Machine learning algorithms are designed to capture complex relationships between features. In this context, the high dimensionality of data often results in poor model performance, with the risk of overfitting. Feature selection, the process of selecting a subset of relevant and non-redundant features, is, therefore, an essential step to mitigate these issues. However, classical feature selection approaches do not inspect the causal relationship between selected features and target, which can lead to misleading results in real-world applications. Causal discovery, instead, aims to identify causal relationships between features with observational data. In this paper, we propose a novel methodology at the intersection between feature selection and causal discovery, focusing on time series. We introduce a new causal feature selection approach that relies on the forward and backward feature selection procedures and leverages transfer entropy to estimate the causal flow of information from the features to the target in time series. Our approach enables the selection of features not only in terms of mere model performance but also captures the causal information flow. In this context, we provide theoretical guarantees on the regression and classification errors for both the exact and the finite-sample cases. Finally, we present numerical validations on synthetic and real-world regression problems, showing results competitive w.r.t. the considered baselines.

我们提出了一种新颖的方法，结合了特征选择和因果发现，专注于时间序列，通过使用前向和后向特征选择程序，并利用传递熵来估计从特征到目标的因果信息流，实现了特征的选择不仅仅基于模型性能，还捕捉到因果信息流。

通过传输熵进行因果特征选择