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This paper investigates the use of stratified sampling as a variance reduction technique for approximating integrals over large dimensional spaces. The accuracy of this method critically depends on the choice of the space partition, the…

Probability · Mathematics 2009-09-15 Pierre Etoré , Gersende Fort , Benjamin Jourdain , Eric Moulines

Loads represent a promising flexibility source to support the integration of renewable energy sources, as they may shift their energy consumption over time. By computing the aggregated flexibility of power and energy-constrained loads,…

Systems and Control · Electrical Eng. & Systems 2025-05-23 Julie Rousseau , Philipp Heer , Kristina Orehounig , Gabriela Hug

The concept of probabilistic values, such as Beta Shapley values and weighted Banzhaf values, has gained recent attention in applications like feature attribution and data valuation. However, exact computation of these values is often…

Machine Learning · Computer Science 2024-11-01 Weida Li , Yaoliang Yu

Collaborative machine learning enables multiple data owners to jointly train models for improved predictive performance. However, ensuring incentive compatibility and fair contribution-based rewards remains a critical challenge. Prior work…

Computer Science and Game Theory · Computer Science 2025-10-16 Björn Filter , Ralf Möller , Özgür Lütfü Özçep

Understanding the energy consumption patterns of different types of consumers is essential in any planning of energy distribution. However, obtaining consumption information for single individuals is often either not possible or too…

Applications · Statistics 2021-12-24 Amanda Lenzi , Camila P. E. de Souza , Ronaldo Dias , Nancy Garcia , Nancy E. Heckman

The Shapley value, and its broader family of semi-values, has received much attention in various attribution problems. A fundamental and long-standing challenge is their efficient approximation, since exact computation generally requires an…

Machine Learning · Computer Science 2026-04-10 Weida Li , Yaoliang Yu , Bryan Kian Hsiang Low

In order to foster renewable energy integration, improve power quality and reliability, and reduce hydrocarbon emissions, there is a strong need to deploy energy storage systems (ESSs), which can provide a control medium for peak hour…

Optimization and Control · Mathematics 2016-11-17 Islam Safak Bayram , Mohamed Abdallah , Ali Tajer , Khalid Qaraqe

Wireless networks are evolving from radio resource providers to complex systems that also involve computing, with the latter being distributed across edge and cloud facilities. Also, their optimization is shifting more and more from a…

Computer Science and Game Theory · Computer Science 2025-08-08 Mandar Datar , Mattia Merluzzi

In this paper, we propose a stratified sampling algorithm in which the random drawings made in the strata to compute the expectation of interest are also used to adaptively modify the proportion of further drawings in each stratum. These…

Methodology · Statistics 2007-12-04 Pierre Etore , Benjamin Jourdain

Shapley values have emerged as a widely accepted and trustworthy tool, grounded in theoretical axioms, for addressing challenges posed by black-box models like deep neural networks. However, computing Shapley values encounters exponential…

Machine Learning · Computer Science 2024-05-24 Borui Zhang , Baotong Tian , Wenzhao Zheng , Jie Zhou , Jiwen Lu

Energy forecasting has attracted enormous attention over the last few decades, with novel proposals related to the use of heterogeneous data sources, probabilistic forecasting, online learn-ing, etc. A key aspect that emerged is that…

Applications · Statistics 2022-04-05 Pierre Pinson , Liyang Han , Jalal Kazempour

Among the various market structures under peer-to-peer energy sharing, one model based on cooperative game theory provides clear incentives for prosumers to collaboratively schedule their energy resources. The computational complexity of…

Computational Engineering, Finance, and Science · Computer Science 2020-08-03 Liyang Han , Thomas Morstyn , Constance Crozier , Malcolm McCulloch

This paper considers the problem of shaping agent utility functions in a transactive energy system to ensure the optimal energy price at a competitive equilibrium is always socially acceptable, that is, below a prescribed threshold. Agents…

Systems and Control · Electrical Eng. & Systems 2021-09-28 Zeinab Salehi , Yijun Chen , Ian R. Petersen , Elizabeth L. Ratnam , Guodong Shi

Energy storage can play an important role in energy management of end users. To promote an efficient utilization of energy storage, we develop a novel business model to enable virtual storage sharing among a group of users. Specifically, a…

Systems and Control · Electrical Eng. & Systems 2021-12-16 Dongwei Zhao , Hao Wang , Jianwei Huang , Xiaojun Lin

The advent of intelligent agents who produce and consume energy by themselves has led the smart grid into the era of "prosumer", offering the energy system and customers a unique opportunity to revaluate/trade their spot energy via a…

Optimization and Control · Mathematics 2019-06-25 Yue Chen , Shengwei Mei , Wei Wei , Steven H. Low , Adam Wierman , Feng Liu

Simulating energy systems is vital for energy planning to understand the effects of fluctuating renewable energy sources and integration of multiple energy sectors. Capacity expansion is a powerful tool for energy analysts and consists of…

Systems and Control · Electrical Eng. & Systems 2020-12-21 Mette Gamst , Stefanie Buchholz , David Pisinger

Changes in input distribution can induce shifts in the average predictions of machine learning models. Such prediction shifts may impact downstream business outcomes (e.g. a bank's loan approval rate), so understanding their causes can be…

Machine Learning · Computer Science 2026-04-14 Tom Bewley , Salim I. Amoukou , Emanuele Albini , Saumitra Mishra , Manuela Veloso

Fair and dynamic energy allocation in community microgrids remains a critical challenge, particularly when serving socio-economically diverse participants. Static optimization and cost-sharing methods often fail to adapt to evolving…

Systems and Control · Electrical Eng. & Systems 2025-07-28 Abhijan Theja , Mayukha Pal

The value and copyright of training data are crucial in the artificial intelligence industry. Service platforms should protect data providers' legitimate rights and fairly reward them for their contributions. Shapley value, a potent tool…

Machine Learning · Computer Science 2025-11-21 Haifeng Sun , Yu Xiong , Runze Wu , Xinyu Cai , Changjie Fan , Lan Zhang , Xiang-Yang Li

In this paper we propose two novel coalitional game theory based optimization methods for minimizing the cost of electricity consumed by households from a smart community. Some households in the community may own renewable energy systems…

Optimization and Control · Mathematics 2017-05-12 Adriana Chis , Visa Koivunen
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