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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...
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...
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...
Nonnegative Matrix Factorization (NMF) has been contin-uously evolving in several areas like pattern recognition and information retrieval methods. It factorizes a matrix into a product of 2 low-rank ...
Recent work in metric learning has signi cantly improved the state-of-the-art ink-nearest neighbor classi cation. Support vector machines (SVM), particularly with RBF kernels, are amongst the most pop...
We present an embedding of stochastic optimal control problems, of the so called path integral form, into reproducing kernel Hilbert spaces. Using consistent, sample based estimates of the embedding l...

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