Related papers: Density-on-Density Regression
The assessment of Alzheimer's Disease (AD) and Mild Cognitive Impairment (MCI) associated with brain changes remains a challenging task. Recent studies have demonstrated that combination of multi-modality imaging techniques can better…
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…
In this paper we refine the procedure proposed by Lin et al. (2015) to estimate the density at a given quantile based on a resampling method. The approach consists on generating multiple samples of the zero-mean Gaussian variable from which…
Accurate approximations to density functionals have recently been obtained via machine learning (ML). By applying ML to a simple function of one variable without any random sampling, we extract the qualitative dependence of errors on…
The problem of modeling the relationship between univariate distributions and one or more explanatory variables has found increasing interest. Traditional functional data methods cannot be applied directly to distributional data because of…
We propose a function-valued evaluation metric for generative models based on the relative density ratio (RDR) designed to characterize distributional differences between real and generated samples. As an evaluation metric, the RDR function…
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…
Deep learning, a cutting-edge machine learning approach, outperforms traditional machine learning in identifying intricate structures in complex high-dimensional data, particularly in the domain of healthcare. This study focuses on…
In frequentist inference, minimizing the Hellinger distance between a kernel density estimate and a parametric family produces estimators that are both robust to outliers and statistically efficienty when the parametric model is correct.…
In this paper we propose an algorithm for aligning three-dimensional objects when represented as density maps, motivated by applications in cryogenic electron microscopy. The algorithm is based on minimizing the 1-Wasserstein distance…
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…
We propose a novel tensor-on-tensor modeling framework that flexibly models nonlinear voxel-level relationships using Gaussian process (GP) priors, while incorporating the spatial structure of the output tensor through low-rank tensor-based…
We introduce a novel and scalable Bayesian framework for multivariate-density-density regression (DDR), designed to model relationships between multivariate distributions. Our approach addresses the critical issue of distributions residing…
The uncertainty of clinical examinations frequently leads to irregular observation intervals in longitudinal imaging data, posing challenges for modeling disease progression.Most existing imaging-based disease prediction models operate in…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…
We consider a generalization of the classifier-based density-ratio estimation task to a quasiprobabilistic setting where probability densities can be negative. The problem with most loss functions used for this task is that they implicitly…
Deep learning (DL) for predicting Alzheimer's disease (AD) has provided timely intervention in disease progression yet still demands attentive interpretability to explain how their DL models make definitive decisions. Recently,…
Alzheimer's disease (AD) is associated with local (e.g. brain tissue atrophy) and global brain changes (loss of cerebral connectivity), which can be detected by high-resolution structural magnetic resonance imaging. Conventionally, these…
Given a random sample from a density function supported on a manifold $M$, a new method for the estimating highest density regions of the underlying population is introduced. The new proposal is based on the empirical version of the opening…
Semisupervised methods inevitably invoke some assumption that links the marginal distribution of the features to the regression function of the label. Most commonly, the cluster or manifold assumptions are used which imply that the…