Related papers: Quasi Monte Carlo methods enable extremely low-dim…

In this paper, we study quasi-Monte Carlo (QMC) integration in weighted Sobolev spaces. In contrast to many previous results the QMC algorithms considered here are of open type, i.e., they are extensible in the number of sample points…

Vision-Language Models (VLMs) learn joint representations by mapping images and text into a shared latent space. However, recent research highlights that deterministic embeddings from standard VLMs often struggle to capture the…

Sequential Monte Carlo algorithms (also known as particle filters) are popular methods to approximate filtering (and related) distributions of state-space models. However, they converge at the slow $1/\sqrt{N}$ rate, which may be an issue…

Quasi-Monte Carlo methods have become the industry standard in computer graphics. For that purpose, efficient algorithms for low discrepancy sequences are discussed. In addition, numerical pitfalls encountered in practice are revealed. We…

This work describes a domain embedding technique between two non-matching meshes used for generating realizations of spatially correlated random fields with applications to large-scale sampling-based uncertainty quantification. The goal is…

Learning compact and meaningful latent space representations has been shown to be very useful in generative modeling tasks for visual data. One particular example is applying Vector Quantization (VQ) in variational autoencoders (VQ-VAEs,…

Support vector machine (SVM) is a particularly powerful and flexible supervised learning model that analyzes data for both classification and regression, whose usual algorithm complexity scales polynomially with the dimension of data space…

Monte Carlo simulations are widely used to simulate complex molecular systems, but standard approaches suffer from metastability. Lately, the use of non-local proposal updates in a collective-variable (CV) space has been proposed in several…

In financial engineering, prices of financial products are computed approximately many times each trading day with (slightly) different parameters in each calculation. In many financial models such prices can be approximated by means of…

We consider quasi maximum likelihood (QML) estimation for general non-Gaussian discrete-ime linear state space models and equidistantly observed multivariate L\'evy-driven continuoustime autoregressive moving average (MCARMA) processes. In…

Recent work has suggested using Monte Carlo methods based on piecewise deterministic Markov processes (PDMPs) to sample from target distributions of interest. PDMPs are non-reversible continuous-time processes endowed with momentum, and…

This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…

The rapid advancement of large language models (LLMs) has intensified the need for effective mechanisms to transform continuous multimodal data into discrete representations suitable for language-based processing. Discrete tokenization,…

The vector quantization is a widely used method to map continuous representation to discrete space and has important application in tokenization for generative mode, bottlenecking information and many other tasks in machine learning. Vector…

We present an adaptive multilevel Monte Carlo (AMLMC) algorithm for approximating deterministic, real-valued, bounded linear functionals that depend on the solution of a linear elliptic PDE with a lognormal diffusivity coefficient and…

Large language models, like transformers, have recently demonstrated immense powers in text and image generation. This success is driven by the ability to capture long-range correlations between elements in a sequence. The same feature…

Monte Carlo methods are widely used importance sampling techniques for studying complex physical systems. Integrating these methods with deep learning has significantly improved efficiency and accuracy in high-dimensional problems and…

We consider the problem of estimating the probability of a large loss from a financial portfolio, where the future loss is expressed as a conditional expectation. Since the conditional expectation is intractable in most cases, one may…

Conventional uncertainty quantification methods usually lacks the capability of dealing with high-dimensional problems due to the curse of dimensionality. This paper presents a semi-supervised learning framework for dimension reduction and…

Diffusion models (DMs) have emerged as powerful image priors in Bayesian computational imaging. Two primary strategies have been proposed for leveraging DMs in this context: Plug-and-Play methods, which are zero-shot and highly flexible but…