CEPAE: Conditional Entropy-Penalized Autoencoders for Time Series Counterfactuals

TL;DR

The Conditional Entropy-Penalized Autoencoder (CEPAE), a novel autoencoder-based approach for counterfactual inference, which employs an entropy penalization loss over the latent space to encourage disentangled data representations.

Abstract

The ability to accurately perform counterfactual inference on time series is crucial for decision-making in fields like finance, healthcare, and marketing, as it allows us to understand the impact of events or treatments on outcomes over time. In this paper, we introduce a new counterfactual inference approach tailored to time series data impacted by market events, which is motivated by an industrial application. Utilizing the abduction-action-prediction procedure and the Structural Causal Model framework, we first adapt methods based on variational autoencoders and adversarial autoencoders, both previously used in counterfactual literature although not in time series settings. Then, we present the Conditional Entropy-Penalized Autoencoder (CEPAE), a novel autoencoder-based approach for counterfactual inference, which employs an entropy penalization loss over the latent space to encourage disentangled data representations. We validate our approach both theoretically and experimentally on synthetic, semi-synthetic, and real-world datasets, showing that CEPAE generally outperforms the other approaches in the evaluated metrics.

Figures (9)

• Figure 1: Example of a time series counterfactual (cf) estimation comparison for our synthetic dataset among a baseline LSTM-based forecast model and CEPAE. The vertical line separates pre-event from post-event observations, counterfactual estimations and ground truth.
• Figure 2: Problem setting’s computational graphs. Solid arrows denote direct influences on $\boldsymbol{Y}$; dotted double arrow reflects the abduction link. The confounded panel adds $\boldsymbol{H}{\rightarrow}E$.
• Figure 3: Scheme of encoder-decoder based methods for counterfactual inference, both in training and counterfactual inference phase.
• Figure 4: Synthetic Control and Causal Impact comparison.
• Figure 5: Convergence of CEPAE with a fixed EP weight of $0.09$ on the unconfounded semi-synthetic dataset. We plot counterfactual MAE versus training epoch. The model converges slowly but reaches a stable low-error region around epoch 100.