相关论文: A segment-wise dynamic programming algorithm for B…

We consider the directed minimum weight cycle problem in the fully dynamic setting. To the best of our knowledge, so far no fully dynamic algorithms have been designed specifically for the minimum weight cycle problem in general digraphs.…

Advanced algorithms are necessary to obtain faster-than-real-time dynamic simulations in a number of different physical problems that are characterized by widely disparate time scales. Recent advanced dynamic Monte Carlo algorithms that…

The availability of data sets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these data sets has proved difficult since available Markov chain…

In the near future, massively parallel computing systems will be necessary to solve computation intensive applications. The key bottleneck in massively parallel implementation of numerical algorithms is the synchronization of data across…

Quasi-Monte Carlo algorithms are studied for designing discrete approximations of two-stage linear stochastic programs. Their integrands are piecewise linear, but neither smooth nor lie in the function spaces considered for QMC error…

We study the approximation of expectations $\operatorname{E}(f(X))$ for solutions $X$ of stochastic differential equations and functionals $f$ on the path space by means of Monte Carlo algorithms that only use random bits instead of random…

Drori and Teboulle [4] conjectured that the minimax optimal constant stepsize for N steps of gradient descent is given by the stepsize that balances performance on Huber and quadratic objective functions. This was numerically supported by…

It is a well-known rule of thumb that approximations of stochastic partial differential equations have essentially twice the order of weak convergence compared to the corresponding order of strong convergence. This is already known for many…

Kinetic equations model distributions of particles in position-velocity phase space. Often, one is interested in studying the long-time behavior of particles in high-collisional regimes in which an approximate (advection)-diffusion model…

We consider the problem of finding a control policy for a Markov Decision Process (MDP) to maximize the probability of reaching some states while avoiding some other states. This problem is motivated by applications in robotics, where such…

We propose some numerical schemes for forward-backward stochastic differential equations (FBSDEs) based on a new fundamental concept of transposition solutions. These schemes exploit time-splitting methods for the variation of constants…

Applying standard Markov chain Monte Carlo (MCMC) algorithms to large data sets is computationally expensive. Both the calculation of the acceptance probability and the creation of informed proposals usually require an iteration through the…

In this paper we consider the parameter estimation problem associated to partially-observed time changed SDEs, with observations that are given at discrete times. In particular we consider both likelihood and Bayesian estimation. We develop…

The Multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty Quantification (UQ) in Partial Differential Equation (PDE) models, combining model computations at different levels…

Several attempts to dampen the curse of dimensionnality problem of the Dynamic Programming approach for solving multistage optimization problems have been investigated. One popular way to address this issue is the Stochastic Dual Dynamic…

Online learning algorithms require to often recompute least squares regression estimates of parameters. We study improving the computational complexity of such algorithms by using stochastic gradient descent (SGD) type schemes in place of…

In this paper, we study the single-source shortest-path (SSSP) problem with positive edge weights, which is a notoriously hard problem in the parallel context. In practice, the $\Delta$-stepping algorithm proposed by Meyer and Sanders has…

In this work, we study the approximation of expected values of functional quantities on the solution of a stochastic differential equation (SDE), where we replace the Monte Carlo estimation with the evaluation of a deep neural network. Once…

Approximate Bayesian computation methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper we discuss and apply an approximate Bayesian computation (ABC) method based on sequential Monte…

In this work we present a new simple but efficient scheme - Subsquares approach - for development of algorithms for enclosing the solution set of overdetermined interval linear systems. We are going to show two algorithms based on this…