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Journal of Computational and Applied Mathematics, ISSN 0377-0427, 01/2015, Volume 274, pp. 1 - 10
Sufficient optimality conditions are established for a class of nondifferentiable generalized minimax fractional programming problem with support functions.... 
Support function | Duality | Sufficiency | Generalized convexity | Minimax fractional programming | MATHEMATICS, APPLIED | Management science
Journal Article
Annals of Statistics, ISSN 0090-5364, 2018, Volume 46, Issue 6B, pp. 3603 - 3642
We show that two polynomial time methods, a Lasso estimator with adaptively chosen tuning parameter and a Slope estimator, adaptively achieve the minimax... 
High-dimensional statistics | Minimax rates | Lasso | Sparse linear regression | Slope | REGRESSION | SPARSITY | RECOVERY | OPTIMAL RATES | MINIMAX | DANTZIG SELECTOR | STATISTICS & PROBABILITY | minimax rates | high-dimensional statistics
Journal Article
JOURNAL OF MACHINE LEARNING RESEARCH, ISSN 1532-4435, 2019, Volume 20
The problem is that of sequential probability forecasting for finite-valued time series. The data is generated by an unknown probability distribution over the... 
sequence prediction | BEHAVIOR | Bayesian prediction | complete-class theorems | AUTOMATION & CONTROL SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | minimax theorems
Journal Article
Biometrika, ISSN 0006-3444, 6/2012, Volume 99, Issue 2, pp. 315 - 325
Journal Article
Mathematics of Operations Research, ISSN 0364-765X, 5/2010, Volume 35, Issue 2, pp. 363 - 394
Journal Article
Neural Networks, ISSN 0893-6080, 03/2020, Volume 123, pp. 343 - 361
Deep learning has been applied to various tasks in the field of machine learning and has shown superiority to other common procedures such as kernel methods.... 
Deep learning | Linear estimator | Neural network | Minimax optimality | Nonparametric regression
Journal Article
Mathematical and Computer Modelling, ISSN 0895-7177, 03/2013, Volume 57, Issue 5-6, pp. 1083 - 1100
Journal Article
The Annals of Statistics, ISSN 0090-5364, 6/2011, Volume 39, Issue 3, pp. 1608 - 1632
We address the problem of density estimation with 𝕃 s -loss by selection of kernel estimators. We develop a selection procedure and derive corresponding 𝕃 s... 
Density estimation | Minimax | Estimate reliability | Mathematical inequalities | Mathematical functions | Density | Estimators | Oracles | Double-struck L | Kernel estimators | Empirical process | risk | Adaptive estimation | Oracle inequalities | oracle inequalities | L-s-risk | kernel estimators | empirical process | STATISTICS & PROBABILITY | adaptive estimation | Mathematics | 62G05 | Ls-risk | 62G20
Journal Article
by Cai, TT and Ma, J and Zhang, LJ
ANNALS OF STATISTICS, ISSN 0090-5364, 06/2019, Volume 47, Issue 3, pp. 1234 - 1267
Unsupervised learning is an important problem in statistics and machine learning with a wide range of applications. In this paper, we study clustering of... 
High-dimensional data | misclustering error | MAXIMUM-LIKELIHOOD | DISCRIMINANT-ANALYSIS | STATISTICS & PROBABILITY | EM algorithm | Minimax optimality | Gaussian mixture model | unsupervised learning
Journal Article
Statistica Sinica, ISSN 1017-0405, 10/2009, Volume 19, Issue 4, pp. 1729 - 1739
In 1961, for detecting a change in the drift of a Brownian motion, Shiryaev introduced what is now usually referred to as the Shiryaev-Roberts procedure. This... 
Brownian motion | Mathematical procedures | Minimax | Surveillance | False alarms | Applied statistics | General | Mathematics | Grants | Stopping distances | Shiryaev-roberts procedures | Changepoint problems | Cusum procedures | Sequential detection | Shiryaev-Roberts procedures | sequential detection | CUSUM | STATISTICS & PROBABILITY | CUSUM procedures
Journal Article
The Annals of Statistics, ISSN 0090-5364, 12/2010, Volume 38, Issue 6, pp. 3445 - 3457
In 1985, for detecting a change in distribution, Pollak introduced a specific minimax performance metric and a randomized version of the Shiryaev—Roberts... 
Mathematical procedures | Minimax | Determinism | False alarms | Differential equations | Applied statistics | Performance metrics | Stopping distances | Statistics | Shiryaev-Roberts procedures | Changepoint problems | Sequential detection | sequential detection | STATISTICS & PROBABILITY | 62L15 | Shiryaev–Roberts procedures | 60G40 | 62L10
Journal Article
Journal of the Royal Statistical Society: Series B (Statistical Methodology), ISSN 1369-7412, 09/2019, Volume 81, Issue 4, pp. 675 - 705
Journal Article
Annals of Statistics, ISSN 0090-5364, 08/2018, Volume 46, Issue 4, pp. 1603 - 1629
Journal Article
ANNALS OF STATISTICS, ISSN 0090-5364, 08/2018, Volume 46, Issue 4, pp. 1603 - 1629
We consider the problem of recovering linear image Bx of a signal x known to belong to a given convex compact set chi from indirect observation omega = Ax +... 
REGRESSION | Linear regression | STATISTICS & PROBABILITY | linear estimation | minimax estimation
Journal Article
The Annals of Statistics, ISSN 0090-5364, 08/2018, Volume 46, Issue 4, pp. 1603 - 1629
We consider the problem of recovering linear image Bx of a signal x known to belong to a given convex compact set X from indirect observation ω = Ax + σξ of x... 
Statistics | Mathematics
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 05/2013, Volume 219, Issue 17, pp. 8881 - 8892
In this paper, we first weaken some assumptions in Jiao et al. (2005) and discuss the continuity and the directional differentiability of the objective... 
Optimality conditions | Constrained | Unconstrained | Generalized minimax programming | MATHEMATICS, APPLIED | ALGORITHMS
Journal Article
Optimization Letters, ISSN 1862-4472, 2/2019, Volume 13, Issue 1, pp. 55 - 68
In this paper, we consider a generalization of the Gerstewitz’s function to present several optimality conditions and existence theorems for a set optimization... 
Optimality conditions | Minimax | Computational Intelligence | Operations Research/Decision Theory | Mathematics | Set-valued maps | Numerical and Computational Physics, Simulation | Optimization | Set optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | VECTOR OPTIMIZATION | THEOREMS | SCALARIZATION | EQUILIBRIUM PROBLEMS
Journal Article
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