TITLE:
Model-Free Ultra-High-Dimensional Feature Screening for Multi-Classified Response Data Based on Weighted Jensen-Shannon Divergence
AUTHORS:
Qingqing Jiang, Guangming Deng
KEYWORDS:
Ultra-High-Dimensional, Multi-Classified, Weighted Jensen-Shannon Divergence, Model-Free, Feature Screening
JOURNAL NAME:
Open Journal of Statistics,
Vol.13 No.6,
December
14,
2023
ABSTRACT: In
ultra-high-dimensional data, it is common for the response variable to be
multi-classified. Therefore, this paper proposes a model-free screening method
for variables whose response variable is multi-classified from the point of
view of introducing Jensen-Shannon divergence to measure the importance of
covariates. The idea of the method is to calculate the Jensen-Shannon
divergence between the conditional probability distribution of the covariates
on a given response variable and the unconditional probability distribution of
the covariates, and then use the probabilities of the response variables as
weights to calculate the weighted Jensen-Shannon divergence, where a larger
weighted Jensen-Shannon divergence means that the covariates are more
important. Additionally, we also investigated an adapted version of the method,
which is to measure the relationship between the covariates and the response
variable using the weighted Jensen-Shannon divergence adjusted by the
logarithmic factor of the number of categories when the number of categories in
each covariate varies. Then, through both theoretical and simulation
experiments, it was demonstrated that the proposed methods have sure screening
and ranking consistency properties. Finally, the results from simulation and
real-dataset experiments show that in feature screening, the proposed methods
investigated are robust in performance and faster in computational speed
compared with an existing method.