4 papers
A Unified Framework for Pattern Recovery in Penalized and Thresholded Estimation and its Geometry
Piotr Graczyk, Ulrike Schneider, Tomasz Skalski +1
We consider the framework of penalized estimation where the penalty term is given by a real-valued polyhedral gauge, which encompasses methods such as LASSO, generalized LASSO, SLO…
Pattern recovery by SLOPE
Małgorzata Bogdan, Xavier Dupuis, Piotr Graczyk +4
SLOPE is a popular method for dimensionality reduction in the high-dimensional regression. Indeed some regression coefficient estimates of SLOPE can be null (sparsity) or can be eq…
Pattern recovery and signal denoising by SLOPE when the design matrix is orthogonal
Tomasz Skalski, Piotr Graczyk, Bartosz Kołodziejek +1
Sorted Penalized Estimator (SLOPE) is a relatively new convex regularization method for fitting high-dimensional regression models. SLOPE allows to reduce the model dimens…
Maximum likelihood estimation for discrete exponential families and random graphs
Krzysztof Bogdan, Michał Bosy, Tomasz Skalski
We characterize the existence of the maximum likelihood estimator for discrete exponential families. Our criterion is simple to apply as we show in various settings, most notably f…