Related papers: A Discrepancy Bound for a Deterministic Acceptance…
Determinantal points processes are a promising but relatively under-developed tool in machine learning and statistical modelling, being the canonical statistical example of distributions with repulsion. While their mathematical formulation…
Hamiltonian Monte Carlo is a prominent Markov Chain Monte Carlo algorithm, which employs symplectic integrators to sample from high dimensional target distributions in many applications, such as statistical mechanics, Bayesian statistics…
One of the most demanding calculations is to generate random samples from a specified probability distribution (usually with an unknown normalizing prefactor) in a high-dimensional configuration space. One often has to resort to using a…
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…
A new method based on a Reverse Monte Carlo [RMC] technique and aimed at the inverse problem in the analysis of interstellar (intergalactic) absorption lines is presented. The line formation process in chaotic media with a finite…
Some recent work on confidence intervals for randomized quasi-Monte Carlo (RQMC) sampling found a surprising result: ordinary Student $t$ 95% confidence intervals based on a modest number of replicates were seen to be very effective and…
We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…
Estimating the density of a continuous random variable X has been studied extensively in statistics, in the setting where n independent observations of X are given a priori and one wishes to estimate the density from that. Popular methods…
We propose a Monte Carlo sampler from the reverse diffusion process. Unlike the practice of diffusion models, where the intermediary updates -- the score functions -- are learned with a neural network, we transform the score matching…
A resampling scheme provides a way to switch low-weight particles for sequential Monte Carlo with higher-weight particles representing the objective distribution. The less the variance of the weight distribution is, the more concentrated…
Monte Carlo methods are often necessary for the implementation of optimal Bayesian estimators. A fundamental technique that can be used to generate samples from virtually any target probability distribution is the so-called rejection…
Rejection sampling is a common tool for low dimensional problems ($d \leq 2$), often touted as an "easy" way to obtain valid samples from a distribution $f(\cdot)$ of interest. In practice it is non-trivial to apply, often requiring…
We present a sequential Monte Carlo sampler variant of the partial rejection control algorithm, and show that this variant can be considered as a sequential Monte Carlo sampler with a modified mutation kernel. We prove that the new sampler…
The standard Kernel Quadrature method for numerical integration with random point sets (also called Bayesian Monte Carlo) is known to converge in root mean square error at a rate determined by the ratio $s/d$, where $s$ and $d$ encode the…
By a profound result of Heinrich, Novak, Wasilkowski, and Wo{\'z}niakowski the inverse of the star-discrepancy $n^*(s,\ve)$ satisfies the upper bound $n^*(s,\ve) \leq c_{\mathrm{abs}} s \ve^{-2}$. This is equivalent to the fact that for any…
We consider an alternative to the Monte Carlo method for dust continuous radiative transfer simulations: the Quasi-Monte Carlo method. We briefly discuss what it is, its history, and possible implementations. We compare the Monte Carlo…
We study numerical integration over bounded regions in $\mathbb{R}^s, s\ge1$ with respect to some probability measure. We replace random sampling with quasi-Monte Carlo methods, where the underlying point set is derived from deterministic…
Training generative models to sample from unnormalized density functions is an important and challenging task in machine learning. Traditional training methods often rely on the reverse Kullback-Leibler (KL) divergence due to its…
Diffusion models accomplish remarkable success in data generation tasks across various domains. However, the iterative sampling process is computationally expensive. Consistency models are proposed to learn consistency functions to map from…
The efficiency of Hamiltonian Monte Carlo (HMC) can suffer when sampling a distribution with a wide range of length scales, because the small step sizes needed for stability in high-curvature regions are inefficient elsewhere. To address…