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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...
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...
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 propose a method for nonparametric density estimation that exhibits robustness to contamination of the training sample. This method achieves robustness by combining a traditional kernel density est...
We introduce a new geometric approach that constructs a transition kernel of Markov chain. Our method always minimizes the average rejection rate and even reduce it to zero in many relevant cases, whi...
On optimal kernel in ABC SMC     =optimal kernel  ABC SMC       2011/7/6
Sequential Monte Carlo (SMC) approaches have become work horses in approximate Bayesian computation (ABC). Here we discuss how to construct the perturbation kernels that are required in ABC-SMC approa...
Despite the recent progress towards efficient multiple kernel learning (MKL), the structured output case remains an open research front. Current approaches involve repeatedly solving a batch learning...
This paper deals with the nonparametric density estimation of the regression error term assuming its independence with the covariate. The difference between the feasible estimator which uses the estim...
In this paper, we present a unified approach to function approximation in reproducing kernel Hilbert spaces (RKHS) that establishes a previously unrecognized optimality property for several well-known...
Maxiset in sup-norm for kernel estimators。
We survey classical kernel methods for providing nonparametric solutions to problems involving measurement error. In particular we outline kernel-basedmethodology in this setting, and discuss its ba...
Inspired by a growing interest in analyzing network data, we study the problem of node classifi- cation on graphs, focusing on approaches based on kernel machines. Conventionally, kernel machines ar...

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