Guided sampling with sparse observations and PDE residuals has recently been combined with neural operator priors to solve partial differential equations in function space, their natural setting. We pair such a prior with pseudo-bootstrap sequential Monte Carlo (pBS SMC), a guided sampling framework that accommodates proposals without tractable densities, and introduce a new proposal by adapting the DPM++ algorithm to the guidance setting. Across five benchmark PDE systems this proposal attains the best error--time trade-off at every step count tested, and wrapping it in pBS gives the lowest error on most inverse-problem settings, with the largest gains when few sampling steps are used.
Dynamical Measure Transport and Neural PDE Solvers for Sampling
California Institute of Technology（加州理工学院）；Zuse Institute Berlin（柏林祖斯研究所）；dida Datenschmiede GmbH（迪达数据 Schmiede 有限公司）；Simula Research Laboratory（西穆拉研究实验室）；University Hospital Freiburg（弗赖堡大学医院）；RWTH Aachen（亚琛工业大学）；NVIDIA（英伟达）
RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations
Department of Civil and Environmental Engineering, Hong Kong Polytechnic University（香港理工大学土木与环境工程系）；Department of Statistics and Data Science, Yale University（耶鲁大学统计与数据科学系）
Canadian University Dubai（迪拜加拿大大学）；Cairo University（开罗大学）
Imbalanced data is a frequently encountered problem in machine learning. Despite a vast amount of literature on sampling techniques for imbalanced data, there is a limited number of studies that address the issue of the optimal sampling ratio. In this paper, we attempt to fill the gap in the literature by conducting a large scale study of the effects of sampling ratio on classification accuracy. We consider 10 popular sampling methods and evaluate their performance over a range of ratios based on 20 datasets. The results of the numerical experiments suggest that the optimal sampling ratio is b…
The University of Tokyo（东京大学）；RIKEN AIP（理化学研究所先进智能项目中心）
We investigate finite stochastic partial monitoring, which is a general model for sequential learning with limited feedback. While Thompson sampling is one of the most promising algorithms on a variety of online decision-making problems, its properties for stochastic partial monitoring have not been theoretically investigated, and the existing algorithm relies on a heuristic approximation of the posterior distribution. To mitigate these problems, we present a novel Thompson-sampling-based algorithm, which enables us to exactly sample the target parameter from the posterior distribution. Beside…
ETH Zurich, Department of Computer Science（苏黎世联邦理工学院计算机科学系）；DeepMind；Google（谷歌）
Partial monitoring is a rich framework for sequential decision making under uncertainty that generalizes many well known bandit models, including linear, combinatorial and dueling bandits. We introduce information directed sampling (IDS) for stochastic partial monitoring with a linear reward and observation structure. IDS achieves adaptive worst-case regret rates that depend on precise observability conditions of the game. Moreover, we prove lower bounds that classify the minimax regret of all finite games into four possible regimes. IDS achieves the optimal rate in all cases up to logarithmic…
We consider the problem of deciding how best to target and prioritize existing vaccines that may offer protection against new variants of an infectious disease. Sequential experiments are a promising approach; however, challenges due to delayed feedback and the overall ebb and flow of disease prevalence make available methods inapplicable for this task. We present a method, partial likelihood Thompson sampling, that can handle these challenges. Our method involves running Thompson sampling with belief updates determined by partial likelihood each time we observe an event. To test our approach,…
DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models
Dept. of Comp. Sci. & Tech., Institute for AI, BNRist Center, THBI Lab（计算机科学与技术系，人工智能研究院，BNRist中心，THBI实验室）；Tsinghua-Bosch Joint ML Center, Tsinghua University, Beijing, 100084 China（清华大学-博世联合机器学习中心，清华大学，北京，100084中国）；Gaoling School of Artificial Intelligence, Renmin University of China（北京人工智能学院，中国人民大学）；Beijing Key Laboratory of Big Data Management and Analysis Methods, Beijing, China（北京大数据管理与分析方法重点实验室，北京，中国）
Posterior Sampling for Competitive RL: Function Approximation and Partial Observation
Hong Kong University of Science and Technology（香港科技大学）；New York University（纽约大学）；Peking University（北京大学）；Northwestern University（西北大学）；Yale University（耶鲁大学）
Solving partial differential equations in high dimensions by deep neural network has brought significant attentions in recent years. In many scenarios, the loss function is defined as an integral over a high-dimensional domain. Monte-Carlo method, together with the deep neural network, is used to overcome the curse of dimensionality, while classical methods fail. Often, a deep neural network outperforms classical numerical methods in terms of both accuracy and efficiency. In this paper, we propose to use quasi-Monte Carlo sampling, instead of Monte-Carlo method to approximate the loss function…
Partial Domain Adaptation via Importance Sampling-based Shift Correction
School of Mathematics, Sun Yat-Sen University（中山大学数学学院）；School of Statistics and Mathematics, Guangdong University of Finance and Economics（广东财经大学统计与数学学院）；Department of Electrical Engineering, City University of Hong Kong（香港城市大学电子工程系）
Information Technology University（信息技术大学）；J. Mack Robinson College of Business（J. Mack Robinson商学院）；Georgia State University（佐治亚州立大学）
Recently, there has been a lot of interest in using neural networks for solving partial differential equations. A number of neural network-based partial differential equation solvers have been formulated which provide performances equivalent, and in some cases even superior, to classical solvers. However, these neural solvers, in general, need to be retrained each time the initial conditions or the domain of the partial differential equation changes. In this work, we posit the problem of approximating the solution of a fixed partial differential equation for any arbitrary initial conditions as…
