Related papers: Bias-Variance Tradeoffs: Novel Applications
Conditional Monte Carlo or pre-integration is a powerful tool for reducing variance and improving the regularity of integrands when using Monte Carlo and quasi-Monte Carlo (QMC) methods. To select the variable to pre-integrate, one must…
The ability of widely used sampling methods, such as molecular dynamics or Monte Carlo, to explore complex free energy landscapes is severely hampered by the presence of kinetic bottlenecks. A large number of solutions have been proposed to…
In this paper, we propose a predictor-corrector type Consensus Based Optimization (CBO) algorithm on a convex feasible set. Our proposed algorithm generalizes the CBO algorithm in [11] to tackle a constrained optimization problem for the…
The Multilevel Monte Carlo (MLMC) approach usually works well when estimating the expected value of a quantity which is a Lipschitz function of intermediate quantities, but if it is a discontinuous function it can lead to a much slower…
This book aims to provide a graduate-level introduction to advanced topics in Markov chain Monte Carlo (MCMC) algorithms, as applied broadly in the Bayesian computational context. Most, if not all of these topics (stochastic gradient MCMC,…
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…
Monte Carlo and Quasi-Monte Carlo methods present a convenient approach for approximating the expected value of a random variable. Algorithms exist to adaptively sample the random variable until a user defined absolute error tolerance is…
Combinatorial Optimization (CO) has been a long-standing challenging research topic featured by its NP-hard nature. Traditionally such problems are approximately solved with heuristic algorithms which are usually fast but may sacrifice the…
The bias-variance decomposition is a central result in statistics and machine learning, but is typically presented only for the squared error. We present a generalization of the bias-variance decomposition where the prediction error is a…
In decision-making problems, the outcome of an intervention often depends on the causal relationships between system components and is highly costly to evaluate. In such settings, causal Bayesian optimization (CBO) can exploit the causal…
A statistical learning approach for parametric PDEs related to Uncertainty Quantification is derived. The method is based on the minimization of an empirical risk on a selected model class and it is shown to be applicable to a broad range…
We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…
Adjustable hyperparameters of machine learning models typically impact various key trade-offs such as accuracy, fairness, robustness, or inference cost. Our goal in this paper is to find a configuration that adheres to user-specified limits…
We use a variational Monte Carlo algorithm to solve the electronic structure of two-dimensional semiconductor quantum dots in external magnetic field. We present accurate many-body wave functions for the system in various magnetic field…
This paper explores the versatility and depth of Bayesian modeling by presenting a comprehensive range of applications and methods, combining Markov chain Monte Carlo (MCMC) techniques and variational approximations. Covering topics such as…
This paper extends the Multilevel Monte Carlo variance reduction technique to nonlinear filtering. In particular, Multilevel Monte Carlo is applied to a certain variant of the particle filter, the Ensemble Transform Particle Filter. A key…
Many popular statistical models for complex phenomena are intractable, in the sense that the likelihood function cannot easily be evaluated. Bayesian estimation in this setting remains challenging, with a lack of computational methodology…
When dealing with difficult inverse problems such as inverse rendering, using Monte Carlo estimated gradients to optimise parameters can slow down convergence due to variance. Averaging many gradient samples in each iteration reduces this…
Monte Carlo estimation in plays a crucial role in stochastic reaction networks. However, reducing the statistical uncertainty of the corresponding estimators requires sampling a large number of trajectories. We propose control variates…
We introduce a new algorithm for approximate inference that combines reparametrization, Markov chain Monte Carlo and variational methods. We construct a very flexible implicit variational distribution synthesized by an arbitrary Markov…