Related papers: Smoothing splines approximation using Hilbert curv…
Nonparametric maximum likelihood estimation is intended to infer the unknown density distribution while making as few assumptions as possible. To alleviate the over parameterization in nonparametric data fitting, smoothing assumptions are…
We present an adaptive smoother for linear state-space models with unknown process and measurement noise covariances. The proposed method utilizes the variational Bayes technique to perform approximate inference. The resulting smoother is…
Reliable estimation and approximation of probability density functions is fundamental for their further processing. However, their specific properties, i.e. scale invariance and relative scale, prevent the use of standard methods of spline…
We propose a scalable divergence estimation method based on hashing. Consider two continuous random variables $X$ and $Y$ whose densities have bounded support. We consider a particular locality sensitive random hashing, and consider the…
This article studies local and global inference for smoothing spline estimation in a unified asymptotic framework. We first introduce a new technical tool called functional Bahadur representation, which significantly generalizes the…
Stein's method for Gaussian process approximation can be used to bound the differences between the expectations of smooth functionals $h$ of a c\`adl\`ag random process $X$ of interest and the expectations of the same functionals of a well…
Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…
The thin plate spline smoother is a classical model for fnding a smooth function from the knowledge of its observation at scattered locations which may have random noises. We consider a nonconforming Morley finite element method to…
The computational cost for inference and prediction of statistical models based on Gaussian processes with Mat\'ern covariance functions scales cubicly with the number of observations, limiting their applicability to large data sets. The…
Constructing confidence intervals for the value of an (unknown) optimal treatment policy is a fundamental problem in causal inference. Insight into the optimal policy value can guide the development of reward-maximizing, individualized…
This paper describes an approach to global smoothing problems for non-dispersive equations based on ideas of comparison principle and canonical transformation established in authors' previous paper, where dispersive equations were treated.…
A noise-reduction algorithm for time-series of non-linear systems is presented. The algorithm smoothes the attractors in phase space using B-splines, allowing a more accurate measure of their dynamics. The algorithm is tested on numerical…
A novel formulation of the clustering problem is introduced in which the task is expressed as an estimation problem, where the object to be estimated is a function which maps a point to its distribution of cluster membership. Unlike…
Unconstrained optimization problems become more common in scientific computing and engineering applications with the rapid development of artificial intelligence, and numerical methods for solving them more quickly and efficiently have been…
In this paper, we analyze several methods for approximating gradients of noisy functions using only function values. These methods include finite differences, linear interpolation, Gaussian smoothing and smoothing on a sphere. The methods…
This paper considers the development of spatially adaptive smoothing splines for the estimation of a regression function with non-homogeneous smoothness across the domain. Two challenging issues that arise in this context are the evaluation…
We propose a new algorithm that finds an $\varepsilon$-approximate fixed point of a smooth function from the $n$-dimensional $\ell_2$ unit ball to itself. We use the general framework of finding approximate solutions to a variational…
This paper addresses the deconvolution problem of estimating a square-integrable probability density from observations contaminated with additive measurement errors having a known density. The estimator begins with a density estimate of the…
This paper considers the estimation of quantiles via a smoothed version of the stochastic gradient descent (SGD) algorithm. By smoothing the score function in the conventional SGD quantile algorithm, we achieve monotonicity in the quantile…
The aim of this paper is to present a new estimation procedure that can be applied in many statistical frameworks including density and regression and which leads to both robust and optimal (or nearly optimal) estimators. In density…