Computationally efficient univariate filtering for massive data

TL;DR

This paper introduces a computationally efficient method for univariate filtering in large datasets by replacing traditional likelihood ratio tests with score tests or Pearson correlation, significantly reducing computation time while maintaining accuracy.

Contribution

It demonstrates that the score test can replace the likelihood ratio test in univariate filtering, achieving 30-60,000 times faster computation with comparable results in massive data analysis.

Findings

Score test is 30-60,000 times faster than likelihood ratio test.

Score test produces nearly the same results as the likelihood ratio test.

Replacing the likelihood ratio test with the score test is recommended for large-scale data analysis.

Abstract

The vast availability of large scale, massive and big data has increased the computational cost of data analysis. One such case is the computational cost of the univariate filtering which typically involves fitting many univariate regression models and is essential for numerous variable selection algorithms to reduce the number of predictor variables. The paper manifests how to dramatically reduce that computational cost by employing the score test or the simple Pearson correlation (or the t-test for binary responses). Extensive Monte Carlo simulation studies will demonstrate their advantages and disadvantages compared to the likelihood ratio test and examples with real data will illustrate the performance of the score test and the log-likelihood ratio test under realistic scenarios. Depending on the regression model used, the score test is 30 - 60,000 times faster than the log-likelihood ratio test and produces nearly the same results. Hence this paper strongly recommends to substitute the log-likelihood ratio test with the score test when coping with large scale data, massive data, big data, or even with data whose sample size is in the order of a few tens of thousands or higher.