37,054 research outputs found
Non-Asymptotic Uniform Rates of Consistency for k-NN Regression
We derive high-probability finite-sample uniform rates of consistency for
-NN regression that are optimal up to logarithmic factors under mild
assumptions. We moreover show that -NN regression adapts to an unknown lower
intrinsic dimension automatically. We then apply the -NN regression rates to
establish new results about estimating the level sets and global maxima of a
function from noisy observations.Comment: In Proceedings of 33rd AAAI Conference on Artificial Intelligence
(AAAI 2019
Multiscale inference for a multivariate density with applications to X-ray astronomy
In this paper we propose methods for inference of the geometric features of a
multivariate density. Our approach uses multiscale tests for the monotonicity
of the density at arbitrary points in arbitrary directions. In particular, a
significance test for a mode at a specific point is constructed. Moreover, we
develop multiscale methods for identifying regions of monotonicity and a
general procedure for detecting the modes of a multivariate density. It is is
shown that the latter method localizes the modes with an effectively optimal
rate. The theoretical results are illustrated by means of a simulation study
and a data example. The new method is applied to and motivated by the
determination and verification of the position of high-energy sources from
X-ray observations by the Swift satellite which is important for a
multiwavelength analysis of objects such as Active Galactic Nuclei.Comment: Keywords and Phrases: multiple tests, modes, multivariate density,
X-ray astronomy AMS Subject Classification: 62G07, 62G10, 62G2
Linear and convex aggregation of density estimators
We study the problem of linear and convex aggregation of estimators of a
density with respect to the mean squared risk. We provide procedures for linear
and convex aggregation and we prove oracle inequalities for their risks. We
also obtain lower bounds showing that these procedures are rate optimal in a
minimax sense. As an example, we apply general results to aggregation of
multivariate kernel density estimators with different bandwidths. We show that
linear and convex aggregates mimic the kernel oracles in asymptotically exact
sense for a large class of kernels including Gaussian, Silverman's and
Pinsker's ones. We prove that, for Pinsker's kernel, the proposed aggregates
are sharp asymptotically minimax simultaneously over a large scale of Sobolev
classes of densities. Finally, we provide simulations demonstrating performance
of the convex aggregation procedure.Comment: 22 page
Bias in nearest-neighbor hazard estimation
In nonparametric curve estimation, the smoothing parameter is critical for performance. In order to estimate the hazard rate, we compare nearest neighbor selectors that minimize the quadratic, the Kullback-Leibler, and the uniform loss. These measures result in a rule of thumb, a cross-validation, and a plug-in selector. A Monte Carlo simulation within the three-parameter exponentiated Weibull distribution indicates that a counter-factual normal distribution, as an input to the selector, does provide a good rule of thumb. If bias is the main concern, minimizing the uniform loss yields the best results, but at the cost of very high variability. Cross-validation has a similar bias to the rule of thumb, but also with high variability. --hazard rate,kernel smoothing,bandwidth selection,nearest neighbor bandwidth,rule of thumb,plug-in,cross-validation,credit risk
Convergence rates for pointwise curve estimation with a degenerate design
The nonparametric regression with a random design model is considered. We
want to recover the regression function at a point x where the design density
is vanishing or exploding. Depending on assumptions on the regression function
local regularity and on the design local behaviour, we find several minimax
rates. These rates lie in a wide range, from slow l(n) rates where l(.) is
slowly varying (for instance (log n)^(-1)) to fast n^(-1/2) * l(n) rates. If
the continuity modulus of the regression function at x can be bounded from
above by a s-regularly varying function, and if the design density is
b-regularly varying, we prove that the minimax convergence rate at x is
n^(-s/(1+2s+b)) * l(n)
Statistical framework for video decoding complexity modeling and prediction
Video decoding complexity modeling and prediction is an increasingly important issue for efficient resource utilization in a variety of applications, including task scheduling, receiver-driven complexity shaping, and adaptive dynamic voltage scaling. In this paper we present a novel view of this problem based on a statistical framework perspective. We explore the statistical structure (clustering) of the execution time required by each video decoder module (entropy decoding, motion compensation, etc.) in conjunction with complexity features that are easily extractable at encoding time (representing the properties of each module's input source data). For this purpose, we employ Gaussian mixture models (GMMs) and an expectation-maximization algorithm to estimate the joint execution-time - feature probability density function (PDF). A training set of typical video sequences is used for this purpose in an offline estimation process. The obtained GMM representation is used in conjunction with the complexity features of new video sequences to predict the execution time required for the decoding of these sequences. Several prediction approaches are discussed and compared. The potential mismatch between the training set and new video content is addressed by adaptive online joint-PDF re-estimation. An experimental comparison is performed to evaluate the different approaches and compare the proposed prediction scheme with related resource prediction schemes from the literature. The usefulness of the proposed complexity-prediction approaches is demonstrated in an application of rate-distortion-complexity optimized decoding
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