Related papers: Baseline zone estimation in two dimensions
Soft-thresholding has been widely used in neural networks. Its basic network structure is a two-layer convolution neural network with soft-thresholding. Due to the network's nature of nonlinearity and nonconvexity, the training process…
A filament consists of local maximizers of a smooth function $f$ when moving in a certain direction. A filamentary structure is an important feature of the shape of an object and is also considered as an important lower dimensional…
Convolutional neural networks are widely used in imaging and image recognition. Learning such networks from training data leads to the minimization of a non-convex function. This makes the analysis of standard optimization methods such as…
We consider the recursive estimation of a regression functional where the explanatory variables take values in some functional space. We prove the almost sure convergence of such estimates for dependent functional data. Also we derive the…
We consider the regression problem of estimating functions on $\mathbb{R}^D$ but supported on a $d$-dimensional manifold $ \mathcal{M} \subset \mathbb{R}^D $ with $ d \ll D $. Drawing ideas from multi-resolution analysis and nonlinear…
We investigate 1) the rate at which refined properties of the empirical risk---in particular, gradients---converge to their population counterparts in standard non-convex learning tasks, and 2) the consequences of this convergence for…
It has been shown that gradient descent can yield the zero training loss in the over-parametrized regime (the width of the neural networks is much larger than the number of data points). In this work, combining the ideas of some existing…
It is often of interest to assess whether a function-valued statistical parameter, such as a density function or a mean regression function, is equal to any function in a class of candidate null parameters. This can be framed as a…
We study nonparametric change-point estimation from indirect noisy observations. Focusing on the white noise convolution model, we consider two classes of functions that are smooth apart from the change-point. We establish lower bounds on…
We study the problem of estimating the effect function for a continuous treatment, which maps each treatment value to a population-averaged outcome. A central challenge in this setting is confounding: treatment assignment often depends on…
Linear regression is often deemed inherently interpretable; however, challenges arise for high-dimensional data. We focus on further understanding how linear regression approximates nonlinear responses from high-dimensional functional data,…
It is a typical standard assumption in the density deconvolution problem that the characteristic function of the measurement error distribution is non-zero on the real line. While this condition is assumed in the majority of existing works…
Various indicators and measures of the real life procedures rise up as functionals of the quantile process of a parent random variable Z. However, Z can be observed only through a response in a linear model whose covariates are not under…
Convex regression is the problem of fitting a convex function to a data set consisting of input-output pairs. We present a new approach to this problem called spectrahedral regression, in which we fit a spectrahedral function to the data,…
In this work, we propose a deep learning-based method to perform semiparametric regression analysis for spatially dependent data. To be specific, we use a sparsely connected deep neural network with rectified linear unit (ReLU) activation…
Because of the advance in technologies, modern statistical studies often encounter linear models with the number of explanatory variables much larger than the sample size. Estimation and variable selection in these high-dimensional problems…
Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models,…
We give a statement on extension with estimates of convex functions defined on a linear subspace, inspired by similar extension results concerning metrics on positive line bundles
We consider the problem of estimating the regression function in functional linear regression models by proposing a new type of projection estimators which combine dimension reduction and thresholding. The introduction of a threshold rule…
This thesis deals with the nonparametric estimation of density f of the regression error term E of the model Y=m(X)+E, assuming its independence with the covariate X. The difficulty linked to this study is the fact that the regression error…