Related papers: Enabling stratified sampling in high dimensions vi…

In stochastic simulation, input uncertainty refers to the output variability arising from the statistical noise in specifying the input models. This uncertainty can be measured by a variance contribution in the output, which, in the…

We introduce a method to construct a stochastic surrogate model from the results of dimensionality reduction in forward uncertainty quantification. The hypothesis is that the high-dimensional input augmented by the output of a computational…

The weight space of an artificial neural network can be systematically explored using tools from statistical mechanics. We employ a combination of a hybrid Monte Carlo algorithm which performs long exploration steps, a ratchet-based…

We present a novel view of nonlinear manifold learning using derivative-free optimization techniques. Specifically, we propose an extension of the classical multi-dimensional scaling (MDS) method, where instead of performing gradient…

Accurate free energy representations are crucial for understanding phase dynamics in materials. We employ a scale-bridging approach to incorporate atomistic information into our free energy model by training a neural network on DFT-informed…

We propose nested sequential Monte Carlo (NSMC), a methodology to sample from sequences of probability distributions, even where the random variables are high-dimensional. NSMC generalises the SMC framework by requiring only approximate,…

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are…

Monte Carlo sampling techniques are used to estimate high-dimensional integrals that model the physics of light transport in virtual scenes for computer graphics applications. These methods rely on the law of large numbers to estimate…

Achieving robust uncertainty quantification for deep neural networks represents an important requirement in many real-world applications of deep learning such as medical imaging where it is necessary to assess the reliability of a neural…

A general adaptive approach rooted in stratified sampling (SS) is proposed for sample-based uncertainty quantification (UQ). To motivate its use in this context the space-filling, orthogonality, and projective properties of SS are compared…

Non-linear manifold learning enables high-dimensional data analysis, but requires out-of-sample-extension methods to process new data points. In this paper, we propose a manifold learning algorithm based on deep learning to create an…

It has been known for a long time that stratification is one possible strategy to obtain higher convergence rates for the Monte Carlo estimation of integrals over the hyper-cube $[0, 1]^s$ of dimension $s$. However, stratified estimators…

The performance of a machine learning system is usually evaluated by using i.i.d.\ observations with true labels. However, acquiring ground truth labels is expensive, while obtaining unlabeled samples may be cheaper. Stratified sampling can…

Deep learning models, including Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs), have achieved state-of-the-art performance on various computer vision tasks such as object classification, detection, segmentation,…

Segmentation is essential for medical image analysis tasks such as intervention planning, therapy guidance, diagnosis, treatment decisions. Deep learning is becoming increasingly prominent for segmentation, where the lack of annotations,…

In the wild, we often encounter collections of sequential data such as electrocardiograms, motion capture, genomes, and natural language, and sequences may be multichannel or symbolic with nonlinear dynamics. We introduce a new method to…

There is emerging evidence that trust-region (TR) algorithms are very effective at solving derivative-free nonconvex stochastic optimization problems in which the objective function is a Monte Carlo (MC) estimate. A recent strand of…

Statistical inference from high-dimensional data with low-dimensional structures has recently attracted lots of attention. In machine learning, deep generative modeling approaches implicitly estimate distributions of complex objects by…

The problem of optimal allocation of samples in surveys using a stratified sampling plan was first discussed by Neyman in 1934. Since then, many researchers have studied the problem of the sample allocation in multivariate surveys and…

Diffusion Map is a spectral dimensionality reduction technique which is able to uncover nonlinear submanifolds in high-dimensional data. And, it is increasingly applied across a wide range of scientific disciplines, such as biology,…