منابع مشابه
Isotonic regression in general dimensions
We study the least squares regression function estimator over the class of real-valued functions on [0, 1]d that are increasing in each coordinate. For uniformly bounded signals and with a fixed, cubic lattice design, we establish that the estimator achieves the minimax rate of order n−min{2/(d+2),1/d} in the empirical L2 loss, up to poly-logarithmic factors. Further, we prove a sharp oracle in...
متن کاملBayesian isotonic density regression.
Density regression models allow the conditional distribution of the response given predictors to change flexibly over the predictor space. Such models are much more flexible than nonparametric mean regression models with nonparametric residual distributions, and are well supported in many applications. A rich variety of Bayesian methods have been proposed for density regression, but it is not c...
متن کاملOptimal Reduced Isotonic Regression
Isotonic regression is a shape-constrained nonparametric regression in which the ordinate is a nondecreasing function of the abscissa. The regression outcome is an increasing step function. For an initial set of n points, the number of steps in the isotonic regression, m, may be as large as n. As a result, the full isotonic regression has been criticized as overfitting the data or making the re...
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Nonasymptotic risk bounds are provided for maximum likelihood-type isotonic estimators of an unknown nondecreasing regression function, with general average loss at design points. These bounds are optimal up to scale constants, and they imply uniform n−1/3-consistency of the p risk for unknown regression functions of uniformly bounded variation, under mild assumptions on the joint probability d...
متن کاملOnline Isotonic Regression
We consider the online version of the isotonic regression problem. Given a set of linearly ordered points (e.g., on the real line), the learner must predict labels sequentially at adversarially chosen positions and is evaluated by her total squared loss compared against the best isotonic (nondecreasing) function in hindsight. We survey several standard online learning algorithms and show that n...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2019
ISSN: 0090-5364
DOI: 10.1214/18-aos1753