Section: New Results
Algorithms and Estimation for graph data
Participants: A. Gégout-Petit, A. Gueudin, C. Karmann
In the purpose to deal with inference for network of zero-inflated variables, we have developped a new regression model. We consider the problem of variable selection when the response is ordinal, that is an ordered categorical variable. In particular, we are interested in selecting quantitative explanatory variables linked with the ordinal response variable and we want to determine which predictors are relevant. In this framework, we choose to use the polytomous ordinal logistic regression model using cumulative logits which generalizes the logistic regression. We then introduce the Lasso estimation of the regression coefficients using the Frank-Wolfe algorithm. To deal with the choice of the penalty parameter, we use the stability selection method and we develop a new method based on the knockoffs idea. This knockoffs method is general and suitable to any regression and besides, gives an order of importance of the covariates. Finally, we provide some experimental results to corroborate our method and we present an application of this regression method for zero-inflated network inference. This work is the object of a presentation in a conference  and a preprint submitted in a journal .