no code implementations • 18 Aug 2023 • Ryan Cory-Wright, Cristina Cornelio, Sanjeeb Dash, Bachir El Khadir, Lior Horesh
The optimization techniques leveraged in this paper allow our approach to run in polynomial time with fully correct background theory under an assumption that the complexity of our derivation is bounded), or non-deterministic polynomial (NP) time with partially correct background theory.
no code implementations • 26 Jun 2023 • Ryan Cory-Wright, Andrés Gómez
Across a suite of 13 real datasets, a calibrated version of our procedure improves the test set error by an average of 4% compared to cross-validating without confidence adjustment.
2 code implementations • 20 May 2023 • Dimitris Bertsimas, Ryan Cory-Wright, Sean Lo, Jean Pauphilet
Low-rank matrix completion consists of computing a matrix of minimal complexity that recovers a given set of observations as accurately as possible.
1 code implementation • 29 Sep 2022 • Ryan Cory-Wright, Jean Pauphilet
We exploit these relaxations and bounds to propose exact methods and rounding mechanisms that, together, obtain solutions with a bound gap on the order of 0%-15% for real-world datasets with p = 100s or 1000s of features and r \in {2, 3} components.
1 code implementation • 26 Sep 2021 • Dimitris Bertsimas, Ryan Cory-Wright, Nicholas A. G. Johnson
We study the Sparse Plus Low-Rank decomposition problem (SLR), which is the problem of decomposing a corrupted data matrix into a sparse matrix of perturbations plus a low-rank matrix containing the ground truth.
1 code implementation • 12 May 2021 • Dimitris Bertsimas, Ryan Cory-Wright, Jean Pauphilet
We invoke the matrix perspective function - the matrix analog of the perspective function - and characterize explicitly the convex hull of epigraphs of simple matrix convex functions under low-rank constraints.
1 code implementation • 22 Sep 2020 • Dimitris Bertsimas, Ryan Cory-Wright, Jean Pauphilet
We propose a framework for modeling and solving low-rank optimization problems to certifiable optimality.
1 code implementation • 11 May 2020 • Dimitris Bertsimas, Ryan Cory-Wright, Jean Pauphilet
Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features.
no code implementations • 8 Oct 2019 • Dimitris Bertsimas, Ryan Cory-Wright
We study a cutting-plane method for semidefinite optimization problems (SDOs), and supply a proof of the method's convergence, under a boundedness assumption.
no code implementations • 3 Jul 2019 • Dimitris Bertsimas, Ryan Cory-Wright, Jean Pauphilet
We propose a unified framework to address a family of classical mixed-integer optimization problems with logically constrained decision variables, including network design, facility location, unit commitment, sparse portfolio selection, binary quadratic optimization, sparse principal analysis and sparse learning problems.
1 code implementation • 31 Oct 2018 • Dimitris Bertsimas, Ryan Cory-Wright
In numerical experiments, we establish that the outer-approximation procedure gives rise to dramatic speedups for sparse portfolio selection problems.
Optimization and Control