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We present a novel method for reliably explaining the predictions of neural networks. We consider an explanation reliable if it identifies input features relevant to the model output by considering the input and the neighboring data points.…

Computer Vision and Pattern Recognition · Computer Science 2021-03-30 Dohun Lim , Hyeonseok Lee , Sungchan Kim

In the functional linear regression model, many methods have been proposed and studied to estimate the slope function while the functional predictor was observed in the entire domain. However, works on functional linear regression models…

Methodology · Statistics 2021-12-21 Yafei Wang , Tingyu Lai , Bei Jiang , Linglong Kong , Zhongzhan Zhang

We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…

Statistics Theory · Mathematics 2020-07-20 Matias D. Cattaneo , Max H. Farrell , Yingjie Feng

In this paper we focus on the linear functionals defining an approximate version of the gradient of a function. These functionals are often used when dealing with optimization problems where the computation of the gradient of the objective…

Optimization and Control · Mathematics 2021-05-21 Marco Boresta , Tommaso Colombo , Alberto De Santis , Stefano Lucidi

We study trend filtering, a recently proposed tool of Kim et al. [SIAM Rev. 51 (2009) 339-360] for nonparametric regression. The trend filtering estimate is defined as the minimizer of a penalized least squares criterion, in which the…

Statistics Theory · Mathematics 2014-03-24 Ryan J. Tibshirani

The non-parametric estimation of average causal effects in observational studies often relies on controlling for confounding covariates through smoothing regression methods such as kernel, splines or local polynomial regression. Such…

Methodology · Statistics 2017-10-20 Jenny Häggström , Xavier de Luna

Functional linear regression analysis aims to model regression relations which include a functional predictor. The analog of the regression parameter vector or matrix in conventional multivariate or multiple-response linear regression…

Statistics Theory · Mathematics 2011-02-28 Yichao Wu , Jianqing Fan , Hans-Georg Müller

Nonparametric estimators for the mean and the covariance functions of functional data are proposed. The setup covers a wide range of practical situations. The random trajectories are, not necessarily differentiable, have unknown regularity,…

Statistics Theory · Mathematics 2025-02-13 Steven Golovkine , Nicolas Klutchnikoff , Valentin Patilea

Covariance function estimation is a fundamental task in multivariate functional data analysis and arises in many applications. In this paper, we consider estimating sparse covariance functions for high-dimensional functional data, where the…

Statistics Theory · Mathematics 2022-07-15 Qin Fang , Shaojun Guo , Xinghao Qiao

This paper addresses asymptotic properties of general penalized spline estimators with an arbitrary B-spline degree and an arbitrary order difference penalty. The estimator is approximated by a solution of a linear differential equation…

Statistics Theory · Mathematics 2009-12-10 Xiao Wang , Jinglai Shen , David Ruppert

We present a novel method for the estimation of variance parameters in generalised linear mixed models. The method has its roots in Harville (1977)'s work, but it is able to deal with models that have a precision matrix for the…

Methodology · Statistics 2018-06-13 María Xosé Rodríguez-Álvarez , Maria Durban , Dae-Jin Lee , Paul H. C. Eilers

This paper discusses a nonparametric regression model that naturally generalizes neural network models. The model is based on a finite number of one-dimensional transformations and can be estimated with a one-dimensional rate of…

Statistics Theory · Mathematics 2008-12-18 Joel L. Horowitz , Enno Mammen

We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting…

Optimization and Control · Mathematics 2011-07-01 Qihang Lin , Xi Chen , Javier Pena

Many problems involve the use of models which learn probability distributions or incorporate randomness in some way. In such problems, because computing the true expected gradient may be intractable, a gradient estimator is used to update…

Machine Learning · Computer Science 2022-12-29 Ronan Keane , H. Oliver Gao

We propose an adaptive accelerated smoothing technique for a nonsmooth convex optimization problem where the smoothing update rule is coupled with the momentum parameter. We also extend the setting to the case where the objective function…

Optimization and Control · Mathematics 2026-04-21 Reza Rahimi Baghbadorani , Sergio Grammatico , Peyman Mohajerin Esfahani

In many classification problems it is desirable to output well-calibrated probabilities on the different classes. We propose a robust, non-parametric method of calibrating probabilities called SplineCalib that utilizes smoothing splines to…

Machine Learning · Statistics 2018-09-21 Brian Lucena

This paper is concerned with model averaging estimation for partially linear functional score models. These models predict a scalar response using both parametric effect of scalar predictors and non-parametric effect of a functional…

Methodology · Statistics 2021-05-04 Shishi Liu , Hao Zhang , Jingxiao Zhang

The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…

Econometrics · Economics 2024-02-27 Felix Chan , Laszlo Matyas

In this paper, we propose a new horseshoe-type prior hierarchy for adaptively shrinking spline-based functional effects towards a predefined vector space of parametric functions. Instead of shrinking each spline coefficient towards zero, we…

Methodology · Statistics 2021-01-15 Paul Wiemann , Thomas Kneib

The function-on-function linear regression model in which the response and predictors consist of random curves has become a general framework to investigate the relationship between the functional response and functional predictors.…

Methodology · Statistics 2021-11-03 Ufuk Beyaztas , Han Lin Shang