Learning conditional independence structure for high-dimensional uncorrelated vector processes
This work addresses the challenge of graphical model selection in high-dimensional, nonstationary time series for researchers in statistics and machine learning, representing an incremental advance in handling uncorrelated processes with time-varying distributions.
The authors tackled the problem of inferring conditional independence graphs for high-dimensional, nonstationary Gaussian time series with uncorrelated samples, proposing a method based on testing conditional variances for small subsets. They characterized the sample size required for successful graph selection with high probability, addressing scenarios where sample size is drastically smaller than process dimension.
We formulate and analyze a graphical model selection method for inferring the conditional independence graph of a high-dimensional nonstationary Gaussian random process (time series) from a finite-length observation. The observed process samples are assumed uncorrelated over time and having a time-varying marginal distribution. The selection method is based on testing conditional variances obtained for small subsets of process components. This allows to cope with the high-dimensional regime, where the sample size can be (drastically) smaller than the process dimension. We characterize the required sample size such that the proposed selection method is successful with high probability.