Related papers: Density-on-Density Regression
Detection of Alzheimer's Disease (AD) from neuroimaging data such as MRI through machine learning have been a subject of intense research in recent years. Recent success of deep learning in computer vision have progressed such research…
Variational representations of divergences and distances between high-dimensional probability distributions offer significant theoretical insights and practical advantages in numerous research areas. Recently, they have gained popularity in…
Density regression provides a flexible strategy for modeling the distribution of a response variable $Y$ given predictors $\mathbf{X}=(X_1,\ldots,X_p)$ by letting that the conditional density of $Y$ given $\mathbf{X}$ as a completely…
Objective: this study has a twofold goal. First, it aims to improve the understanding of the impact of Dementia of type Alzheimer's Disease (AD) on different aspects of the lexicon. Second, it aims to demonstrate that such aspects of the…
We propose a novel Riemannian geometric framework for variational inference in Bayesian models based on the nonparametric Fisher-Rao metric on the manifold of probability density functions. Under the square-root density representation, the…
We propose a novel deep neural network methodology for density estimation on product Riemannian manifold domains. In our approach, the network directly parameterizes the unknown density function and is trained using a penalized maximum…
Multimodal neuroimage can provide complementary information about the dementia, but small size of complete multimodal data limits the ability in representation learning. Moreover, the data distribution inconsistency from different…
Despite the strong predictive performance achieved by machine learning models across many application domains, assessing their trustworthiness through reliable estimates of predictive confidence remains a critical challenge. This issue…
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…
Computer vision systems that are deployed in safety-critical applications need to quantify their output uncertainty. We study regression from images to parameter values and here it is common to detect uncertainty by predicting probability…
Weak gravitational lensing surveys have the potential to directly probe mass density fluctuation in the universe. Recent studies have shown that it is possible to model the statistics of the convergence field at small angular scales by…
To consider model uncertainty in global Fr\'{e}chet regression and improve density response prediction, we propose a frequentist model averaging method. The weights are chosen by minimizing a cross-validation criterion based on Wasserstein…
Nearest neighbor (NN) matching as a tool to align data sampled from different groups is both conceptually natural and practically well-used. In a landmark paper, Abadie and Imbens (2006) provided the first large-sample analysis of NN…
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…
Here we present a new non-parametric approach to density estimation and classification derived from theory in Radon transforms and image reconstruction. We start by constructing a "forward problem" in which the unknown density is mapped to…
We propose a new wavelet-based method for density estimation when the data are size-biased. More specifically, we consider a power of the density of interest, where this power exceeds 1/2. Warped wavelet bases are employed, where warping is…
This paper explores deterioration in Alzheimers Disease using Machine Learning. Subjects were split into two datasets based on baseline diagnosis (Cognitively Normal, Mild Cognitive Impairment), with outcome of deterioration at final visit…
For effective treatment of Alzheimer disease (AD), it is important to identify subjects who are most likely to exhibit rapid cognitive decline. Herein, we developed a novel framework based on a deep convolutional neural network which can…
White matter hyperintensities (WMH) are key imaging markers in cognitive aging, Alzheimer's disease (AD), and related dementias. Although automated methods for WMH segmentation have advanced, most provide only global lesion load and…
Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one-dimensional box as a functional of their density. The properties of different kernels and methods of cross-validation are explored, and…