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Control system analysis and synthesis via linear matrix inequalities
Control system analysis synthesis linear matrix inequalities
2015/7/13
A wide variety of problems in systems and control theory can be cast or recast as convex problems that involve linear matrix inequalities (LMIs). For a few very special cases there are “analytical sol...
A Primal-Dual Potential Reduction Method for Problems Involving Matrix Inequalities
Interior point algorithms Linear matrix inequaliües Semidefinite programming
2015/7/13
We describe a potential reduction method for convex optimization problems involving matrix inequalities. The method is based on the theory developed by Nesterov and Nemirovsky and generalizes Gonzaga ...
Multi-objective H2/H-infinity-Optimal Control via Finite Dimensional Q-Parametrization and Linear Matrix Inequalities
Finite Dimensional Q-Parametrization Linear Matrix Inequalities
2015/7/13
The problem of multi-objective H2/H-infinity optimal controller design is reviewed. There is as yet no exact solution to this problem. We present a method based on that proposed by Scherer. The proble...
Approximate Dynamic Programming via Iterated Bellman Inequalities
Convex Optimization Dynamic Programming Stochastic Control
2015/7/9
In this paper we introduce new methods for finding functions that lower bound the value function of a stochastic control problem, using an iterated form of the Bellman inequality. Our method is based ...
On Lyapunov Inequalities and Subsolutions for Efficient Importance Sampling
Lyapunov Inequalities Efficient Importance Sampling
2015/7/6
In this article we explain some connections between Lyapunov methods and subsolutions of an associated Isaacs equation for the design of efficient importance sampling schemes. As we shall see, subsolu...
Modern statistical estimation via oracle inequalities
Modern statistical estimation oracle inequalities
2015/6/17
A number of fundamental results in modern statistical theory involve thresholding estimators. This survey paper aims at reconstructing the history of how thresholding rules came to be popular in stati...
Some results on a $χ$-divergence, an~extended~Fisher information and~generalized~Cramer-Rao inequalities
Some results $χ$-divergence an~extended~Fisher information generalized~Cramer-Rao inequalities
2013/6/17
We propose a modified $\chi^{\beta}$-divergence, give some of its properties, and show that this leads to the definition of a generalized Fisher information. We give generalized Cram\'er-Rao inequalit...
Anisotropic oracle inequalities in noisy quantization
Quantization Deconvolution Fast rates Margin assumption,k-means clus-tering
2013/6/13
The effect of errors in variables in quantization is investigated. We prove general exact and non-exact oracle inequalities with fast rates for an empirical minimization based on a noisy sample $Z_i=X...
Testing Functional Inequalities
Conditional moment inequalities kernel estimation one-sided test local power Lp norm Poissonization
2012/9/17
This paper develops tests for inequality constraints of nonparametric re-gression functions. The test statistics involve a one-sided versionofLp-type functionals of kernel estimators (1≤p <∞). Drawing...
Lasso and probabilistic inequalities for multivariate point processes
Multivariate counting process Hawkes processes adaptive estimation Lasso procedure Bernstein-type inequalities.
2012/9/17
Due to its low computational cost, Lasso is an attractive regularization method for high-dimensional statistical settings. In this paper, we consider multivariate counting processes depending on an un...
Oracle inequalities for computationally adaptive model selection
Oracle computationally adaptive model selection
2012/9/17
We analyze general model selection procedures using penalized empirical loss minimization under computational constraints. While classical model selection approaches do not consider computational aspe...
Gaussian Oracle Inequalities for Structured Selection in Non-Parametric Cox Model
Gaussian Oracle Inequalities Structured Selection Non-Parametric Cox Model
2012/9/19
To better understand the interplay of censoring and sparsity we develop finite sample properties of nonparametric Cox proportional hazard乫s model. Due to high impact of sequencing data, carrying genet...
The Lasso, correlated design, and improved oracle inequalities
compatibility correlation entropy high-dimensional model
2011/7/19
We study high-dimensional linear models and the $\ell_1$-penalized least squares estimator, also known as the Lasso estimator.
Sharp oracle inequalities and slope heuristic for specification probabilities estimation in general random fields
Sharp oracle inequalities slope heuristic specification probabilities estimation
2011/7/5
We provide new methods for estimation of the one-point specification probabilities in general discrete random fields.
Transportation inequalities: From Poisson to Gibbs measures
Gibbs measures Poisson point processes transportation inequalities
2011/3/21
We establish an optimal transportation inequality for the Poisson measure on the configuration space. Furthermore, under the Dobrushin uniqueness condition, we obtain a sharp transportation inequality...