相关论文: Robust Deep Neural Network Estimation for Multi-di…

In this work, we propose a deep neural network method to perform nonparametric regression for functional data. The proposed estimators are based on sparsely connected deep neural networks with ReLU activation function. By properly choosing…

Estimation of a regression function from independent and identically distributed data is considered. The $L_2$ error with integration with respect to the distribution of the predictor variable is used as the error criterion. The rate of…

In this paper, we consider robust nonparametric regression using deep neural networks with ReLU activation function. While several existing theoretically justified methods are geared towards robustness against identical heavy-tailed noise…

There has been a growing interest in expressivity of deep neural networks. However, most of the existing work about this topic focuses only on the specific activation function such as ReLU or sigmoid. In this paper, we investigate the…

We propose a new approach, called as functional deep neural network (FDNN), for classifying multi-dimensional functional data. Specifically, a deep neural network is trained based on the principle components of the training data which shall…

Traditional Convolutional Neural Networks (CNNs) typically use the same activation function (usually ReLU) for all neurons with non-linear mapping operations. For example, the deep convolutional architecture Inception-v4 uses ReLU. To…

Deep learning has exhibited remarkable results across diverse areas. To understand its success, substantial research has been directed towards its theoretical foundations. Nevertheless, the majority of these studies examine how well deep…

Alzheimer's disease is one of the most common types of neurodegenerative disease, characterized by the accumulation of amyloid-beta plaque and tau tangles. Recently, deep learning approaches have shown promise in Alzheimer's disease…

Magnetic Resonance Imaging (MRI) provides detailed structural information, while functional MRI (fMRI) captures temporal brain activity. In this work, we present a multimodal deep learning framework that integrates MRI and fMRI for…

This paper deals with robust marginal estimation under a general regression model when missing data occur in the response and also in some of covariates. The target is a marginal location parameter which is given through an $M-$functional.…

Understanding the relationship between cognition and intrinsic brain activity through purely data-driven approaches remains a significant challenge in neuroscience. Resting-state functional magnetic resonance imaging (rs-fMRI) offers a…

The intrinsically infinite-dimensional features of the functional observations over multidimensional domains render the standard classification methods effectively inapplicable. To address this problem, we introduce a novel multiclass…

Whereas recovery of the manifold from data is a well-studied topic, approximation rates for functions defined on manifolds are less known. In this work, we study a regression problem with inputs on a $d^*$-dimensional manifold that is…

Early diagnosis of Alzheimer Diagnostics (AD) is a challenging task due to its subtle and complex clinical symptoms. Deep learning-assisted medical diagnosis using image recognition techniques has become an important research topic in this…

In this paper, we develop a novel efficient and robust nonparametric regression estimator under a framework of feedforward neural network. There are several interesting characteristics for the proposed estimator. First, the loss function is…

Current neuroimaging techniques provide paths to investigate the structure and function of the brain in vivo and have made great advances in understanding Alzheimer's disease (AD). However, the group-level analyses prevalently used for…

The ability to predict the future trajectory of a patient is a key step toward the development of therapeutics for complex diseases such as Alzheimer's disease (AD). However, most machine learning approaches developed for prediction of…

Recent developments on deep learning established some theoretical properties of deep neural networks estimators. However, most of the existing works on this topic are restricted to bounded loss functions or (sub)-Gaussian or bounded input.…

In recent years, functional neural networks have been proposed and studied in order to approximate nonlinear continuous functionals defined on $L^p([-1, 1]^s)$ for integers $s\ge1$ and $1\le p<\infty$. However, their theoretical properties…

We introduce a novel framework for the classification of functional data supported on nonlinear, and possibly random, manifold domains. The motivating application is the identification of subjects with Alzheimer's disease from their…