Search Results for author:
Found 11 papers, 7 papers with code
Evolving Scientific Discovery by Unifying Data and Background Knowledge with AI Hilbert
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.
Gain Confidence, Reduce Disappointment: A New Approach to Cross-Validation for Sparse Regression
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.
Optimal Low-Rank Matrix Completion: Semidefinite Relaxations and Eigenvector Disjunctions
Low-rank matrix completion consists of computing a matrix of minimal complexity that recovers a given set of observations as accurately as possible.
Sparse PCA With Multiple Components
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.
Sparse Plus Low Rank Matrix Decomposition: A Discrete Optimization Approach
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.
A new perspective on low-rank optimization
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.
Mixed-Projection Conic Optimization: A New Paradigm for Modeling Rank Constraints
We propose a framework for modeling and solving low-rank optimization problems to certifiable optimality.
Solving Large-Scale Sparse PCA to Certifiable (Near) Optimality
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.
On Polyhedral and Second-Order Cone Decompositions of Semidefinite Optimization Problems
We study a cutting-plane method for semidefinite optimization problems (SDOs), and supply a proof of the method's convergence, under a boundedness assumption.
A unified approach to mixed-integer optimization problems with logical constraints
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.
A Scalable Algorithm For Sparse Portfolio Selection
In numerical experiments, we establish that the outer-approximation procedure gives rise to dramatic speedups for sparse portfolio selection problems.
Optimization and Control
