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Support Vector Machines (SVMs) are an important tool for performing classification on scattered data, where one usually has to deal with many data points in high-dimensional spaces. We propose solving SVMs in primal form using feature maps…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
In spatial regression models, collinearity between covariates and spatial effects can lead to significant bias in effect estimates. This problem, known as spatial confounding, is encountered modelling forestry data to assess the effect of…
The purpose of this work is to study the existence and analytic smoothing effect for the compressible Navier- Stokes system with quantum pressure in pseudo-measure spaces. This system has been considered by B. Haspot and an analytic…
This paper concerns robust inference on average treatment effects following model selection. In the selection on observables framework, we show how to construct confidence intervals based on a doubly-robust estimator that are robust to…
Motivated by applications in emergency response and experimental design, we consider smooth stochastic optimization problems over probability measures supported on compact subsets of the Euclidean space. With the influence function as the…
A new estimator, named S-LASSO, is proposed for the coefficient function of the Function-on-Function linear regression model. The S-LASSO estimator is shown to be able to increase the interpretability of the model, by better locating…
We propose a new inferential framework for constructing confidence regions and testing hypotheses in statistical models specified by a system of high dimensional estimating equations. We construct an influence function by projecting the…
We develop joint confidence regions for linear regression coefficients when the regressors and errors are jointly stationary and ergodic with unspecified serial dependence. The method applies random smoothing, using an independent auxiliary…
Inspired by the analysis of variance (ANOVA) decomposition of functions we propose a Gaussian-Uniform mixture model on the high-dimensional torus which relies on the assumption that the function we wish to approximate can be well explained…
We describe an iterative formalism to compute influence functionals that describe the general quantum dynamics of a subsystem beyond the assumption of linear coupling to a quadratic bath. We use a space-time tensor network representation of…
This paper studies estimation of a smooth function $f(t,s)$ when we are given functional responses of the form $f(t,\cdot)$ + error, but scientific interest centers on the collection of functions $f(\cdot,s)$ for different $s$. The…
The semivarying coefficient models are widely used in the application of finance, economics, medical science and many other areas. The functional coefficients are commonly estimated by local smoothing methods, e.g. local linear estimator.…
In recent years, denoising diffusion models have become a crucial area of research due to their abundance in the rapidly expanding field of generative AI. While recent statistical advances have delivered explanations for the generation…
We consider design-based causal inference for spatial experiments in which treatments may have effects that bleed out and feed back in complex ways. Such spatial spillover effects violate the standard ``no interference'' assumption for…
We propose and implement an approach to inference in linear instrumental variables models which is simultaneously robust and computationally tractable. Inference is based on self-normalization of sample moment conditions, and allows for…
In this paper, we propose a new regularization technique called "functional SCAD". We then combine this technique with the smoothing spline method to develop a smooth and locally sparse (i.e., zero on some sub-regions) estimator for the…
We derive the properties and demonstrate the desirability of a model-based method for estimating the spatially-varying effects of covariates on the quantile function. By modeling the quantile function as a combination of I-spline basis…
Analysis of variance (ANOVA) is an extremely important method in exploratory and confirmatory data analysis. Unfortunately, in complex problems (e.g., split-plot designs), it is not always easy to set up an appropriate ANOVA. We propose a…
Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…