Related papers: A Nonlinear Hierarchical Model for Longitudinal Da…

To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear…

Given data, deep generative models, such as variational autoencoders (VAE) and generative adversarial networks (GAN), train a lower dimensional latent representation of the data space. The linear Euclidean geometry of data space pulls back…

In this paper, we study linear regression applied to data structured on a manifold. We assume that the data manifold is smooth and is embedded in a Euclidean space, and our objective is to reveal the impact of the data manifold's extrinsic…

Many measurements in computer vision and machine learning manifest as non-Euclidean data samples. Several researchers recently extended a number of deep neural network architectures for manifold valued data samples. Researchers have…

International comparisons of hierarchical time series data sets based on survey data, such as annual country-level estimates of school enrollment rates, can suffer from large amounts of missing data due to differing coverage of surveys…

The majority of Americans fail to achieve recommended levels of physical activity, which leads to numerous preventable health problems such as diabetes, hypertension, and heart diseases. This has generated substantial interest in monitoring…

Major postoperative complications are devastating to surgical patients. Some of these complications are potentially preventable via early predictions based on intraoperative data. However, intraoperative data comprise long and fine-grained…

The systematic collection of longitudinal data is very common in practice, making mixed models widely used. Most developments around these models focus on modeling the mean trajectory of repeated measurements, typically under the assumption…

In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…

Modeling and computation for multivariate longitudinal surveys have proven challenging, particularly when data are not all continuous and Gaussian but contain discrete measurements. In many social science surveys, study participants are…

In clinical practice and biomedical research, measurements are often collected sparsely and irregularly in time while the data acquisition is expensive and inconvenient. Examples include measurements of spine bone mineral density, cancer…

In geosciences, the use of classical Euclidean methods is unsuitable for treating and analyzing some types of data, as this may not belong to a vector space. This is the case for correlation matrices, belonging to a subfamily of symmetric…

In many applications, data can be heterogeneous in the sense of spanning latent groups with different underlying distributions. When predictive models are applied to such data the heterogeneity can affect both predictive performance and…

Medical data range from genomic sequences and retinal photographs to structured laboratory results and unstructured clinical narratives. Although these modalities appear disparate, many encode convergent information about a single…

Many of the tools available for robot learning were designed for Euclidean data. However, many applications in robotics involve manifold-valued data. A common example is orientation; this can be represented as a 3-by-3 rotation matrix or a…

Longitudinal magnetic resonance imaging data is used to model trajectories of change in brain regions of interest to identify areas susceptible to atrophy in those with neurodegenerative conditions like Alzheimer's disease. Most methods for…

We propose a novel framework to learn the spatiotemporal variability in longitudinal 3D shape data sets, which contain observations of objects that evolve and deform over time. This problem is challenging since surfaces come with arbitrary…

When considering functional principal component analysis for sparsely observed longitudinal data that take values on a nonlinear manifold, a major challenge is how to handle the sparse and irregular observations that are commonly…

Modeling non-Euclidean data is drawing extensive attention along with the unprecedented successes of deep neural networks in diverse fields. Particularly, a symmetric positive definite matrix is being actively studied in computer vision,…

There are many issues that can cause problems when attempting to infer model parameters from data. Data and models are both imperfect, and as such there are multiple scenarios in which standard methods of inference will lead to misleading…