  Estimating treatment effects over time holds significance in various domains,
including precision medicine, epidemiology, economy, and marketing. This paper
introduces a unique approach to counterfactual regression over time,
emphasizing long-term predictions. Distinguishing itself from existing models
like Causal Transformer, our approach highlights the efficacy of employing RNNs
for long-term forecasting, complemented by Contrastive Predictive Coding (CPC)
and Information Maximization (InfoMax). Emphasizing efficiency, we avoid the
need for computationally expensive transformers. Leveraging CPC, our method
captures long-term dependencies in the presence of time-varying confounders.
Notably, recent models have disregarded the importance of invertible
representation, compromising identification assumptions. To remedy this, we
employ the InfoMax principle, maximizing a lower bound of mutual information
between sequence data and its representation. Our method achieves
state-of-the-art counterfactual estimation results using both synthetic and
real-world data, marking the pioneering incorporation of Contrastive Predictive
Encoding in causal inference.
