ORCID Profile
0000-0003-0224-9216
Current Organisation
University of Sydney
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Publisher: Elsevier BV
Date: 10-2008
Publisher: Elsevier BV
Date: 07-1994
Publisher: Elsevier BV
Date: 07-2016
Publisher: No publisher found
Date: 2002
Publisher: World Scientific Pub Co Pte Lt
Date: 28-04-2015
DOI: 10.1142/S0219530514500110
Abstract: We introduce a learning algorithm for regression generated by a minimum error entropy (MEE) principle and regularization schemes in reproducing kernel Hilbert spaces. This empirical MEE algorithm is highly related to a scaling parameter arising from Parzen windowing. The purpose of this paper is to carry out consistency analysis when the scaling parameter is large. Explicit learning rates are provided. Novel approaches are proposed to overcome the difficulties in bounding the output function uniformly and in the special MEE feature that the regression function may not be a minimizer of the error entropy.
Publisher: Hindawi Limited
Date: 2013
DOI: 10.1155/2013/715683
Publisher: Elsevier BV
Date: 03-1994
Publisher: Springer Science and Business Media LLC
Date: 09-06-2004
Publisher: Elsevier BV
Date: 03-1994
Publisher: Elsevier BV
Date: 12-2012
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 05-2019
Publisher: Elsevier BV
Date: 12-2008
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 2022
Publisher: Springer Science and Business Media LLC
Date: 22-08-2023
Publisher: Cambridge University Press (CUP)
Date: 1995
DOI: 10.1017/S0308210500022563
Abstract: Cardinal interpolation by integer translates of shifted three-directional box splines is studied. It is shown that, for arbitrary orders, k, l, m ∈ N of the directional vectors, this problem is correct if and only if the shift vector is taken from the hexagonal shift region (modulo translation with respect to the lattice Z 2 ). This confirms a conjecture of S. D. Riemenschneider [9], and settles the problem studied in [5] for the special case k = l = m in full generality. The method of proof is from homotopy theory.
Publisher: Elsevier BV
Date: 10-1995
Publisher: Elsevier BV
Date: 02-2011
Publisher: Hindawi Limited
Date: 2012
DOI: 10.1155/2012/902139
Abstract: We study learning algorithms generated by regularization schemes in reproducing kernel Hilbert spaces associated with an ϵ -insensitive pinball loss. This loss function is motivated by the ϵ -insensitive loss for support vector regression and the pinball loss for quantile regression. Approximation analysis is conducted for these algorithms by means of a variance-expectation bound when a noise condition is satisfied for the underlying probability measure. The rates are explicitly derived under a priori conditions on approximation and capacity of the reproducing kernel Hilbert space. As an application, we get approximation orders for the support vector regression and the quantile regularized regression.
Publisher: Wiley
Date: 23-11-2012
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 07-2003
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 11-2006
Publisher: IOP Publishing
Date: 21-09-2021
Publisher: Wiley
Date: 2010
Publisher: Elsevier BV
Date: 07-2002
Publisher: Elsevier BV
Date: 03-2013
Publisher: Elsevier BV
Date: 12-2011
Publisher: Elsevier BV
Date: 08-1994
Publisher: Elsevier BV
Date: 12-2021
Publisher: Elsevier BV
Date: 03-2010
Publisher: Oxford University Press (OUP)
Date: 08-04-2010
Publisher: World Scientific Pub Co Pte Lt
Date: 13-04-2016
DOI: 10.1142/S0219530515500050
Abstract: Additive models play an important role in semiparametric statistics. This paper gives learning rates for regularized kernel-based methods for additive models. These learning rates compare favorably in particular in high dimensions to recent results on optimal learning rates for purely nonparametric regularized kernel-based quantile regression using the Gaussian radial basis function kernel, provided the assumption of an additive model is valid. Additionally, a concrete ex le is presented to show that a Gaussian function depending only on one variable lies in a reproducing kernel Hilbert space generated by an additive Gaussian kernel, but does not belong to the reproducing kernel Hilbert space generated by the multivariate Gaussian kernel of the same variance.
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 04-2022
Publisher: Elsevier BV
Date: 03-1993
Publisher: Elsevier BV
Date: 09-1995
Publisher: Elsevier BV
Date: 09-1991
Publisher: Springer Science and Business Media LLC
Date: 11-10-2013
Publisher: Elsevier BV
Date: 02-1996
Publisher: Wiley
Date: 21-02-2011
DOI: 10.1002/NLA.722
Publisher: Elsevier BV
Date: 2000
Publisher: Cambridge University Press (CUP)
Date: 03-2012
Abstract: We consider the uniqueness and extinction properties of the interacting branching collision process (IBCP), which consists of two strongly interacting components: an ordinary Markov branching process and a collision branching process. We establish that there is a unique IBCP, and derive necessary and sufficient conditions for it to be nonexplosive that are easily checked. Explicit expressions are obtained for the extinction probabilities for both regular and irregular cases. The associated expected hitting times are also considered. Ex les are provided to illustrate our results.
