Related papers: Scalable Importance Sampling in High Dimensions wi…
The Effective Sample Size (ESS) is an important measure of efficiency of Monte Carlo methods such as Markov Chain Monte Carlo (MCMC) and Importance Sampling (IS) techniques. In the IS context, an approximation $\widehat{ESS}$ of the…
Importance sampling with data-driven proposal distributions is widely used in practice. A common workflow first generates an auxiliary sample of size $N$ from an approximation of the target distribution, constructs a density estimate $\hat…
This work introduces a novel framework for precisely and efficiently estimating rare event probabilities in complex, high-dimensional non-Gaussian spaces, building on our foundational Approximate Sampling Target with Post-processing…
Monte Carlo integration is a commonly used technique to compute intractable integrals and is typically thought to perform poorly for very high-dimensional integrals. To show that this is not always the case, we examine Monte Carlo…
Principal component analysis (PCA) is perhaps the most widely used method for data dimensionality reduction. A key question in PCA is deciding how many factors to retain. This manuscript describes a new approach to automatically selecting…
Importance sampling (IS) is a Monte Carlo technique that relies on weighted samples, simulated from a proposal distribution, to estimate intractable integrals. The quality of the estimators improves with the number of samples. However, for…
Importance sampling has become an important tool for the computation of tail-based risk measures. Since such quantities are often determined mainly by rare events standard Monte Carlo can be inefficient and importance sampling provides a…
Monte Carlo methods can provide accurate p-value estimates of word counting test statistics and are easy to implement. They are especially attractive when an asymptotic theory is absent or when either the search sequence or the word pattern…
High-dimensional count data poses significant challenges for statistical analysis, necessitating effective methods that also preserve explainability. We focus on a low rank constrained variant of the Poisson log-normal model, which relates…
The preferential sampling of locations chosen to observe a spatio-temporal process has been identified as a major problem across multiple fields. Predictions of the process can be severely biased when standard statistical methodologies are…
The probability of rare and extreme events is an important quantity for design purposes. However, computing the probability of rare events can be expensive because only a few events, if any, can be observed. To this end, it is necessary to…
Hamiltonian Monte Carlo (HMC) is a Markov chain algorithm for sampling from a high-dimensional distribution with density $e^{-f(x)}$, given access to the gradient of $f$. A particular case of interest is that of a $d$-dimensional Gaussian…
We discuss estimating the probability that the sum of nonnegative independent and identically distributed random variables falls below a given threshold, i.e., $\mathbb{P}(\sum_{i=1}^{N}{X_i} \leq \gamma)$, via importance sampling (IS). We…
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…
A method based on multicanonical Monte Carlo is applied to the calculation of large deviations in the largest eigenvalue of random matrices. The method is successfully tested with the Gaussian orthogonal ensemble (GOE), sparse random…
We describe an adaptive importance sampling algorithm for rare events that is based on a dual stochastic control formulation of a path sampling problem. Specifically, we focus on path functionals that have the form of cumulate generating…
In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…
This work presents a novel gradient-free importance sampling-based framework for precisely and efficiently estimating rare event probabilities, often encountered in reliability analyses of engineering systems. The approach is formulated…
The scalability of statistical estimators is of increasing importance in modern applications. One approach to implementing scalable algorithms is to compress data into a low dimensional latent space using dimension reduction methods. In…
Simulated tempering (ST) is an established Markov chain Monte Carlo (MCMC) method for sampling from a multimodal density $\pi(\theta)$. Typically, ST involves introducing an auxiliary variable $k$ taking values in a finite subset of $[0,1]$…