Introduction to Nonparametric Estimation

Tsybakov, Alexandre B.

doi:10.1007/b13794

Cited by 1,816 publications

(2,068 citation statements)

References 0 publications

Supporting

Mentioning

1,975

Contrasting

Unclassified

Order By: Relevance

“…To put Theorem 1.10 is some perspective, note that in the standard framework of aggregation, F is a finite dictionary and both the dictionary and the target are bounded in L ∞ (see, for example, [25,10] and references therein). Within that framework one has the following: Theorem 1.11 [11] There exists an aggregation procedure Ψ for which the following holds.…”

Section: Assuming Of Course That a Minimizer Existsmentioning

confidence: 99%

On aggregation for heavy-tailed classes

Mendelson

2016

Probab. Theory Relat. Fields

View full text Add to dashboard Cite

We introduce an alternative to the notion of 'fast rate' in Learning Theory, which coincides with the optimal error rate when the given class happens to be convex and regular in some sense. While it is well known that such a rate cannot always be attained by a learning procedure (i.e., a procedure that selects a function in the given class), we introduce an aggregation procedure that attains that rate under rather minimal assumptions -for example, that the L q and L 2 norms are equivalent on the linear span of the class for some q > 2, and the target random variable is square-integrable.

show abstract

Section: Assuming Of Course That a Minimizer Existsmentioning

confidence: 99%

On aggregation for heavy-tailed classes

Mendelson

2016

Probab. Theory Relat. Fields

View full text Add to dashboard Cite

show abstract

“…Overfitting will be further discussed in Section 3.2.4. For more information about nonparametric regression, the reader is advised to consult the books by Härdle (1990); Tsybakov (2009). Although our discussion below will assume a parametric function approximation method (and in many cases linear function approximation), many of the algorithms can be extended to nonparametric techniques.…”

Section: One Particularly Popular Choice Is To Use Radial Basis Functmentioning

confidence: 99%

Algorithms for Reinforcement Learning

Szepesvári¹

2010

Synthesis Lectures on Artificial Intelligence and Machine Learn

605

406

View full text Add to dashboard Cite

“…The RIP property has been established for a large number of matrix constructions. For instance partial Fourier matrices 2 satisfy RIP with high probability for n ≥ C 1 k(log p) 4 , as shown in [27].…”

Section: Behavior Of the Lasso Under Restricted Isometry Propertymentioning

confidence: 99%

“…Very readable introductions to the fundamentals of statistical estimation can be found in the books by Wasserman [1,2]. More advanced references (with a focus on high-dimensional and non-parametric settings) are the monographs by Johnstone [3] and Tsybakov [4]. The recent book by Bühlmann and van de Geer [5] provides a useful survey of recent research in high-dimensional statistics.…”

mentioning

confidence: 99%

Statistical estimation: from denoising to sparse regression and hidden cliques

Tramel¹,

Kumar²,

Giurgiu³

et al. 2015

Statistical Physics, Optimization, Inference, and Message-Passing Algorithms

View full text Add to dashboard Cite

Abstract. These notes review six lectures given by Prof. Andrea Montanari on the topic of statistical estimation for linear models. The first two lectures cover the principles of signal recovery from linear measurements in terms of minimax risk. Subsequent lectures demonstrate the application of these principles to several practical problems in science and engineering. Specifically, these topics include denoising of error-laden signals, recovery of compressively sensed signals, reconstruction of low-rank matrices, and also the discovery of hidden cliques within large networks.These are notes from the lecture of Andrea Montanari given at the autumn school "Statistical Physics, Optimization, Inference, and Message-Passing Algorithms", that took place in Les Houches,

show abstract

Introduction to Nonparametric Estimation

Cited by 1,816 publications

References 0 publications

On aggregation for heavy-tailed classes

On aggregation for heavy-tailed classes

Algorithms for Reinforcement Learning

Statistical estimation: from denoising to sparse regression and hidden cliques

Contact Info

Product

Resources

About