Related papers: LeStrat-Net: Lebesgue style stratification for Mon…

This paper concerns the identification of continuous-time systems in state-space form that are subject to Lebesgue sampling. Contrary to equidistant (Riemann) sampling, Lebesgue sampling consists of taking measurements of a continuous-time…

Monte Carlo sampling techniques have broad applications in machine learning, Bayesian posterior inference, and parameter estimation. Often the target distribution takes the form of a product distribution over a dataset with a large number…

We consider the problem of adaptive stratified sampling for Monte Carlo integration of a noisy function, given a finite budget n of noisy evaluations to the function. We tackle in this paper the problem of adapting to the function at the…

We propose the use of Monte Carlo histogram reweighting to extrapolate predictions of machine learning methods. In our approach, we treat the output from a convolutional neural network as an observable in a statistical system, enabling its…

Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds, that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their…

Deep learning has led to state-of-the-art results for many medical imaging tasks, such as segmentation of different anatomical structures. With the increased numbers of deep learning publications and openly available code, the approach to…

In this paper, we apply the Monte Carlo stochastic optimization (MOST) proposed by the authors to a deep learning of XOR gate and verify its effectiveness. Deep machine learning based on neural networks is one of the most important keywords…

Inspired by the latest developments in multilevel Monte Carlo (MLMC) methods and randomised sketching for linear algebra problems we propose a MLMC estimator for real-time processing of matrix structured random data. Our algorithm is…

Despite recent improvements using fully convolutional networks, in general, the segmentation produced by most state-of-the-art semantic segmentation methods does not show satisfactory adherence to the object boundaries. We propose a method…

Self-learning Monte Carlo (SLMC) method is a general algorithm to speedup MC simulations. Its efficiency has been demonstrated in various systems by introducing an effective model to propose global moves in the configuration space. In this…

In this chapter, we discuss recent work on learning sparse approximations to high-dimensional functions on data, where the target functions may be scalar-, vector- or even Hilbert space-valued. Our main objective is to study how the…

We present a procedure that in many cases enables the Monte Carlo sampling of states of a large system from the sampling of states of a smaller system. We illustrate this procedure, which we call the sewing algorithm, for sampling states…

We construct Monte Carlo methods for the $L^2$-approximation in Hilbert spaces of multivariate functions sampling no more than $n$ function values of the target function. Their errors catch up with the rate of convergence and the…

Monte Carlo method is a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. They are often used in physical and mathematical problems and are most useful when it is difficult or…

Machine learning models are commonly applied to human brain imaging datasets in an effort to associate function or structure with behaviour, health, or other individual phenotypes. Such models often rely on low-dimensional maps generated by…

This paper investigates the use of stratified sampling as a variance reduction technique for approximating integrals over large dimensional spaces. The accuracy of this method critically depends on the choice of the space partition, the…

We compare estimators of the (essential) supremum and the integral of a function $f$ defined on a measurable space when $f$ may be observed at a sample of points in its domain, possibly with error. The estimators compared vary in their…

Elastic systems that are spatially heterogeneous in their mechanical response pose special challenges for molecular simulations. Standard methods for sampling thermal fluctuations of a system's size and shape proceed through a series of…

Uncertainty estimation in deep models is essential in many real-world applications and has benefited from developments over the last several years. Recent evidence suggests that existing solutions dependent on simple Gaussian formulations…

Artificial Neural Networks were recently shown to be an efficient representation of highly-entangled many-body quantum states. In practical applications, neural-network states inherit numerical schemes used in Variational Monte Carlo, most…