Uncertainty of Tensor Graphical Model Selection

Graphical modeling is a powerful tool for various applied research. Usually, graphical models are associated with some multivariate (vector) distribution including Gaussian and others. It means that for each entity within a dataset, each feature would be a univariate random variable (scalar). However, in some applications, it may be beneficial to represent features associated with a single entity as multidimensional random variables. This idea leads to tensor graphical models where the dataset is given as tensor data, for example, vectors (1st order tensor, classic graphical models), matrices (2nd order tensor) or tensors of higher order. A key question is: what is the relationship between the expected quality of tensor graphical model selection and the edge density of true underlying graph? In this talk, we will present the results of the uncertainty analysis of one of the popular tensor graphical model selection algorithms, TLasso.
This is a joint work with V. A. Kalyagin, HSE NN.