Publisher: Elsevier BV
Date: 10-2008
Publisher: Elsevier BV
Date: 11-2001
Publisher: Elsevier BV
Date: 05-1992
Publisher: Springer Science and Business Media LLC
Date: 03-1993
DOI: 10.1007/BF01904041
Publisher: Elsevier BV
Date: 09-2013
Publisher: Elsevier BV
Date: 06-1995
Publisher: Elsevier BV
Date: 05-2012
Publisher: Elsevier BV
Date: 09-2002
Publisher: Springer Science and Business Media LLC
Date: 29-08-2017
Publisher: Springer Science and Business Media LLC
Date: 11-2002
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 09-2023
Publisher: Springer Science and Business Media LLC
Date: 28-07-2023
Publisher: Elsevier BV
Date: 06-1995
Publisher: Elsevier BV
Date: 11-2005
Publisher: Elsevier BV
Date: 11-2020
Publisher: Elsevier BV
Date: 05-2003
Publisher: Elsevier BV
Date: 03-2017
Publisher: No publisher found
Date: 2002
DOI: 10.1109/78.984728
Publisher: Springer Science and Business Media LLC
Date: 2001
Publisher: Canadian Mathematical Society
Date: 09-2011
Abstract: We consider approximation of multivariate functions in Sobolev spaces by high order Parzen windows in a non-uniform s ling setting. S ling points are neither i.i.d. nor regular, but are noised from regular grids by non-uniform shifts of a probability density function. S le function values at s ling points are drawn according to probability measures with expected values being values of the approximated function. The approximation orders are estimated by means of regularity of the approximated function, the density function, and the order of the Parzen windows, under suitable choices of the scaling parameter.
Publisher: Elsevier BV
Date: 07-1992
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 06-2018
Publisher: Elsevier BV
Date: 11-2017
Publisher: Elsevier BV
Date: 09-2011
Publisher: Springer Science and Business Media LLC
Date: 15-03-2007
Publisher: Springer Science and Business Media LLC
Date: 08-1995
DOI: 10.1007/BF03322250
Publisher: Springer Science and Business Media LLC
Date: 12-1995
DOI: 10.1007/BF01208430
Publisher: Elsevier BV
Date: 10-1996
Publisher: Elsevier BV
Date: 12-2009
Publisher: Springer Science and Business Media LLC
Date: 30-04-2009
Publisher: Elsevier BV
Date: 04-2020
Publisher: Springer Science and Business Media LLC
Date: 24-01-2008
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 07-2022
Publisher: American Mathematical Society (AMS)
Date: 13-04-2004
Publisher: Elsevier BV
Date: 02-2007
Publisher: Elsevier
Date: 2006
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2001
Publisher: Springer Science and Business Media LLC
Date: 12-2022
DOI: 10.1007/S10444-022-09991-X
Abstract: The efficiency of deep convolutional neural networks (DCNNs) has been demonstrated empirically in many practical applications. In this paper, we establish a theory for approximating functions from Korobov spaces by DCNNs. It verifies rigorously the efficiency of DCNNs in approximating functions of many variables with some variable structures and their abilities in overcoming the curse of dimensionality.
Publisher: Springer Science and Business Media LLC
Date: 1994
DOI: 10.1007/BF02006260
Publisher: Elsevier BV
Date: 04-2010
Publisher: Springer Science and Business Media LLC
Date: 05-03-2015
Publisher: Hindawi Limited
Date: 2014
DOI: 10.1155/2014/454375
Abstract: This paper is concerned with approximation on variable L ρ p ( · ) spaces associated with a general exponent function p and a general bounded Borel measure ρ on an open subset Ω of R d . We mainly consider approximation by Bernstein type linear operators. Under an assumption of log-Hölder continuity of the exponent function p , we verify a conjecture raised previously about the uniform boundedness of Bernstein-Durrmeyer and Bernstein-Kantorovich operators on the L ρ p ( · ) space. Quantitative estimates for the approximation are provided for high orders of approximation by linear combinations of such positive linear operators. Motivating connections to classification and quantile regression problems in learning theory are also described.
Publisher: Elsevier BV
Date: 05-2008
Publisher: Springer Science and Business Media LLC
Date: 10-2009
Publisher: MIT Press - Journals
Date: 05-2005
Abstract: Support vector machine (SVM) soft margin classifiers are important learning algorithms for classification problems. They can be stated as convex optimization problems and are suitable for a large data setting. Linear programming SVM classifiers are especially efficient for very large size s les. But little is known about their convergence, compared with the well-understood quadratic programming SVM classifier. In this article, we point out the difficulty and provide an error analysis. Our analysis shows that the convergence behavior of the linear programming SVM is almost the same as that of the quadratic programming SVM. This is implemented by setting a stepping-stone between the linear programming SVM and the classical 1-norm soft margin classifier. An upper bound for the misclassification error is presented for general probability distributions. Explicit learning rates are derived for deterministic and weakly separable distributions, and for distributions satisfying some Tsybakov noise condition.
Publisher: Elsevier BV
Date: 11-2003
Publisher: Cambridge University Press (CUP)
Date: 03-2014
Abstract: Although the exact expressions for the extinction probabilities of the Interacting Branching Collision Processes (IBCP) were very recently given by Chen et al. [4], some of these expressions are very complicated hence, useful information regarding asymptotic behaviour, for ex le, is harder to obtain. Also, these exact expressions take very different forms for different cases and thus seem lacking in homogeneity. In this paper, we show that the asymptotic behaviour of these extremely complicated and tangled expressions for extinction probabilities of IBCP follows an elegant and homogenous power law which takes a very simple form. In fact, we are able to show that if the extinction is not certain then the extinction probabilities { a n } follow an harmonious and simple asymptotic law of a n ∼ kn -α ρ c n as n → ∞, where k and α are two constants, ρ c is the unique positive zero of the C ( s ), and C ( s ) is the generating function of the infinitesimal collision rates. Moreover, the interesting and important quantity α takes a very simple and uniform form which could be interpreted as the ‘spectrum’, ranging from -∞ to +∞, of the interaction between the two components of branching and collision of the IBCP.
Publisher: Springer Science and Business Media LLC
Date: 07-2006
Publisher: Springer Science and Business Media LLC
Date: 23-09-2005
Publisher: Bernoulli Society for Mathematical Statistics and Probability
Date: 02-2010
DOI: 10.3150/09-BEJ206
No related grants have been discovered for Ding-Xuan Zhou.