Related papers: Estimation of the Mean Function of Functional Data…

The computation of integrals is a fundamental task in the analysis of functional data, which are typically considered as random elements in a space of squared integrable functions. Borrowing ideas from recent advances in the Monte Carlo…

As shown in computer vision, the power of deep learning lies in automatically learning relevant and powerful features for any perdition task, which is made possible through end-to-end architectures. However, deep learning approaches applied…

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 present a general principle for estimating a regression function nonparametrically, allowing for a wide variety of data filtering, for example, repeated left truncation and right censoring. Both the mean and the median regression cases…

The accurate diagnosis of Alzheimer's disease (AD) and prognosis of mild cognitive impairment (MCI) conversion are crucial for early intervention. However, existing multimodal methods face several challenges, from the heterogeneity of input…

In this paper, we develop a general theory for adaptive nonparametric estimation of the mean function of a non-stationary and nonlinear time series model using deep neural networks (DNNs). We first consider two types of DNN estimators,…

\citet{farrell2021deep} establish non-asymptotic high-probability bounds for general deep feedforward neural network (with rectified linear unit activation function) estimators, with \citet[Theorem 1]{farrell2021deep} achieving a suboptimal…

Activity recognition has become a popular research branch in the field of pervasive computing in recent years. A large number of experiments can be obtained that activity sensor-based data's characteristic in activity recognition is…

Activation functions play a decisive role in determining the capacity of Deep Neural Networks as they enable neural networks to capture inherent nonlinearities present in data fed to them. The prior research on activation functions…

Using deep neural networks to solve PDEs has attracted a lot of attentions recently. However, why the deep learning method works is falling far behind its empirical success. In this paper, we provide a rigorous numerical analysis on deep…

Tensor regression models, such as CP regression and Tucker regression, have many successful applications in neuroimaging analysis where the covariates are of ultrahigh dimensionality and possess complex spatial structures. The…

Objective: This paper presents an Alzheimer's disease (AD) detection method based on learning structural similarity between Magnetic Resonance Images (MRIs) and representing this similarity as a graph. Methods: We construct the similarity…

The joint alignment of multivariate functional data plays an important role in various fields such as signal processing, neuroscience and medicine, including the statistical analysis of data from wearable devices. Traditional methods often…

We present polynomial time and sample efficient algorithms for learning an unknown depth-2 feedforward neural network with general ReLU activations, under mild non-degeneracy assumptions. In particular, we consider learning an unknown…

Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression,…

Alzheimer's disease (AD) is a neurodegenerative disorder marked by memory loss and cognitive decline, making early detection vital for timely intervention. However, early diagnosis is challenging due to the heterogeneous presentation of…

We propose a deep neural network for supervised learning on neuroanatomical shapes. The network directly operates on raw point clouds without the need for mesh processing or the identification of point correspondences, as spatial…

We consider neural networks with rational activation functions. The choice of the nonlinear activation function in deep learning architectures is crucial and heavily impacts the performance of a neural network. We establish optimal bounds…

Activation function is a key component in deep learning that performs non-linear mappings between the inputs and outputs. Rectified Linear Unit (ReLU) has been the most popular activation function across the deep learning community.…

Alzheimer's Disease (AD) is an irreversible neurodegenerative disease characterized by progressive cognitive decline as its main symptom. In the research field of deep learning-assisted diagnosis of AD, traditional convolutional neural…