Related papers: Nonparametric function-on-scalar regression using …
Semi-functional linear regression models postulate a linear relationship between a scalar response and a functional covariate, and also include a non-parametric component involving a univariate explanatory variable. It is of practical…
To have a superior generalization, a deep learning neural network often involves a large size of training sample. With increase of hidden layers in order to increase learning ability, neural network has potential degradation in accuracy.…
We investigate structured sparsity methods for variable selection in regression problems where the target depends nonlinearly on the inputs. We focus on general nonlinear functions not limiting a priori the function space to additive…
We develop adaptive estimation and inference methods for high-dimensional Gaussian copula regression that achieve the same performance without the knowledge of the marginal transformations as that for high-dimensional linear regression.…
We introduce directional regularity, a new definition of anisotropy for multivariate functional data. Instead of taking the conventional view, which determines anisotropy as a notion of smoothness along a dimension, directional regularity…
We develop a fully Bayesian nonparametric regression model based on a L\'evy process prior named MLABS (Multivariate L\'evy Adaptive B-Spline regression) model, a multivariate version of the LARK (L\'evy Adaptive Regression Kernels) models,…
We develop nonparametric regression methods for the case when the true regression function is not necessarily smooth. More specifically, our approach is using the fractional Laplacian and is designed to handle the case when the true…
This paper is concerned with convergence estimates for fully discrete tree tensor network approximations of high-dimensional functions from several model classes. For functions having standard or mixed Sobolev regularity, new estimates…
Linear regression on network-linked observations has been an essential tool in modeling the relationship between response and covariates with additional network structures. Previous methods either lack inference tools or rely on restrictive…
Traditional neural networks (multi-layer perceptrons) have become an important tool in data science due to their success across a wide range of tasks. However, their performance is sometimes unsatisfactory, and they often require a large…
Robust estimation has played an important role in statistical and machine learning. However, its applications to functional linear regression are still under-developed. In this paper, we focus on Huber's loss with a diverging robustness…
We study adaptive estimation and inference in ill-posed linear inverse problems defined by conditional moment restrictions. Existing regularized estimators such as Regularized DeepIV (RDIV) require prior knowledge of the smoothness of the…
Performative prediction is an emerging paradigm in machine learning that addresses scenarios where the model's prediction may induce a shift in the distribution of the data it aims to predict. Current works in this field often rely on…
Function regression/approximation is a fundamental application of machine learning. Neural networks (NNs) can be easily trained for function regression using a sufficient number of neurons and epochs. The forward-forward learning algorithm…
In the present paper we consider the problem of estimating a periodic $(r+1)$-dimensional function $f$ based on observations from its noisy convolution. We construct a wavelet estimator of $f$, derive minimax lower bounds for the $L^2$-risk…
For multivariate nonparametric regression, functional analysis-of-variance (ANOVA) modeling aims to capture the relationship between a response and covariates by decomposing the unknown function into various components, representing main…
Accurately estimating parameters in complex nonlinear systems is crucial across scientific and engineering fields. We present a novel approach for parameter estimation using a neural network with the Huber loss function. This method taps…
Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…
This paper provides a new avenue for exploiting deep neural networks to improve physics-based simulation. Specifically, we integrate the classic Lagrangian mechanics with a deep autoencoder to accelerate elastic simulation of deformable…
Adaptive gradient methods have been widely adopted in training large-scale deep neural networks, especially large foundation models. Despite the huge success in practice, their theoretical advantages over classical gradient methods with…