Model-Augmented Estimation of Conditional Mutual Information for Feature Selection
This work addresses the problem of efficient and accurate feature selection for high-dimensional data, which is incremental as it builds on existing conditional independence testing methods.
The paper tackles the challenge of Markov blanket feature selection in high dimensions by proposing a two-step method that uses neural networks to map features to low-dimensional representations and then applies a k-NN estimator for conditional independence testing, showing improved performance on synthetic and real data.
Markov blanket feature selection, while theoretically optimal, is generally challenging to implement. This is due to the shortcomings of existing approaches to conditional independence (CI) testing, which tend to struggle either with the curse of dimensionality or computational complexity. We propose a novel two-step approach which facilitates Markov blanket feature selection in high dimensions. First, neural networks are used to map features to low-dimensional representations. In the second step, CI testing is performed by applying the $k$-NN conditional mutual information estimator to the learned feature maps. The mappings are designed to ensure that mapped samples both preserve information and share similar information about the target variable if and only if they are close in Euclidean distance. We show that these properties boost the performance of the $k$-NN estimator in the second step. The performance of the proposed method is evaluated on both synthetic and real data.