Related papers: Reliable Adaptive Cubature Using Digital Sequences
The inchworm expansion is a promising approach to solving strongly correlated quantum impurity models due to its reduction of the sign problem in real and imaginary time. However, inchworm Monte Carlo is computationally expensive,…
In this paper we discuss new adaptive proposal strategies for sequential Monte Carlo algorithms--also known as particle filters--relying on criteria evaluating the quality of the proposed particles. The choice of the proposal distribution…
The well-known Caputo fractional derivative and the corresponding Caputo fractional integral occur naturally in many equations that model physical phenomena under inhomogeneous media. The relationship between the two fractional terms can be…
In this paper we give explicit constructions of point sets in the $s$ dimensional unit cube yielding quasi-Monte Carlo algorithms which achieve the optimal rate of convergence of the worst-case error for numerically integrating high…
The development of numerical methods capable of simulating realistic materials with strongly correlated electrons, with controllable errors, is a central challenge in quantum many-body physics. Here we describe how a hybrid between…
Probabilistic prediction of sequences from images and other high-dimensional data is a key challenge, particularly in risk-sensitive applications. In these settings, it is often desirable to quantify the uncertainty associated with the…
We propose an adaptive importance sampling scheme for Gaussian approximations of intractable posteriors. Optimization-based approximations like variational inference can be too inaccurate while existing Monte Carlo methods can be too slow.…
Quasi-Monte Carlo (QMC) methods for estimating integrals are attractive since the resulting estimators typically converge at a faster rate than pseudo-random Monte Carlo. However, they can be difficult to set up on arbitrary posterior…
We investigate quasi-Monte Carlo integration using higher order digital nets in weighted Sobolev spaces of arbitrary fixed smoothness $\alpha \in \mathbb{N}$, $\alpha \ge 2$, defined over the $s$-dimensional unit cube. We prove that…
In this study, we give an extension of Montanaro's arXiv/archive:1504.06987 quantum Monte Carlo method, tailored for computing expected values of random variables that exhibit infinite variance. This addresses a challenge in analyzing…
Intractable generative models are models for which the likelihood is unavailable but sampling is possible. Most approaches to parameter inference in this setting require the computation of some discrepancy between the data and the…
We describe an algorithm for controlling the relative error in the numerical evaluation of a bivariate integral, without prior knowledge of the magnitude of the integral. In the event that the magnitude of the integral is less than unity,…
Based on the algorithm Informed Importance Tempering (IIT) proposed by Li et al. (2023) we propose an algorithm that uses an adaptive bounded balancing function. We argue why implementing parallel tempering where each replica uses a…
Cubature formulas, asymptotically optimal with respect to accuracy, are derived for calculating multidimensional weakly singular integrals. They are used for developing a universal code for calculating capacitances of conductors of…
We present two new adaptive quadrature routines. Both routines differ from previously published algorithms in many aspects, most significantly in how they represent the integrand, how they treat non-numerical values of the integrand, how…
Given a probability measure $\mu$ on a set $\mathcal{X}$ and a vector-valued function $\varphi$, a common problem is to construct a discrete probability measure on $\mathcal{X}$ such that the push-forward of these two probability measures…
Auxiliary variable methods such as the Parallel Tempering and the cluster Monte Carlo methods generate samples that follow a target distribution by using proposal and auxiliary distributions. In sampling from complex distributions, these…
Cubature formulas, asymptotically optimal with respect to accuracy, are derived for calculating multidimensional weakly singular integrals. They are used for developing a universal code for calculating capacitances of conductors of…
In many financial applications Quasi Monte Carlo (QMC) based on Sobol low-discrepancy sequences (LDS) outperforms Monte Carlo showing faster and more stable convergence. However, unlike MC QMC lacks a practical error estimate. Randomized…
Monte Carlo (MC) integration has been employed as the standard approximation method for the Sliced Wasserstein (SW) distance, whose analytical expression involves an intractable expectation. However, MC integration is not optimal in terms…