Related papers: Conditional Monte Carlo: A Change-of-Variables App…
In predictive modeling with simulation or machine learning, it is critical to accurately assess the quality of estimated values through output analysis. In recent decades output analysis has become enriched with methods that quantify the…
Interest is in evaluating, by Markov chain Monte Carlo (MCMC) simulation, the expected value of a function with respect to a, possibly unnormalized, probability distribution. A general purpose variance reduction technique for the MCMC…
In statistics and machine learning, approximation of an intractable integration is often achieved by using the unbiased Monte Carlo estimator, but the variances of the estimation are generally high in many applications. Control variates…
Sequence generation models are commonly refined with reinforcement learning over user-defined metrics. However, high gradient variance hinders the practical use of this method. To stabilize this method, we adapt to contextual generation of…
Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for defining distant proposals with high acceptance probabilities in a Metropolis-Hastings framework, enabling more efficient exploration of the state space than standard…
The multilevel Monte Carlo (MLMC) method has been used for a wide variety of stochastic applications. In this paper we consider its use in situations in which input random variables can be replaced by similar approximate random variables…
Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation.…
We study statistical model checking of continuous-time stochastic hybrid systems. The challenge in applying statistical model checking to these systems is that one cannot simulate such systems exactly. We employ the multilevel Monte Carlo…
A novel class of non-reversible Markov chain Monte Carlo schemes relying on continuous-time piecewise-deterministic Markov Processes has recently emerged. In these algorithms, the state of the Markov process evolves according to a…
We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the…
Many machine learning problems involve Monte Carlo gradient estimators. As a prominent example, we focus on Monte Carlo variational inference (MCVI) in this paper. The performance of MCVI crucially depends on the variance of its stochastic…
Sequential Monte Carlo (SMC) is a methodology for sampling approximately from a sequence of probability distributions of increasing dimension and estimating their normalizing constants. We propose here an alternative methodology named…
We introduce Multistage Conditional Compositional Optimization (MCCO) as a new paradigm for decision-making under uncertainty that combines aspects of multistage stochastic programming and conditional stochastic optimization. MCCO minimizes…
We present simple and practical strategies to reduce the variance of Monte Carlo estimators. Our focus is on variational Monte Carlo calculations of atomic forces and pressure in electronic systems, although we show that the underlying…
The theme of the present paper is numerical integration of $C^r$ functions using randomized methods. We consider variance reduction methods that consist in two steps. First the initial interval is partitioned into subintervals and the…
We introduce a new class of Monte Carlo based approximations of expectations of random variables such that their laws are only available via certain discretizations. Sampling from the discretized versions of these laws can typically…
A simple and stable method for computing accurate expectation values of observable with Variational Monte Carlo (VMC) or Diffusion Monte Carlo (DMC) algorithms is presented. The basic idea consists in replacing the usual ``bare'' estimator…
Reaction networks are often used to model interacting species in fields such as biochemistry and ecology. When the counts of the species are sufficiently large, the dynamics of their concentrations are typically modeled via a system of…
While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…
We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. This setting is ubiquitous…