# Spatially-adaptive sensing in nonparametric regression

@article{Bull2012SpatiallyadaptiveSI, title={Spatially-adaptive sensing in nonparametric regression}, author={Adam D. Bull}, journal={arXiv: Statistics Theory}, year={2012} }

While adaptive sensing has provided improved rates of convergence in sparse regression and classification, results in nonparametric regression have so far been restricted to quite specific classes of functions. In this paper, we describe an adaptive-sensing algorithm which is applicable to general nonparametric-regression problems. The algorithm is spatially adaptive, and achieves improved rates of convergence over spatially inhomogeneous functions. Over standard function classes, it likewise…

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## References

SHOWING 1-10 OF 39 REFERENCES

Distilled Sensing: Adaptive Sampling for Sparse Detection and Estimation

- Computer ScienceIEEE Transactions on Information Theory
- 2011

It is shown that using adaptive sampling, reliable detection is possible provided the amplitude exceeds a constant, and localization is possible when the amplitudes exceeds any arbitrarily slowly growing function of the dimension.

Adaptive sensing performance lower bounds for sparse estimation and testing

- Computer Science
- 2012

The results show that the adaptive sensing methodologies proposed previously in the literature are essentially optimal, and cannot be substantially improved, and provide further insights on the limits of adaptive compressive sensing.

On the Fundamental Limits of Adaptive Sensing

- Computer ScienceIEEE Transactions on Information Theory
- 2013

It is proved that the advantages offered by clever adaptive strategies and sophisticated estimation procedures-no matter how intractable-over classical compressed acquisition/recovery schemes are, in general, minimal.

Group testing strategies for recovery of sparse signals in noise

- Computer Science2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers
- 2009

It is demonstrated that group testing measurement matrix constructions may be combined with statistical binary detection and estimation methods to produce efficient adaptive sequential algorithms for sparse signal support recovery.

Ideal spatial adaptation by wavelet shrinkage

- Mathematics
- 1994

SUMMARY With ideal spatial adaptation, an oracle furnishes information about how best to adapt a spatially variable estimator, whether piecewise constant, piecewise polynomial, variable knot spline,…

Rates of convergence in active learning

- Computer Science
- 2011

The general problem of model selection for active learning with a nested hierarchy of hypothesis classes is studied and an algorithm whose error rate provably converges to the best achievable error among classifiers in the hierarchy at a rate adaptive to both the complexity of the optimal classifier and the noise conditions is proposed.

Faster Rates in Regression via Active Learning

- Computer ScienceNIPS
- 2005

A practical algorithm capable of exploiting the extra flexibility of the active setting and provably improving upon the classical passive techniques is described.

Data‐Driven Bandwidth Selection in Local Polynomial Fitting: Variable Bandwidth and Spatial Adaptation

- Mathematics
- 1995

When estimating a mean regression function and its derivatives, locally weighted least squares regression has proven to be a very attractive technique. The present paper focuses on the important…

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.…

Wavelet Shrinkage: Asymptopia?

- Computer Science
- 1995

A method for curve estimation based on n noisy data: translate the empirical wavelet coefficients towards the origin by an amount √(2 log n) /√n and draw loose parallels with near optimality in robustness and also with the broad near eigenfunction properties of wavelets themselves.