Conditional Semi-Distance Correlation

Music City Center 

Measuring conditional dependence is crucial in various fields, including genetic association studies and graphical models. In spatial transcriptomics, one of the focuses is on elucidating the relationships between gene expression levels (continuous variables) and spatially-related covariates, such as spatial locations, brain layers, and cell types (categorical variables), conditioning on other factors.

We introduce a novel measure of conditional dependence that assesses the relationship between a categorical random variable and a potentially high-dimensional random vector, conditioned on another random vector. This measure is based on semi-distance correlation and extends the concept of conditional distance correlation to incorporate categorical variables. Importantly, it serves as a general conditional dependence metric, unrestricted by linear or monotonic relationships. Further, we will develop a conditional independence test and derive its asymptotic distributions under the null hypothesis. This allows us to efficiently compute p-values, providing a significant computational advantage for high-dimensional data analysis over traditional regression tests, which will be especially useful for spatial transcriptomics data.