Related papers: Quasi Monte Carlo methods enable extremely low-dim…
This paper establishes the almost sure convergence and asymptotic normality of levels and differenced quasi maximum-likelihood (QML) estimators of dynamic panel data models. The QML estimators are robust with respect to initial conditions,…
Efficient uncertainty quantification algorithms are key to understand the propagation of uncertainty -- from uncertain input parameters to uncertain output quantities -- in high resolution mathematical models of brain physiology. Advanced…
Probabilistic Latent Variable Models (LVMs) excel at modeling complex, high-dimensional data through lower-dimensional representations. Recent advances show that equipping these latent representations with a Riemannian metric unlocks…
Deep generative models like VAEs and diffusion models have advanced various generation tasks by leveraging latent variables to learn data distributions and generate high-quality samples. Despite the field of explainable AI making strides in…
Deep neural networks with discrete latent variables offer the promise of better symbolic reasoning, and learning abstractions that are more useful to new tasks. There has been a surge in interest in discrete latent variable models, however,…
Concept-bottleneck models (CBMs) are neural classifiers that compute predictions from high-level concepts extracted from the input. CBMs ensure stakeholders can understand the concepts -- and the predictions they entail -- by learning these…
We propose a theoretical framework to analyze semi-supervised classification under the low density separation assumption in a high-dimensional regime. In particular, we introduce QLDS, a linear classification model, where the low density…
We propose a new computationally efficient sampling scheme for Bayesian inference involving high dimensional probability distributions. Our method maps the original parameter space into a low-dimensional latent space, explores the latent…
The subsurface flow is usually subject to uncertain porous media structures. In most cases, however, we only have partial knowledge about the porous media properties. A common approach is to model the uncertain parameters of porous media as…
Many large scale problems in computational fluid dynamics such as uncertainty quantification, Bayesian inversion, data assimilation and PDE constrained optimization are considered very challenging computationally as they require a large…
Generalized linear latent variable models (GLLVMs) are a class of methods for analyzing multi-response data which has garnered considerable popularity in recent years, for example, in the analysis of multivariate abundance data in ecology.…
The development of quantum-classical hybrid (QCH) algorithms is critical to achieve state-of-the-art computational models. A QCH variational autoencoder (QVAE) was introduced in Ref. [1] by some of the authors of this paper. QVAE consists…
Monte Carlo methods are widely used for approximating complicated, multidimensional integrals for Bayesian inference. Population Monte Carlo (PMC) is an important class of Monte Carlo methods, which utilizes a population of proposals to…
This article provides a high-level overview of some recent works on the application of quasi-Monte Carlo (QMC) methods to PDEs with random coefficients. It is based on an in-depth survey of a similar title by the same authors, with an…
We propose a general framework using spike-and-slab prior distributions to aid with the development of high-dimensional Bayesian inference. Our framework allows inference with a general quasi-likelihood function. We show that highly…
Latent variables (LVs) play a crucial role in encoder-decoder models by enabling effective data compression, prediction, and generation. Although their theoretical properties, such as generalization, have been extensively studied in…
Quasi-Monte Carlo (QMC) is a powerful method for evaluating high-dimensional integrals. However, its use is typically limited to distributions where direct sampling is straightforward, such as the uniform distribution on the unit hypercube…
Quasi-stationary distributions (QSDs)arise from stochastic processes that exhibit transient equilibrium behaviour on the way to absorption QSDs are often mathematically intractable and even drawing samples from them is not straightforward.…
A rich supply of data and innovative algorithms have made data-driven modeling a popular technique in modern industry. Among various data-driven methods, latent variable models (LVMs) and their counterparts account for a major share and…
Multi-sample, importance-weighted variational autoencoders (IWAE) give tighter bounds and more accurate uncertainty estimates than variational autoencoders (VAE) trained with a standard single-sample objective. However, IWAEs scale poorly:…