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The radiative transfer equation models various physical processes ranging from plasma simulations to radiation therapy. In practice, these phenomena are often subject to uncertainties. Modeling and propagating these uncertainties requires…

Multitask learning is widely used in practice to train a low-resource target task by augmenting it with multiple related source tasks. Yet, naively combining all the source tasks with a target task does not always improve the prediction…

Control variates are variance reduction techniques for Monte Carlo estimators. They play a critical role in improving Monte Carlo estimators in scientific and machine learning applications that involve computationally expensive integrals.…

Atomistic simulations provide valuable insights into the physical processes governing material behavior. However, their applicability is fundamentally constrained by the limited time scales accessible to brute-force simulations. This…

Machine learning models are increasingly being utilized across various fields and tasks due to their outstanding performance and strong generalization capabilities. Nonetheless, their success hinges on the availability of large volumes of…

The performance of land surface models (LSMs) significantly affects the understanding of atmospheric and related processes. Many of the LSMs' soil and vegetation parameters were unknown so that it is crucially important to efficiently…

Being the most classical generative model for serial data, state-space models (SSM) are fundamental in AI and statistical machine learning. In SSM, any form of parameter learning or latent state inference typically involves the computation…

Sampling-based motion planning methods, while effective in high-dimensional spaces, often suffer from inefficiencies due to irregular sampling distributions, leading to suboptimal exploration of the configuration space. In this paper, we…

Traditionally, the field of computational Bayesian statistics has been divided into two main subfields: variational methods and Markov chain Monte Carlo (MCMC). In recent years, however, several methods have been proposed based on combining…

The Area under the ROC curve (AUC) is a well-known ranking metric for problems such as imbalanced learning and recommender systems. The vast majority of existing AUC-optimization-based machine learning methods only focus on binary-class…

Multi-agent reinforcement learning (MARL) algorithms have accomplished remarkable breakthroughs in solving large-scale decision-making tasks. Nonetheless, most existing MARL algorithms are model-free, limiting sample efficiency and…

Improving performance in multiple domains is a challenging task, and often requires significant amounts of data to train and test models. Active learning techniques provide a promising solution by enabling models to select the most…

The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…

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…

Active learning is a type of sequential design for supervised machine learning, in which the learning algorithm sequentially requests the labels of selected instances from a large pool of unlabeled data points. The objective is to produce a…

This paper proposes a new multilevel Monte Carlo (MLMC) method for the ergodic SDEs which do not satisfy the contractivity condition. By introducing the change of measure technique, we simulate the path with contractivity and add the…

Multiscale simulations utilizing high-fidelity, microscopic Monte Carlo models to provide the nonlinear response for continuum models can easily become computationally intractable. Surrogate models for the high-fidelity Monte Carlo models…

We present an adaptive multilevel Monte Carlo (AMLMC) algorithm for approximating deterministic, real-valued, bounded linear functionals that depend on the solution of a linear elliptic PDE with a lognormal diffusivity coefficient and…

This survey gives an overview of Monte Carlo methodologies using surrogate models, for dealing with densities which are intractable, costly, and/or noisy. This type of problem can be found in numerous real-world scenarios, including…

Model-based Reinforcement Learning (MBRL) allows data-efficient learning which is required in real world applications such as robotics. However, despite the impressive data-efficiency, MBRL does not achieve the final performance of…