Variable screening for high-dimensional data via Pearson's chi-square statistic

The current era of data abundance presents a new challenge: the number of predictors can now reach thousands or even millions. This is particularly prevalent in medical studies involving gene expression patterns or MRI-based morphology.

Variable/feature screening is a powerful tool for reducing the massive number of predictors to a manageable scale, often smaller than the sample size. We derive conditions for guaranteeing the validity of variable screening first for the case when both the predictor and the response variables are categorical, which is subsequently extended to encompass other data types, including continuous variables.

Our theoretical contributions in categorical feature screening are twofold: First, we derive conditions for controlling the false discovery rate through Bayesian model averaging. Second, we establish a certain rate of uniform consistency of the screening statistics, which holds even with increasing number of categories, and some of which may be of nearly zero probabilities.

Leveraging on these theoretical results and data-based binning, we extend the categorical-based screening method to non-categorical variables including continuous variables commonly found in practice.

We present findings from extensive numerical studies contrasting the proposed methods with existing methods. We complement these findings with real applications to illustrate the practical implications of our work.