Related papers: Estimation of the Mean Function of Functional Data…
The most frequent kind of dementia of the nervous system, Alzheimer's disease, weakens several brain processes (such as memory) and eventually results in death. The clinical study uses magnetic resonance imaging to diagnose AD. Deep…
As with classic statistics, functional regression models are invaluable in the analysis of functional data. While there are now extensive tools with accompanying theory available for linear models, there is still a great deal of work to be…
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…
Alzheimers Disease (AD) is a progressive neurodegenerative disorder that poses significant challenges in its early diagnosis, often leading to delayed treatment and poorer outcomes for patients. Traditional diagnostic methods, typically…
Fusing structural-functional images of the brain has shown great potential to analyze the deterioration of Alzheimer's disease (AD). However, it is a big challenge to effectively fuse the correlated and complementary information from…
The primary motivation and application in this article come from brain imaging studies on cognitive impairment in elderly subjects with brain disorders. We propose a regularized Haar wavelet-based approach for the analysis of…
We present a theoretically well-founded deep learning algorithm for nonparametric regression. It uses over-parametrized deep neural networks with logistic activation function, which are fitted to the given data via gradient descent. We…
Activation functions have been shown to affect the performance of deep neural networks significantly. While the Rectified Linear Unit (ReLU) remains the dominant choice in practice, the optimal activation function for deep neural networks…
Recent results in nonparametric regression show that deep learning, i.e., neural network estimates with many hidden layers, are able to circumvent the so-called curse of dimensionality in case that suitable restrictions on the structure of…
We consider nonparametric estimation of the mean and covariance functions for functional/longitudinal data. Strong uniform convergence rates are developed for estimators that are local-linear smoothers. Our results are obtained in a unified…
Multi-modal biological, imaging, and neuropsychological markers have demonstrated promising performance for distinguishing Alzheimer's disease (AD) patients from cognitively normal elders. However, it remains difficult to early predict when…
We propose a mesh-based technique to aid in the classification of Alzheimer's disease dementia (ADD) using mesh representations of the cortex and subcortical structures. Deep learning methods for classification tasks that utilize structural…
Most machine learning algorithms, such as classification or regression, treat the individual data point as the object of interest. Here we consider extending machine learning algorithms to operate on groups of data points. We suggest…
Many classic methods have shown non-local self-similarity in natural images to be an effective prior for image restoration. However, it remains unclear and challenging to make use of this intrinsic property via deep networks. In this paper,…
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…
Deep neural networks (DNNs) achieve impressive results for complicated tasks like object detection on images and speech recognition. Motivated by this practical success, there is now a strong interest in showing good theoretical properties…
Functional MRI is a neuroimaging technique that analyzes the functional activity of the brain by measuring blood-oxygen-level-dependent signals throughout the brain. The derived functional features can be used for investigating brain…
Early and accurate diagnosis of Alzheimer Disease is critical for effective clinical intervention, particularly in distinguishing it from Mild Cognitive Impairment, a prodromal stage marked by subtle structural changes. In this study, we…
Imaging-based early diagnosis of Alzheimer Disease (AD) has become an effective approach, especially by using nuclear medicine imaging techniques such as Positron Emission Topography (PET). In various literature it has been found that PET…
Alzheimer's disease is a progressive neurodegenerative disorder that gradually deprives the patient of cognitive function and can end in death. With the advancement of technology today, it is possible to detect Alzheimer's disease through…