Time Series Prediction Problems Under Covariate Drift
Xiaoxue Liang, Kuangrong Hao, Lei Chen, Lihong Ren · 2024
In the real world, time series data are ubiquitous, and the prediction task of time series data is very important. Most real-world time series data do not satisfy the assumption of independent and identical distribution (i.i.d.) due to environmental changes, that is, the distribution of the training datasets is different from the distribution of the test datasets,$P(X_{i})= P(X_{j})$, but the conditional distribution is usually considered to be unchanged,$P(y\vert x_{i})= P(y\vert x_{j})$. In this case, it is defined as covariate drift. However, most of the existing prediction algorithms are based on the assumption of i.i.d., so these algorithms have great limitations in the prediction of time series data under covariant drift. Therefore, the AEIF-MLP model is proposed, a time series data prediction model based on MLP and causal structures. The model mainly consists of two modules. Based on the principle of maximum entropy, we propose an adaptive environment segmentation module to separate different environments in the training datasets. Based on the causal structure, we propose an invariant feature learning module to learn common invariant features in different environments to train the model to deal with test datasets of unknown distribution. In summary, this method solves the problem of time series prediction under covariate drift. The validity of the model is verified by drift data sets in different environments for the first time, and the validity of the model is further verified on two real data sets.