Related papers: Parallelization of adaptive MC Integrators
Adaptive Markov chain Monte Carlo (MCMC) algorithms, which automatically tune their parameters based on past samples, have proved extremely useful in practice. The self-tuning mechanism makes them `non-Markovian', which means that their…
In this paper, the minimization of computational cost on evaluating multi-dimensional integrals is explored. More specifically, a method based on an adaptive scheme for error variance selection in Monte Carlo integration (MCI) is presented.…
Importance sampling (IS) is commonly used for cross validation (CV) in Bayesian models, because it only involves reweighting existing posterior draws without needing to re-estimate the model by re-running Markov chain Monte Carlo (MCMC).…
We introduce Markov chain Monte Carlo (MCMC) algorithms based on numerical approximations of piecewise-deterministic Markov processes obtained with the framework of splitting schemes. We present unadjusted as well as adjusted algorithms,…
Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different…
Monte Carlo sampling methods often suffer from long correlation times. Consequently, these methods must be run for many steps to generate an independent sample. In this paper a method is proposed to overcome this difficulty. The method…
Many problems in the physical sciences, machine learning, and statistical inference necessitate sampling from a high-dimensional, multi-modal probability distribution. Markov Chain Monte Carlo (MCMC) algorithms, the ubiquitous tool for this…
The efficient evaluation of high-dimensional integrals is of importance in both theoretical and practical fields of science, such as data science, statistical physics, and machine learning. However, exact computation methods suffer from the…
We present a new adaptive Monte Carlo integration algorithm for ill-behaved integrands with non-factorizable singularities. The algorithm combines Vegas with multi channel sampling and performs significantly better than Vegas for a large…
Prior work on Automatically Scalable Computation (ASC) suggests that it is possible to parallelize sequential computation by building a model of whole-program execution, using that model to predict future computations, and then…
In this paper we introduce a new algorithm for American Monte Carlo that can be used either for American-style options, callable structured products or for computing counterparty credit risk (e.g. CVA or PFE computation). Leveraging least…
Recently developed adaptive Markov chain Monte Carlo (MCMC) methods have been applied successfully to many problems in Bayesian statistics. Grapham is a new open source implementation covering several such methods, with emphasis on…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…
We consider the problem of estimating the probability of a large loss from a financial portfolio, where the future loss is expressed as a conditional expectation. Since the conditional expectation is intractable in most cases, one may…
We consider the problem of adaptive stratified sampling for Monte Carlo integration of a differentiable function given a finite number of evaluations to the function. We construct a sampling scheme that samples more often in regions where…
We present a case-study on the utility of graphics cards to perform massively parallel simulation of advanced Monte Carlo methods. Graphics cards, containing multiple Graphics Processing Units (GPUs), are self-contained parallel…
We propose a variant of the Simulated Annealing method for optimization in the multivariate analysis of differentiable functions. The method uses global actualizations via the Hybrid Monte Carlo algorithm in their generalized version for…
Training Gaussian process-based models typically involves an $ O(N^3)$ computational bottleneck due to inverting the covariance matrix. Popular methods for overcoming this matrix inversion problem cannot adequately model all types of latent…
Markov chain Monte Carlo (MCMC) methods are ubiquitous tools for simulation-based inference in many fields but designing and identifying good MCMC samplers is still an open question. This paper introduces a novel MCMC algorithm, namely,…