We propose kernel regression for signals over graphs. The optimal regression coefficients are learnt using a constraint that the target vector is a smooth signal over an underlying graph. The constraint is imposed using a graph-Laplacian based regularization. We discuss how the proposed kernel regression exhibits a smoothing effect, simultaneously achieving noise-reduction and graph-smoothness....

In various statistical model, such as density estimation and estimation of regression curves or hazard rates, monotonicity constraints can arise naturally. A frequently encountered problem in nonparametric statistics is to estimate a monotone density function f on a compact interval. A known estimator for density function of f under the restriction that f is decreasing, is Grenander estimator, ...

This paper tackles the problem of selecting among several linear estimators in nonparametric regression; this includes model selection for linear regression, the choice of a regularization parameter in kernel ridge regression or spline smoothing, and the choice of a kernel in multiple kernel learning. We propose a new algorithm which first estimates consistently the variance of the noise, based...

The accuracy and interpretation of results obtained by Diffusion Tensor Imaging (DTI) are largely influenced by several experimental parameter settings. In Voxel-Based (VB) analysis images are smoothed, in order to improve their Signal to Noise Ratio (SNR) and to reduce the impact of normalization and artifacts. This is a critical step and care must be taken so that directional information and ...

The asymptotic behavior of penalised spline estimators is studied in the univariate case. B-splines are used and a penalty is placed on mth order differences of the coefficients. The number of knots is assumed to converge to ∞ as the sample size increases. We show that penalised splines behave similarly to Nadaraya-Watson kernel estimators with an “equivalent” kernels depending upon m. The equi...

The histogram estimator of a discrete probability mass function often exhibits undesirable properties related to zero estimation both within the observed range counts and outside into tails distribution. To circumvent this, we formulate novel second-order kernel smoother based on recently developed mean-parametrized Conway--Maxwell--Poisson distribution which allows for over- under-dispersion. ...