Related papers: Smoothing splines with varying smoothing parameter

We propose a novel family of multivariate robust smoothers based on the thin-plate (Sobolev) penalty that is particularly suitable for the analysis of spatial data. The proposed family of estimators can be expediently computed even in high…

State estimation is a key ingredient in most robotic systems. Often, state estimation is performed using some form of least squares minimization. Basically, all error minimization procedures that work on real-world data use robust kernels…

This paper proposes nonparametric kernel-smoothing estimation for panel data to examine the degree of heterogeneity across cross-sectional units. We first estimate the sample mean, autocovariances, and autocorrelations for each unit and…

We study a class of optimization problems on Riemannian manifolds, where the objective function consists of a smooth term and quasi-norm type penalties with exponent $p \in (0, 1]$. The essential difficulty lies in the fact that the…

In this work, we consider a constrained convex problem with linear inequalities and provide an inexact penalty re-formulation of the problem. The novelty is in the choice of the penalty functions, which are smooth and can induce a non-zero…

One of the challenges with functional data is incorporating spatial structure, or local correlation, into the analysis. This structure is inherent in the output from an increasing number of biomedical technologies, and a functional linear…

In this paper, we investigate the adversarial robustness of nonparametric regression, a fundamental problem in machine learning, under the setting where an adversary can arbitrarily corrupt a subset of the input data. While the robustness…

We propose an $L_{2}$-based penalization algorithm for functional linear regression models, where the coefficient function is shrunk towards a data-driven shape template $\gamma$, which is constrained to belong to a class of piecewise…

Rescaled spike and slab models are a new Bayesian variable selection method for linear regression models. In high dimensional orthogonal settings such models have been shown to possess optimal model selection properties. We review…

Isotonic regression provides a flexible, tuning-free approach to estimating monotonic functions without imposing global curvature constraints, yet the estimated regression function is inherently a step function. This paper addresses a key…

This paper discusses the local linear smoothing to estimate the unknown first and second infinitesimal moments in second-order jump-diffusion model based on Gamma asymmetric kernels. Under the mild conditions, we obtain the weak consistency…

Penalized quantile regression (QR) is widely used for studying the relationship between a response variable and a set of predictors under data heterogeneity in high-dimensional settings. Compared to penalized least squares, scalable…

In this paper we introduce a new class of diffeomorphic smoothers based on general spline smoothing techniques and on the use of some tools that have been recently developed in the context of image warping to compute smooth diffeomorphisms.…

Ensuring reliable confidence scores from deep networks is of pivotal importance in critical decision-making systems, notably in the medical domain. While recent literature on calibrating deep segmentation networks has led to significant…

Many recent problems in signal processing and machine learning such as compressed sensing, image restoration, matrix/tensor recovery, and non-negative matrix factorization can be cast as constrained optimization. Projected gradient descent…

This paper investigates the nonparametric estimation of a circular regression function in an errors-in-variables framework. Two settings are studied, depending on whether the covariates are circular or linear. Adaptive estimators are…

We extend the adaptive regression spline model by incorporating saturation, the natural requirement that a function extend as a constant outside a certain range. We fit saturating splines to data using a convex optimization problem over a…

In this paper, we establish minimax optimal rates of convergence for prediction in a semi-functional linear model that consists of a functional component and a less smooth nonparametric component. Our results reveal that the smoother…

A liquid scorecard has liquid characteristics, for which the characteristic score is a smooth function of the characteristic over a liquid range. The smooth function is based on B-splines, typically cubic. In contrast, the characteristic…

In this article we propose a new adaptive numerical quadrature procedure which includes both local subdivision of the integration domain, as well as local variation of the number of quadrature points employed on each subinterval. In this…