Inferring Networks from High-Dimensional Data with Mixed Variables

Abstract

We present two methodologies to deal with high-dimensional data with mixed variables, the strongly decomposable graphical model and the regression-type graphical model. The first model is used to infer conditional independence graphs. The latter model is applied to compute the relative importance or contribution of each predictor to the response variables. Recently, penalized likelihood approaches have also been proposed to estimate graph structures. In a simulation study, we compare the performance of the strongly decomposable graphical model and the graphical lasso in terms of graph recovering. Five different graph structures are used to simulate the data: the banded graph, the cluster graph, the random graph, the hub graph and the scale-free graph. We assume the graphs are sparse. Our finding, in the simulation study, is that the strongly decomposable graphical model shows, generally, comparable or better performance both in low and high-dimensional case. Finally, we show an application on mixed data.

Use of High Dimensional Modeling for automatic variables selection: the best path algorithm

“…The novelty of this paper is to present an algorithm that it is suitable for each of this point. Indeed, this method is compatible with large datasets, and works with continuous and discrete data [Abbruzzo and Mineo, 2015]. Furthermore, I will show that this algorithm in an exercise of prediction minimizes both the loss of information and its redundancy.…”

“…If we consider two mixed model M 0 and M 1 where M 0 ⊂ M 1 and them differ only by one edge e = (v i , v j ). The Likelihood ration test for M 0 and M 1 can be computed as a test of v i ⊥ v j |C \{vi,vj } , where C is a clique of M 1 that contain e only [Abbruzzo and Mineo, 2015]. In other words, these computations only involve the variables in C.…”

Drift Estimation with Graphical Models

“…Strongly decomposable model is an important class of model that can be used to analyze mixed data. This class restrict the class of possible interaction model which would be to huge to be explored [Abbruzzo and Mineo, 2015]. The graph build to find the best spanning tree, can be see with a symmetric adjacency matrix AM , with dimension V × V , in which each element takes value of 1 if an edge exists between two of the V variables, and zero otherwise.…”