13 citations · 28 across the 5 of their papers we have counts for
7 papers
The Trimmed Lasso: Sparsity and Robustness
Dimitris Bertsimas, Martin S. Copenhaver, Rahul Mazumder
Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions t…
Certifiably Optimal Low Rank Factor Analysis
Dimitris Bertsimas, Martin S. Copenhaver, Rahul Mazumder
Factor Analysis (FA) is a technique of fundamental importance that is widely used in classical and modern multivariate statistics, psychometrics and econometrics. In this paper, we…
On Structural Decompositions of Finite Frames
Alice Z. -Y. Chan, Martin S. Copenhaver, Sivaram K. Narayan +2
A frame in an -dimensional Hilbert space is a possibly redundant collection of vectors that span the space. A tight frame is a generalization of an orth…
Factor posets of frames and dual frames in finite dimensions
Kileen Berry, Martin S. Copenhaver, Eric Evert +4
We consider frames in a finite-dimensional Hilbert space where frames are exactly the spanning sets of the vector space. A factor poset of a frame is defined to be a collection of…
Characterization of the equivalence of robustification and regularization in linear and matrix regression
Dimitris Bertsimas, Martin S. Copenhaver
The notion of developing statistical methods in machine learning which are robust to adversarial perturbations in the underlying data has been the subject of increasing interest in…
Maximum Robustness and Surgery of Frames in finite dimensions
Martin S. Copenhaver, Yeon Hyang Kim, Cortney Logan +3
We consider frames in a finite-dimensional Hilbert space Hn where frames are exactly the spanning sets of the vector space. We present a method to determine the maximum robustness…
Diagram vectors and Tight Frame Scaling in Finite Dimensions
Martin S. Copenhaver, Yeon Hyang Kim, Cortney Logan +4
We consider frames in a finite-dimensional Hilbert space Hn where frames are exactly the spanning sets of the vector space. The diagram vector of a vector in R2 was previously defi…