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When the functional data are not homogeneous, e.g., there exist multiple classes of func-tional curves in the dataset, traditional estimation methods may fail. In this paper, we propose a new estimati...
When the functional data are not homogeneous, e.g., there exist multiple classes of func-tional curves in the dataset, traditional estimation methods may fail. In this paper, we propose a new estimati...
The performance of a kernel-based learning algorithm depends very much on the choice of the kernel. Recently, much attention has been paid to the problem of learning the kernel itself from given train...
Reinforcement learning (RL) is concerned with the identification of optimal controls in Markov decision processes (MDPs) where no explicit model of the transition probabilities is available. Many exis...
In this paper, we construct a moment inequality for mixing dependent random variables, it is of independent interest. As applications, the consistency of the kernel density estimation is investigated....
We establish optimal convergence rates for a decomposition-based scalable approach to kernel ridge regression. The method is simple to describe: it randomly partitions a dataset of size N into m subse...
Given a class of closed Riemannian manifolds with prescribed geometric conditions, we introduce an embedding of the manifolds into $\ell^2$ based on the heat kernel of the Connection Laplacian associa...
Regularized kernel methods such as support vector machines (SVM) and support vector regression (SVR) constitute a broad and flexible class of methods which are theoretically well investigated and comm...
Kernel estimation of a probability density function supported on the unit interval has proved difficult, because of the well known boundary bias issues a conventional kernel density estimator would ne...
We present a variational Bayesian method of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semi-blind d...
We establish a link between Fourier optics and a recent construction from the machine learning community termed the kernel mean map. Using the Fraunhofer approximation, it identifies the kernel with t...
由于数据被核化后不能还原, 使核方法的应用受到局限. 对此, 提出一种基于Multi-kernelKRR的数据还原算法. 首先, 通过同类数据中已知数据进行多次核化迭代, 使已知数据在超高维欧氏空间中呈线性; 然后, 利用已知数据对同类未知数据进行线性表示, 并以Kernel ridge regression (KRR) 算法进行未知数据的回归; 最后实现数据还原. 选取Iris flower...
Recent contributions to kernel smoothing show that the performance of cross-validated bandwidth selectors improve significantly from indirectness. Indirect crossvalidation first estimates the classica...
In a previous paper [3], we studied a kernel estimate of the upper edge of a two-dimensional bounded set, based upon the extreme values of a Poisson point process. The initial paper [1] on the subject...

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