Related papers: Work-Efficient Parallel Counting via Sampling

Boson sampling has been theoretically proposed and experimentally demonstrated to show quantum computational advantages. However, it still lacks the deep understanding of the practical applications of boson sampling. Here we propose that…

Exploring the dependence between covariates across distributions is crucial for many applications. Copulas serve as a powerful tool for modeling joint variable dependencies and have been effectively applied in various practical contexts due…

In this paper, we explore how numerical calculations can be accelerated by implementing several numerical methods of fractional-order systems using parallel computing techniques. We investigate the feasibility of parallel computing…

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.…

The Hidden Markov Model (HMM) is a widely-used statistical model for handling sequential data. However, the presence of missing observations in real-world datasets often complicates the application of the model. The EM algorithm and Gibbs…

The approximate minimum degree algorithm is widely used before numerical factorization to reduce fill-in for sparse matrices. While considerable attention has been given to the numerical factorization process, less focus has been placed on…

Bayesian inference with stochastic models is often difficult because their likelihood functions involve high-dimensional integrals. Approximate Bayesian Computation (ABC) avoids evaluating the likelihood function and instead infers model…

In this paper we describe how MAP inference can be used to sample efficiently from Gibbs distributions. Specifically, we provide means for drawing either approximate or unbiased samples from Gibbs' distributions by introducing low…

Topic modeling is a very powerful technique in data analysis and data mining but it is generally slow. Many parallelization approaches have been proposed to speed up the learning process. However, they are usually not very efficient because…

This paper explores a surprising equivalence between two seemingly-distinct convex optimization methods. We show that simulated annealing, a well-studied random walk algorithms, is directly equivalent, in a certain sense, to the central…

We present a fast Gauss transform in one dimension using nearly optimal sum-of-exponentials approximations of the Gaussian kernel. For up to about ten-digit accuracy, the approximations are obtained via best rational approximations of the…

The Gibbs sampler (GS) is a crucial algorithm for approximating complex calculations, and it is justified by Markov chain theory, the alternating projection theorem, and $I$-projection, separately. We explore the equivalence between these…

With appropriately chosen sampling probabilities, sampling-based random projection can be used to implement large-scale statistical methods, substantially reducing computational cost while maintaining low statistical error. However,…

Bayesian estimation of Gaussian graphical models has proven to be challenging because the conjugate prior distribution on the Gaussian precision matrix, the G-Wishart distribution, has a doubly intractable partition function. Recent…

We analyze the computational efficiency of approximate Bayesian computation (ABC), which approximates a likelihood function by drawing pseudo-samples from the associated model. For the rejection sampling version of ABC, it is known that…

We study Bayesian estimation of mixture models and argue in favor of fitting the marginal posterior distribution over component assignments directly, rather than Gibbs sampling from the joint posterior on components and parameters as is…

Variational Bayesian inference and (collapsed) Gibbs sampling are the two important classes of inference algorithms for Bayesian networks. Both have their advantages and disadvantages: collapsed Gibbs sampling is unbiased but is also…

Asynchronous Bayesian optimization is a recently implemented technique that allows for parallel operation of experimental systems and disjointed workflows. Contrasting with serial Bayesian optimization which individually selects experiments…

Machine learning models, and deep neural networks in particular, are increasingly deployed in risk-sensitive domains such as healthcare, environmental forecasting, and finance, where reliable quantification of predictive uncertainty is…

Drawing independent samples from high-dimensional probability distributions represents the major computational bottleneck for modern algorithms, including powerful machine learning frameworks such as deep learning. The quest for discovering…