CMStatistics 2018: Start Registration
View Submission - CMStatistics
B1548
Title: On the properties of sign estimators derived from hard thresholded lasso and hard thresholded basis pursuit Authors:  Patrick Tardivel - University of Wroclaw (Poland) [presenting]
Abstract: In the high-dimensional linear model, when the number of observations is lower than the number of explanatory variables, we aim at estimating the sign of the model. It is well known that the irrepresentable condition is a necessary and ``almost'' sufficient condition to recover exactly the sign of the model with the lasso sign estimator. In a first step, we provide a new result about the irrepresentable condition: the probability to recover the sign of the model with the lasso sign estimator is smaller than 1/2 once the irrepresentable condition does not hold. Consequently, there is an issue to provide a sign estimator able to recover the sign of the model under a weaker assumption than the irrepresentable condition. In a second step, we show that sign estimators derived from hard thresholded lasso and hard thresholded basis pursuit only need identifiability condition to recover exactly the sign of the model. Because the identifiability condition is a weaker condition than the irrepresentable condition, these sign estimators are theoretically better than the lasso sign estimator. Finally, the irrepresentability and identifiability curves, function of the signal sparsity, show that the gap between the irrepresentable condition and the identifiability condition is huge. That is the reason why sign estimators derived from hard thresholded lasso and hard thresholded basis pursuit outperform the lasso sign estimator.