Related papers: Data driven Dirichlet sampling on manifolds

Modern sample points in many applications no longer comprise real vectors in a real vector space but sample points of much more complex structures, which may be represented as points in a space with a certain underlying geometric structure,…

Huge amount of data is the key of the success of deep learning, however, redundant information impairs the generalization ability of the model and increases the burden of calculation. Dataset Distillation (DD) compresses the original…

Dynamical models underpin our ability to understand and predict the behavior of natural systems. Whether dynamical models are developed from first-principles derivations or from observational data, they are predicated on our choice of state…

We develop algorithms for sampling from a probability distribution on a submanifold embedded in Rn. Applications are given to the evaluation of algorithms in 'Topological Statistics'; to goodness of fit tests in exponential families and to…

The paper advocates the use of a statistical tool dedicated to the exploration of data samples populated by several sources of events. This new technique, called sPlot, is able to unfold the contributions of the different sources to the…

This paper describes a novel approach to change-point detection when the observed high-dimensional data may have missing elements. The performance of classical methods for change-point detection typically scales poorly with the…

In population studies, it is standard to sample data via designs in which the population is divided into strata, with the different strata assigned different probabilities of inclusion. Although there have been some proposals for including…

We consider the problem of propagating the uncertainty from a possibly large number of random inputs through a computationally expensive model. Stratified sampling is a well-known variance reduction strategy, but its application, thus far,…

The manifold scattering transform is a deep feature extractor for data defined on a Riemannian manifold. It is one of the first examples of extending convolutional neural network-like operators to general manifolds. The initial work on this…

We consider the problem of selecting an optimal mask for an image manifold, i.e., choosing a subset of the pixels of the image that preserves the manifold's geometric structure present in the original data. Such masking implements a form of…

Transformation-invariant analysis of signals often requires the computation of the distance from a test pattern to a transformation manifold. In particular, the estimation of the distances between a transformed query signal and several…

Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance,…

We present a generative learning framework for probabilistic sampling based on an extension of the Probabilistic Learning on Manifolds (PLoM) approach, which is designed to generate statistically consistent realizations of a random vector…

Autoencoding is a popular method in representation learning. Conventional autoencoders employ symmetric encoding-decoding procedures and a simple Euclidean latent space to detect hidden low-dimensional structures in an unsupervised way.…

Deep learning methods have played a more and more important role in hyperspectral image classification. However, the general deep learning methods mainly take advantage of the information of sample itself or the pairwise information between…

The data-aware method of distributions (DA-MD) is a low-dimension data assimilation procedure to forecast the behavior of dynamical systems described by differential equations. It combines sequential Bayesian update with the MD, such that…

Deep learning models lack shift invariance, making them sensitive to input shifts that cause changes in output. While recent techniques seek to address this for images, our findings show that these approaches fail to provide…

Multiple time scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is often essential for scientific computation and further analysis.…

Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step…

A novel strategy for generating datasets is developed within the context of drag prediction for automotive geometries using neural networks. A primary challenge in this space is constructing a training databse of sufficient size and…