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.

提出了一种新的方法 DeepLINK-T，结合深度学习和 Knockoffs 推断，在高维长时序数据中控制假发现率（FDR），实现特征选择。该方法通过使用 LSTM 自编码器生成时间序列的 Knockoff 变量，使用原始和 Knockoff 变量的 LSTM 预测网络以及应用 Knockoffs 框架进行变量选择来解决时间和特征之间的依赖关系，并通过大量模拟研究来评估其性能，表明其相对于非时序模型具有更好的特征选择能力，并应用于三个元基因组数据集来验证其实用性和有效性，展示了其在实际应用中的潜力。

DeepLINK-T：使用 knockoffs 和 LSTM 进行时间序列数据的深度学习推理

DeepLINK-T: deep learning inference for time series data using knockoffs  and LSTM

A concept-based classifier can explain the decision process of a deep
learning model by human-understandable concepts in image classification
problems. However, sometimes concept-based explanations may cause false
positives, which misregards unrelated concepts as important for the prediction
task. Our goal is to find the statistically significant concept for
classification to prevent misinterpretation. In this study, we propose a method
using a deep learning model to learn the image concept and then using the
Knockoff samples to select the important concepts for prediction by controlling
the False Discovery Rate (FDR) under a certain value. We evaluate the proposed
method in our synthetic and real data experiments. Also, it shows that our
method can control the FDR properly while selecting highly interpretable
concepts to improve the trustworthiness of the model.

本研究提出了一种利用深度学习模型学习图像概念，然后使用 Knockoff 样本选择重要概念进行预测的方法来控制误发现率，实验结果表明该方法可以控制 FDR 并选择高度可解释的概念来提高模型的可靠性。