Results 1  10
of
230
Ideal spatial adaptation by wavelet shrinkage
 Biometrika
, 1994
"... 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, or variable bandwidth kernel, to the unknown function. Estimation with the aid of an oracle o ers dramatic ad ..."
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Cited by 1269 (5 self)
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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, or variable bandwidth kernel, to the unknown function. Estimation with the aid of an oracle o ers dramatic
Adapting to unknown smoothness via wavelet shrinkage
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 1995
"... We attempt to recover a function of unknown smoothness from noisy, sampled data. We introduce a procedure, SureShrink, which suppresses noise by thresholding the empirical wavelet coefficients. The thresholding is adaptive: a threshold level is assigned to each dyadic resolution level by the princip ..."
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Cited by 1006 (18 self)
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on the choice of mother wavelet. We know from a previous paper by the authors that traditional smoothing methods  kernels, splines, and orthogonal series estimates  even with optimal choices of the smoothing parameter, would be unable to perform
Fas algorithm for estimating mutual information, entropies ans score functions
 in Proceedings of ICA2003
, 2003
"... This papers proposes a fast algorithm for estimating the mutual information, difference score function, conditional score and conditional entropy, in possibly high dimensional space. The idea is to discretise the integral so that the density needs only be estimated over a regular grid, which can be ..."
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Cited by 23 (0 self)
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be done with little cost through the use of a cardinal spline kernel estimator. Score functions are then obtained as gradient of the entropy. An example of application to the blind separation of postnonlinear mixture is given. 1.
Minimax Estimation via Wavelet Shrinkage
, 1992
"... We attempt to recover an unknown function from noisy, sampled data. Using orthonormal bases of compactly supported wavelets we develop a nonlinear method which works in the wavelet domain by simple nonlinear shrinkage of the empirical wavelet coe cients. The shrinkage can be tuned to be nearly minim ..."
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Cited by 321 (29 self)
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method (kernel, smoothing spline, sieve,:::) in a minimax sense. Variants of our method based on simple threshold nonlinearities are nearly minimax. Our method possesses the interpretation of spatial adaptivity: it reconstructs using a kernel which mayvary in shape and bandwidth from point to point
KernelBased Skyline Cardinality Estimation
"... The skyline of a ddimensional dataset consists of all points not dominated by others. The incorporation of the skyline operator into practical database systems necessitates an efficient and effective cardinality estimation module. However, existing theoretical work on this problem is limited to the ..."
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Cited by 13 (1 self)
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The skyline of a ddimensional dataset consists of all points not dominated by others. The incorporation of the skyline operator into practical database systems necessitates an efficient and effective cardinality estimation module. However, existing theoretical work on this problem is limited
Support Vector Machines, Reproducing Kernel Hilbert Spaces and the Randomized GACV
, 1998
"... this paper we very briefly review some of these results. RKHS can be chosen tailored to the problem at hand in many ways, and we review a few of them, including radial basis function and smoothing spline ANOVA spaces. Girosi (1997), Smola and Scholkopf (1997), Scholkopf et al (1997) and others have ..."
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Cited by 189 (11 self)
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this paper we very briefly review some of these results. RKHS can be chosen tailored to the problem at hand in many ways, and we review a few of them, including radial basis function and smoothing spline ANOVA spaces. Girosi (1997), Smola and Scholkopf (1997), Scholkopf et al (1997) and others have
Cardinal spline filters: Stability and convergence to the ideal sinc interpolator
, 1992
"... In this paper, we provide an interpretation of polynomial spline interpolation as a continuous filtering process. We prove that the frequency responses of the cardinal spline filters converge to the ideal lowpass filter in all L fnorms with 1 ~<p < + ~ as the order of the spline tends to inf ..."
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Cited by 61 (28 self)
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In this paper, we provide an interpretation of polynomial spline interpolation as a continuous filtering process. We prove that the frequency responses of the cardinal spline filters converge to the ideal lowpass filter in all L fnorms with 1 ~<p < + ~ as the order of the spline tends
Pointwise Error Bounds for Orthogonal Cardinal Spline Approximation
"... For orthogonal cardinal spline approximation, closed form expressions of the reproducing kernel and the Peano kernels in terms of exponential splines are proved. Concrete and sharp pointwise error bounds are deduced for low degree splines. 1991 Mathematics Subject Classification: 41A15,42C15,65D07 ..."
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For orthogonal cardinal spline approximation, closed form expressions of the reproducing kernel and the Peano kernels in terms of exponential splines are proved. Concrete and sharp pointwise error bounds are deduced for low degree splines. 1991 Mathematics Subject Classification: 41A15,42C15,65D07
The pyramid match kernel: Efficient learning with sets of features
 Journal of Machine Learning Research
, 2007
"... In numerous domains it is useful to represent a single example by the set of the local features or parts that comprise it. However, this representation poses a challenge to many conventional machine learning techniques, since sets may vary in cardinality and elements lack a meaningful ordering. Kern ..."
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Cited by 136 (10 self)
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the pyramid match yields a Mercer kernel, and we prove bounds on its error relative to the optimal partial matching cost. We demonstrate our algorithm on both classification and regression tasks, including object recognition, 3D human pose inference, and time of publication estimation for documents, and we
Estimates for the spectral condition number of cardinal Bspline collocation matrices∗,†
, 2009
"... Abstract. The famous de Boor conjecture states that the condition of the polynomial Bspline collocation matrix at the knot averages is bounded independently of the knot sequence, i.e., it depends only on the spline degree. For highly nonuniform knot meshes, like geometric meshes, the conjecture is ..."
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is known to be false. As an effort towards finding an answer for uniform meshes, we investigate the spectral condition number of cardinal Bspline collocation matrices. Numerical testing strongly suggests that the conjecture is true for cardinal Bsplines.
Results 1  10
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230