High-dimensional longitudinal time series data is prevalent across various real-world applications. Many such applications can be modeled as regression problems with high-dimensional time series covariates. Deep learning has been a popular and powerful tool for fitting these regression models. Yet, the development of interpretable and reproducible deep-learning models is challenging and remains underexplored. This study introduces a novel method, Deep Learning Inference using Knockoffs for Time series data (DeepLINK-T), focusing on the selection of significant time series variables in regression while controlling the false discovery rate (FDR) at a predetermined level. DeepLINK-T combines deep learning with knockoff inference to control FDR in feature selection for time series models, accommodating a wide variety of feature distributions. It addresses dependencies across time and features by leveraging a time-varying latent factor structure in time series covariates. Three key ingredients for DeepLINK-T are 1) a Long Short-Term Memory (LSTM) autoencoder for generating time series knockoff variables, 2) an LSTM prediction network using both original and knockoff variables, and 3) the application of the knockoffs framework for variable selection with FDR control. Extensive simulation studies have been conducted to evaluate DeepLINK-T's performance, showing its capability to control FDR effectively while demonstrating superior feature selection power for high-dimensional longitudinal time series data compared to its non-time series counterpart. DeepLINK-T is further applied to three metagenomic data sets, validating its practical utility and effectiveness, and underscoring its potential in real-world applications.
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