction horizons simultaneously in a single forward pass. CSSPD (Causal State-Space model with Predictive regularisation and Direct decoder) augments CSSD with Contrastive Predictive Coding and Local Information Maximisation to reinforce temporal predictability in the balancing representation and recover local covariate information destroyed by domain confusion. On MIMIC-III, CSSPD achieves lower counterfactual RMSE than the Causal Transformer at every horizon tau >= 2 at O(T) encoder cost, with gains from 0.02 (2-step) to 0.07 (6-step). On Cancer Simulation across confounding strengths gamma in {0,1,2,3,4}, CSSPD outperforms CT at gamma <= 3 (margins 25.9%--37.0%), and CSSD achieves the lowest overall average RMSE (12.7% reduction over CT), confirming the MI conflict analysis. To our knowledge, this is the first work to formalise the balancing-prediction MI conflict and propose a structured resolution through complementary predictive and information-theoretic training objectives.