Ultra-high-dimensional feature screening of binary categorical response data based on Jensen-Shannon divergence

Currently, most of the ultra-high-dimensional feature screening methods for categorical data are based on the correlation between covariates and response variables, using some statistics as the screening index to screen important covariates. Thus, with the increasing number of data types and model availability limitations, there may be a potential problem with the existence of a class of unimportant covariates that are also highly correlated with the response variable due to their high correlation with the other covariates. To address this issue, in this paper, we establish a model-free feature screening procedure for binary categorical response variables from the perspective of the contribution of features to classification. The idea is to introduce the Jensen-Shannon divergence to measure the difference between the conditional probability distributions of the covariates when the response variables take on different values. The larger the value of the Jensen-Shannon divergence, the stronger the covariate's contribution to the classification of the response variable, and the more important the covariate is. We propose two kinds of model-free ultra-high-dimensional feature screening methods for binary response data. Meanwhile, the methods are suitable for continuous or categorical covariates. When the numbers of covariate categories are the same, the feature screening is based on traditional Jensen-Shannon divergence. When the numbers of covariate categories are different, the Jensen-Shannon divergence is adjusted using the logarithmic factor of the number of categories. We theoretically prove that the proposed methods have sure screening and ranking consistency properties, and through simulations and real data analysis, we demonstrate that, in feature screening, the approaches proposed in this paper have the advantages of effectiveness, stability, and less computing time compared with an existing method

The relationship between gut microbiota and insomnia: a bi-directional two-sample Mendelian randomization research

IntroductionInsomnia is the second most common mental health issue, also is a social and financial burden. Insomnia affects the balance between sleep, the immune system, and the central nervous system, which may raise the risk of different systemic disorders. The gut microbiota, referred to as the “second genome,” has the ability to control host homeostasis. It has been discovered that disruption of the gut-brain axis is linked to insomnia.MethodsIn this study, we conducted MR analysis between large-scale GWAS data of GMs and insomnia to uncover potential associations.ResultsTen GM taxa were detected to have causal associations with insomnia. Among them, class Negativicutes, genus Clostridiuminnocuumgroup, genus Dorea, genus Lachnoclostridium, genus Prevotella7, and order Selenomonadalesare were linked to a higher risk of insomnia. In reverse MR analysis, we discovered a causal link between insomnia and six other GM taxa.ConclusionIt suggested that the relationship between insomnia and intestinal flora was convoluted. Our findings may offer beneficial biomarkers for disease development and prospective candidate treatment targets for insomnia

Morse set classification and hierarchical refinement using Conley index

Reliable analysis of vector elds is crucial for the rigorous interpretation of the ow data stemming from a wide range of engineering applications. Morse decomposition of a vector field has proven a useful topological representation that is more numerically stable than previous vector field skeletons. In this paper, we enhance the procedure of Morse decomposition and propose an automatic refinement scheme to construct the Morse Connection Graph (MCG) of a given vector eld in a hierarchical fashion. Our framework allows a Morse set to be re ned through a local update of the flow combinatorialization, which leads to a more detailed MCG. This refined MCG has consistent topology with the original MCG because the refinement is conducted locally. The computation is faster than the original t-map approach because we reuse the previous tracing information and perform only local updates. The classification of the exetracted Morse sets is a crucial step for the construction of MCG. In this work, we advocate the use of Conley index for the classification. Conley index is a more general characteristic than Poincar´e index for the classi cation of flow dynamics. We present a framework to compute the Conley index of an isolating block in a flow. In addition, an efficient algorithm for computing an upper bound of the Conley index of any given Morse set is introduced to assist the automatic refinement process. Furthermore, an improved visualization technique for MCG is described which conveys the classification information of different Morse sets with the aid of the visualization of their Conley indices. Finally, we apply the proposed techniques to a number of synthetic and simulation data sets to demonstrate their utility