A Projection Based Conditional Dependence Measure with Applications to High-dimensional Undirected Graphical Models
This work addresses conditional dependence measurement for statisticians and data scientists working with high-dimensional graphical models, representing an incremental improvement with a novel method for a known bottleneck.
The authors tackled the problem of measuring conditional dependence in high-dimensional settings by proposing a new projection-based conditional dependence measure and developing an efficient conditional independence test with asymptotic guarantees. Numerical results and real data analysis demonstrated the superiority of their method.
Measuring conditional dependence is an important topic in statistics with broad applications including graphical models. Under a factor model setting, a new conditional dependence measure based on projection is proposed. The corresponding conditional independence test is developed with the asymptotic null distribution unveiled where the number of factors could be high-dimensional. It is also shown that the new test has control over the asymptotic significance level and can be calculated efficiently. A generic method for building dependency graphs without Gaussian assumption using the new test is elaborated. Numerical results and real data analysis show the superiority of the new method.