Related papers: A Fast Monte Carlo algorithm for evaluating matrix…
Monte Carlo methods are widely used in particle physics to integrate and sample probability distributions (differential cross sections or decay rates) on multi-dimensional phase spaces. We present a Neural Network (NN) algorithm optimized…
Uncertainty estimation in deep models is essential in many real-world applications and has benefited from developments over the last several years. Recent evidence suggests that existing solutions dependent on simple Gaussian formulations…
Estimating failure probabilities of engineering systems is an important problem in many engineering fields. In this work we consider such problems where the failure probability is extremely small (e.g $\leq10^{-10}$). In this case, standard…
Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from…
Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical…
Probabilistic models are conceptually powerful tools for finding structure in data, but their practical effectiveness is often limited by our ability to perform inference in them. Exact inference is frequently intractable, so approximate…
A number of applications require the computation of the trace of a matrix that is implicitly available through a function. A common example of a function is the inverse of a large, sparse matrix, which is the focus of this paper. When the…
The standard kinetic Monte Carlo algorithm is an extremely efficient method to carry out serial simulations of dynamical processes such as thin-film growth. However, in some cases it is necessary to study systems over extended time and…
This paper addresses matrix approximation problems for matrices that are large, sparse and/or that are representations of large graphs. To tackle these problems, we consider algorithms that are based primarily on coarsening techniques,…
We propose a new framework for how to use sequential Monte Carlo (SMC) algorithms for inference in probabilistic graphical models (PGM). Via a sequential decomposition of the PGM we find a sequence of auxiliary distributions defined on a…
In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of…
The trace of a matrix function f(A), most notably of the matrix inverse, can be estimated stochastically using samples< x,f(A)x> if the components of the random vectors x obey an appropriate probability distribution. However such a…
To deal with very large datasets a mini-batch version of the Monte Carlo Markov Chain Stochastic Approximation Expectation-Maximization algorithm for general latent variable models is proposed. For exponential models the algorithm is shown…
Monte Carlo sampling is a powerful toolbox of algorithmic techniques widely used for a number of applications wherein some noisy quantity, or summary statistic thereof, is sought to be estimated. In this paper, we survey the literature for…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition…
We use a Monte Carlo method to assemble finite element matrices for polynomial Chaos approximations of elliptic equations with random coefficients. In this approach, all required expectations are approximated by a Monte Carlo method. The…
We introduce and analyze a parallel sequential Monte Carlo methodology for the numerical solution of optimization problems that involve the minimization of a cost function that consists of the sum of many individual components. The proposed…
We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…