Related papers: Low-rank variance reduction for uncertain radiativ…
Random features (RFs) are a popular technique to scale up kernel methods in machine learning, replacing exact kernel evaluations with stochastic Monte Carlo estimates. They underpin models as diverse as efficient transformers (by…
The Reduced-Basis Control-Variate Monte-Carlo method was introduced recently in [S. Boyaval and T. Leli\`evre, CMS, 8 2010] as an improved Monte-Carlo method, for the fast estimation of many parametrized expected values at many parameter…
We propose and analyse a numerical integrator that computes a low-rank approximation to large time-dependent matrices that are either given explicitly via their increments or are the unknown solution to a matrix differential equation.…
In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in data analysis and machine learning. But often, images are not…
A novel hybrid Monte Carlo transport scheme is demonstrated in a scene with solar illumination, scattering and absorbing 2D atmosphere, a textured reflecting mountain, and a small detector located in the sky (mounted on a satellite or a…
In this paper, we evaluate the performance of the multilevel Monte Carlo method (MLMC) for deterministic and uncertain hyperbolic systems, where randomness is introduced either in the modeling parameters or in the approximation algorithms.…
We present a Multi-Index Quasi-Monte Carlo method for the solution of elliptic partial differential equations with random coefficients. By combining the multi-index sampling idea with randomly shifted rank-1 lattice rules, the algorithm…
We propose a new algorithm for variance reduction when estimating $f(X_T)$ where $X$ is the solution to some stochastic differential equation and $f$ is a test function. The new estimator is $(f(X^1_T) + f(X^2_T))/2$, where $X^1$ and $X^2$…
We present benchmark problems and solutions for the continuum radiative transfer (RT) in a 2D disk configuration. The reliability of three Monte-Carlo and two grid-based codes is tested by comparing their results for a set of well-defined…
This paper addresses optimization problems constrained by partial differential equations with uncertain coefficients. In particular, the robust control problem and the average control problem are considered for a tracking type cost…
The dynamical low-rank (DLR) approximation is an efficient technique to approximate the solution to matrix differential equations. Recently, the DLR method was applied to radiation transport calculations to reduce memory requirements and…
Low-rank decomposition (LRD) is a state-of-the-art method for visual data reconstruction and modelling. However, it is a very challenging problem when the image data contains significant occlusion, noise, illumination variation, and…
Monte Carlo methods are widely used for neutron transport simulations at least partly because of the accuracy they bring to the modeling of these problems. However, the computational burden associated with the slow convergence rate of Monte…
Recent progress in deep latent variable models has largely been driven by the development of flexible and scalable variational inference methods. Variational training of this type involves maximizing a lower bound on the log-likelihood,…
In this work, we propose an alternating low-rank decomposition (ALRD) approach and novel subspace algorithms for direction-of-arrival (DOA) estimation. In the ALRD scheme, the decomposition matrix for rank reduction is composed of a set of…
We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex…
The problem of optimising functions with intractable gradients frequently arise in machine learning and statistics, ranging from maximum marginal likelihood estimation procedures to fine-tuning of generative models. Stochastic approximation…
We present an unbiased numerical integration algorithm that handles both low-frequency regions and high frequency details of multidimensional integrals. It combines quadrature and Monte Carlo integration, by using a quadrature-base…
When dealing with difficult inverse problems such as inverse rendering, using Monte Carlo estimated gradients to optimise parameters can slow down convergence due to variance. Averaging many gradient samples in each iteration reduces this…
The Plackett-Luce (PL) model is ubiquitous in learning-to-rank (LTR) because it provides a useful and intuitive probabilistic model for sampling ranked lists. Counterfactual offline evaluation and optimization of ranking metrics are pivotal…