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Theoretically Principled Trade-off between Robustness and Accuracy
- Hongyang R. Zhang, Yaodong Yu, Jiantao Jiao, E. Xing, L. Ghaoui, Michael I. Jordan
- Computer ScienceICML
- 24 January 2019
The prediction error for adversarial examples (robust error) is decompose as the sum of the natural (classification) error and boundary error, and a differentiable upper bound is provided using the theory of classification-calibrated loss, which is shown to be the tightest possible upper bound uniform over all probability distributions and measurable predictors.
Learning the Kernel Matrix with Semidefinite Programming
- G. Lanckriet, N. Cristianini, P. Bartlett, L. Ghaoui, Michael I. Jordan
- Computer ScienceJ. Mach. Learn. Res.
- 8 July 2002
This paper shows how the kernel matrix can be learned from data via semidefinite programming (SDP) techniques and leads directly to a convex method for learning the 2-norm soft margin parameter in support vector machines, solving an important open problem.
Model Selection Through Sparse Maximum Likelihood Estimation for Multivariate Gaussian or Binary Data
This work considers the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse, and presents two new algorithms for solving problems with at least a thousand nodes in the Gaussian case.
Tod Morrison University of Colorado at Denver and Health Sciences Center 14.0 is celebrating its 20th anniversary with a celebration and celebration of the life of Tod Morrison, the first openly gay president of the United States.
Linear Matrix Inequalities in System and Control Theory [Book Reviews]
- Stephen P. Boyd, L. Ghaoui, E. Feron, V. Balakrishnan
- MathematicsIEEE Transactions on Automatic Control
- 1 January 1994
This chapter discusses Transformations in Applications, Functional Analysis and Approximation Theory in Numerical Analysis, and Mathematical Problems in Linear Viscoelasticity.
A Direct Formulation for Sparse Pca Using Semidefinite Programming
A modification of the classical variational representation of the largest eigenvalue of a symmetric matrix, where cardinality is constrained, is used and derived to derive a semidefinite programming based relaxation for the problem.
A Robust Minimax Approach to Classification
- G. Lanckriet, L. Ghaoui, C. Bhattacharyya, Michael I. Jordan
- Mathematics, Computer ScienceJ. Mach. Learn. Res.
- 1 March 2003
This work considers a binary classification problem where the mean and covariance matrix of each class are assumed to be known, and addresses the issue of robustness with respect to estimation errors via a simple modification of the input data.
Robust Solutions to Least-Squares Problems with Uncertain Data
We consider least-squares problems where the coefficient matrices A,b are unknown but bounded. We minimize the worst-case residual error using (convex) second-order cone programming, yielding an…
A cone complementarity linearization algorithm for static output-feedback and related problems
- L. Ghaoui, F. Oustry, M. A. Rami
- MathematicsProceedings of Joint Conference on Control…
- 15 September 1996
This paper describes a linear matrix inequality (LMI)-based algorithm for the static and reduced-order output-feedback synthesis problems of n-th order linear time invariant (LTI) systems with n/sub…
Robust Control of Markov Decision Processes with Uncertain Transition Matrices
This work considers a robust control problem for a finite-state, finite-action Markov decision process, where uncertainty on the transition matrices is described in terms of possibly nonconvex sets, and shows that perfect duality holds for this problem, and that it can be solved with a variant of the classical dynamic programming algorithm, the "robust dynamic programming" algorithm.