Estimating Counterfactual Outcomes of Time-varying Treatments using Deep Gaussian Process

Estimating counterfactual outcomes of time-varying treatments is important for medication, vaccination, advertisement and maintenance of equipment. However, it is more difficult than prediction of one-time treatment effect because of lasting treatment effect and time-varying confounders. The current method CRN predicts counterfactual outcomes of time-varying treatments with high accuracy by using LSTM-based Encoder-Decoder to consider lasting treatment effect and learning representations to reduce the effect of time-varying confounders. However, CRN needs a lot of training data and cannot calculate the reliability of the prediction when forecasting counterfactual data. In this study, we introduce a new method Deep CMGP that is a combination of CRN and CMGP. CMGP is a method for estimating one-time treatment effect using multi-task Gaussian process that can be trained on small amounts of training data and calculate the reliability of the prediction. We extend CMGP to estimation of counterfactual outcomes of time-varying treatments by replacing the deep learning part of CRN with deep multi-task Gaussian process. The experimental results show that when the number of training data is limited (Ntrain=1000, 2000), the prediction accuracy is improved compared to baseline methods, and the reliability of the prediction of the counterfactual data is also obtained. In the case of Ntrain=5000, 10000, the accuracy was not as good as those of the baseline methods based on deep learning, but it was found that Deep CMGP can be trained using stochastic variational inference method on a large amount of data (Ntrain=10000), which Gaussian process is not good at.