# Classification via local multi-resolution projections

@article{Monnier2011ClassificationVL, title={Classification via local multi-resolution projections}, author={Jean-Baptiste Monnier}, journal={arXiv: Statistics Theory}, year={2011} }

We focus on the supervised binary classification problem, which consists in guessing the label $Y$ associated to a co-variate $X \in \R^d$, given a set of $n$ independent and identically distributed co-variates and associated labels $(X_i,Y_i)$. We assume that the law of the random vector $(X,Y)$ is unknown and the marginal law of $X$ admits a density supported on a set $\A$. In the particular case of plug-in classifiers, solving the classification problem boils down to the estimation of the…

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## References

SHOWING 1-10 OF 54 REFERENCES

### Classification via local multi-resolution projections (extended version)

- Mathematics, Computer Science
- 2011

This novel estimation procedure presents similar theoretical performances as the celebrated local-polynomial estimator (LPE) and thus outperforms the LPE from a computational standpoint and can reach super-fast rates under a margin assumption.

### Minimax nonparametric classification - Part I: Rates of convergence

- Computer Science, MathematicsIEEE Trans. Inf. Theory
- 1999

It is shown that the two problems are in fact of the same difficulty in terms of rates of convergence under a sufficient condition, which is satisfied by many function classes including Besov (Sobolev), Lipschitz, and bounded variation.

### Fourier and Hermite series estimates of regression functions

- Mathematics
- 1985

SummaryIn the paper we estimate a regressionm(x)=E {Y|X=x} from a sequence of independent observations (X1,Y1),…, (Xn, Yn) of a pair (X, Y) of random variables. We examine an estimate of a type…

### Classification under polynomial entropy and margin assump-tions and randomized estimators

- Mathematics, Computer Science
- 2004

The aim of this paper is to develop the PAC-Bayesian point of view and show how the efficiency of a Gibbs estimator relies on the weights given by the prior distribution to the balls centered at the best function in the model and associated with the pseudodistance.

### Model selection for regression on a random design

- Mathematics
- 2002

We consider the problem of estimating an unknown regression function when the design is random with values in . Our estimation procedure is based on model selection and does not rely on any prior…

### ON POINTWISE ADAPTIVE CURVE ESTIMATION BASED ON INHOMOGENEOUS DATA

- Mathematics, Computer Science
- 2007

This work proposes a method which adapts both to the local amount of data (the design density is unknown) and to theLocal smoothness of the regression function, which allows situations with strong variations in the concentration of the observations.

### Fast learning rates for plug-in classifiers

- Computer Science
- 2007

This work constructs plug-in classifiers that can achieve not only fast, but also super-fast rates, that is, rates faster than n -1 , and establishes minimax lower bounds showing that the obtained rates cannot be improved.

### Optimal spatial adaptation to inhomogeneous smoothness: an approach based on kernel estimates with variable bandwidth selectors

- Mathematics
- 1997

A new v~ria~~,E_<:.~_~1~!~_s,~~~,!?E_0r estimation is proposed. The application-of this bandwidth selector leads to kernel estimates that achieve optimal rates of convergence over B£~~.£~:3.sses.…

### De-noising by soft-thresholding

- Computer ScienceIEEE Trans. Inf. Theory
- 1995

The authors prove two results about this type of estimator that are unprecedented in several ways: with high probability f/spl circ/*/sub n/ is at least as smooth as f, in any of a wide variety of smoothness measures.