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A Minimax Theorem with Applications to Machine Learning, Signal Processing, and Finance
convex optimization minimax theorem robust optimization
2015/7/9
This paper concerns a fractional function of the form x^Ta/sqrt{x^TBx}, where B is positive definite. We consider the game of choosing x from a convex set, to maximize the function, and choosing (a,B)...
Local Privacy and Minimax Bounds: Sharp Rates for Probability Estimation
Local Privacy Minimax Bounds Sharp Rates Probability Estimation
2013/6/14
We provide a detailed study of the estimation of probability distributions---discrete and continuous---in a stringent setting in which data is kept private even from the statistician. We give sharp mi...
Divide and Conquer Kernel Ridge Regression: A Distributed Algorithm with Minimax Optimal Rates
Divide and Conquer Kernel Ridge Regression A Distributed Algorithm Minimax Optimal Rates
2013/6/14
We establish optimal convergence rates for a decomposition-based scalable approach to kernel ridge regression. The method is simple to describe: it randomly partitions a dataset of size N into m subse...
Learning subgaussian classes : Upper and minimax bounds
Learning subgaussian classes Upper and minimax bounds
2013/6/14
We obtain sharp oracle inequalities for the empirical risk minimization procedure in the regression model under the assumption that the target $Y$ and the model $\cF$ are subgaussian. The bound we obt...
Multichannel Deconvolution with Long-Range Dependence: A Minimax Study
adaptivity Besov spaces block thresholding deconvolu-tion Fourier analysis functional data long-range dependence,Meyer wavelets mini-max estimators multichannel deconvolution partial differential equations stationary sequences wavelet analysis
2013/6/13
We consider the problem of estimating the unknown response function in the multichannel deconvolution model with long-range dependent Gaussian errors. We do not limit our consideration to a specific t...
Minimax Multi-Task Learning and a Generalized Loss-Compositional Paradigm for MTL
Minimax Multi-Task Learning a Generalized Loss-Compositional Paradigm MTL
2012/11/23
Since its inception, the modus operandi of multi-task learning (MTL) has been to minimize the task-wise mean of the empirical risks. We introduce a generalized loss-compositional paradigm for MTL that...
Minimax testing of a composite null hypothesis defined via a quadratic functional in the model of regression
Nonparametric hypotheses testing sharp asymptotics separation rates minimax approach high-dimensional regression.
2012/9/17
We consider the problem of testing a particular type of composite null hypothesis under a nonparametric multivariate regression model. For a given quadraticfunctional Q, the null hypothesis states tha...
Nonparametric Regression Estimation with Incomplete Data: Minimax Global Convergence Rates and Adaptivity
Adaptivity Besov spaces inhomogeneous data minimax estimation
2011/7/6
We consider the nonparametric regression estimation problem of recovering an unknown response function $f$ on the basis of incomplete data when the design points follow a known density $g$ with a fini...
Essentially ML ASN-Minimax double sampling plans
Acceptance sampling by variables ASN-Minimax double sampling plan
2011/7/6
Subject of this paper is ASN-Minimax (AM) double sampling plans by variables for a normally distributed quality characteristic with unknown standard deviation and two-sided specification limits.
Minimax Policies for Combinatorial Prediction Games
Minimax Policies Combinatorial Prediction Games
2011/6/20
We address the online linear optimization problem when the actions of the forecaster are represented by
binary vectors. Our goal is to understand the magnitude of the minimax regret for the worst pos...
Asymptotic minimax risk of predictive density estimation for non-parametric regression
asymptotic minimax risk convergence rate non-parametric regression
2010/10/19
We consider the problem of estimating the predictive density of future observations from a non-parametric regression model. The density estimators are evaluated under Kullback--Leibler divergence and ...
Minimax Robust Function Approximation in Reproduction Kernel Hilbert Spaces
RKHS Thin-Plate Splines Smoothing Splines Scattered Data Interpolation and Approximation
2010/4/30
In this paper, we present a unified approach to function approximation in reproducing kernel Hilbert spaces (RKHS) that establishes a previously unrecognized optimality property for several well-known...
Nearly unbiased variable selection under minimax concave penalty
Variable selection model selection penalized estimation leastsquares correct selection minimax unbiasedness mean squared error
2010/3/10
We propose MC+, a fast, continuous, nearly unbiased and accu-
rate method of penalized variable selection in high-dimensional linear
regression. The LASSO is fast and continuous, but biased. The bia...
Lower bounds for the minimax risk using $f$-divergences and applications
Minimax lower bounds f-divergences Fano’sinequality Pinsker’s inequality Reconstruction from supportfunctions
2010/3/10
A new lower bound involving f-divergences between
the underlying probability measures is proved for the minimax
risk in estimation problems. The proof just uses the convexity
of the function f and ...
Minimax properties of beta kernel density estimators
Beta Kernel Density Minimax estimation
2010/3/9
In this paper, we are interested in the study of beta kernel estimators from
an asymptotic minimax point of view. It is well known that beta kernel estimators
are—on the contrary of classical kernel...