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Many signal processing and machine learning applications are built from evaluating a kernel on pairs of signals, e.g. to assess the similarity of an incoming query to a database of known signals. This nonlinear evaluation can be simplified…
This paper tackles the problem of selecting among several linear estimators in non-parametric regression; this includes model selection for linear regression, the choice of a regularization parameter in kernel ridge regression, spline…
This article is dedicated to the estimation of the regression function when the explanatory variable is a weakly dependent process whose correlation coefficient exhibits exponential decay and has a known bounded density function. The…
The traditional kernel density estimator of an unknown density is by construction completely nonparametric, in the sense that it has no preferences and will work reasonably well for all shapes. The present paper develops a class of…
The problem of estimation of analytic density function using L_p minimax risk is considered. A kernel-type estimator of an unknown density function is proposed and the upper bound on its limiting local minimax risk is established. Our…
Nonlinear kernels can be approximated using finite-dimensional feature maps for efficient risk minimization. Due to the inherent trade-off between the dimension of the (mapped) feature space and the approximation accuracy, the key problem…
When nonlinear measures are estimated from sampled temporal signals with finite-length, a radius parameter must be carefully selected to avoid a poor estimation. These measures are generally derived from the correlation integral which…
We perform a study on kernel regression for large-dimensional data (where the sample size $n$ is polynomially depending on the dimension $d$ of the samples, i.e., $n\asymp d^{\gamma}$ for some $\gamma >0$ ). We first build a general tool to…
We study harmonic map regression, a nonparametric estimator for manifold-valued responses, that penalizes the empirical Fr\'echet risk by the Dirichlet energy. By connecting penalized regression to the theory of harmonic maps, the estimator…
We consider the problem of nonparametric regression under shape constraints. The main examples include isotonic regression (with respect to any partial order), unimodal/convex regression, additive shape-restricted regression, and…
Kernel quadrature is widely used to approximate integrals of smooth functions, with worst-case error typically decaying at the minimax rate $n^{-\alpha/d}$ for smoothness $\alpha$ in dimension $d$. Existing rate-optimal methods often depend…
We design a new nonparametric method that allows one to estimate the matrix of integrated kernels of a multivariate Hawkes process. This matrix not only encodes the mutual influences of each nodes of the process, but also disentangles the…
We consider a nonparametric regression setup, where the covariate is a random element in a complete separable metric space, and the parameter of interest associated with the conditional distribution of the response lies in a separable…
Consistent weighted least square estimators are proposed for a wide class of nonparametric regression models with random regression function, where this real-valued random function of $k$ arguments is assumed to be continuous with…
Difficulties may arise when analyzing longitudinal data using mixed-effects models if there are nonparametric functions present in the linear predictor component. This study extends the use of semiparametric mixed-effects modeling in cases…
A nonparametric kernel density estimator for directional-linear data is introduced. The proposal is based on a product kernel accounting for the different nature of both (directional and linear) components of the random vector. Expressions…
In the framework of nonparametric multivariate function estimation we are interested in structural adaptation. We assume that the function to be estimated possesses the single-index structure where neither the link function nor the index…
Modal regression estimates the local modes of the distribution of $Y$ given $X=x$, instead of the mean, as in the usual regression sense, and can hence reveal important structure missed by usual regression methods. We study a simple…
We study the problem of estimating a nonparametric probability density under a large family of losses called Besov IPMs, which include, for example, $\mathcal{L}^p$ distances, total variation distance, and generalizations of both…
We propose two approaches to estimate semiparametric discrete choice models for bundles. Our first approach is a kernel-weighted rank estimator based on a matching-based identification strategy. We establish its complete asymptotic…