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This paper derives analytic expressions for the expected value of sample information (EVSI), the expected value of distribution information (EVDI), and the optimal sample size when data consists of independent draws from a bounded sequence…

Methodology · Statistics 2024-03-13 Adam Fleischhacker , Pak-Wing Fok , Mokshay Madiman , Nan Wu

We consider the problem of choosing the best of $n$ samples, out of a large random pool, when the sampling of each member is associated with a certain cost. The quality (worth) of the best sample clearly increases with $n$, but so do the…

Statistics Theory · Mathematics 2015-06-16 Joseph D. Skufca , Daniel ben-Avraham

While Shapley Values (SV) are one of the gold standard for interpreting machine learning models, we show that they are still poorly understood, in particular in the presence of categorical variables or of variables of low importance. For…

Machine Learning · Statistics 2022-04-07 Salim I. Amoukou , Nicolas J-B. Brunel , Tangi Salaün

We consider the problem of payoff division in indivisible coalitional games, where the value of the grand coalition is a natural number. This number represents a certain quantity of indivisible objects, such as parliamentary seats, kidney…

Computer Science and Game Theory · Computer Science 2026-04-02 Mikołaj Czarnecki , Michał Korniak , Oskar Skibski , Piotr Skowron

Collaborative causal inference (CCI) is a federated learning method for pooling data from multiple, often self-interested, parties, to achieve a common learning goal over causal structures, e.g. estimation and optimization of treatment…

Machine Learning · Computer Science 2024-07-17 Björn Filter , Ralf Möller , Özgür Lütfü Özçep

In recent years, an increasing amount of data is collected in different and often, not cooperative, databases. The problem of privacy-preserving, distributed calculations over separated databases and, a relative to it, issue of private data…

Databases · Computer Science 2016-05-23 Philip Derbeko , Shlomi Dolev , Ehud Gudes , Jeffrey D. Ullman

Estimating feature importance is a significant aspect of explaining data-based models. Besides explaining the model itself, an equally relevant question is which features are important in the underlying data generating process. We present a…

Machine Learning · Computer Science 2021-09-21 Pål Vegard Johnsen , Inga Strümke , Signe Riemer-Sørensen , Andrew Thomas DeWan , Mette Langaas

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

Feature selection is one of the most relevant processes in any methodology for creating a statistical learning model. Usually, existing algorithms establish some criterion to select the most influential variables, discarding those that do…

Machine Learning · Statistics 2024-05-10 Carlos Sebastián , Carlos E. González-Guillén

Shapley values are widely recognized as a principled method for attributing importance to input features in machine learning. However, the exact computation of Shapley values scales exponentially with the number of features, severely…

Machine Learning · Computer Science 2025-08-21 Majid Mohammadi , Krikamol Muandet , Ilaria Tiddi , Annette Ten Teije , Siu Lun Chau

When dealing with datasets containing a billion instances or with simulations that require a supercomputer to execute, computational resources become part of the equation. We can improve the efficiency of learning and inference by…

Machine Learning · Computer Science 2014-03-06 Max Welling

Data valuation seeks to answer the important question, "How much is this data worth?" Existing data valuation methods have largely focused on discriminative models, primarily examining data value through the lens of its utility in training.…

Machine Learning · Computer Science 2024-10-17 Mohamad Rida Rammal , Ruida Zhou , Suhas Diggavi

We study instancewise feature importance scoring as a method for model interpretation. Any such method yields, for each predicted instance, a vector of importance scores associated with the feature vector. Methods based on the Shapley score…

Machine Learning · Computer Science 2018-08-09 Jianbo Chen , Le Song , Martin J. Wainwright , Michael I. Jordan

In this paper, we develop a computational approach for estimating the mean value of a quantity in the presence of uncertainty. We demonstrate that, under some mild assumptions, the upper and lower bounds of the mean value are efficiently…

Statistics Theory · Mathematics 2013-11-05 Xinjia Chen

We consider the problem of testing whether two samples of contaminated data, possibly paired, are from the same distribution. Is is assumed that the contaminations are additive noises with known moments of all orders. The test statistic is…

Statistics Theory · Mathematics 2011-05-11 Denys Pommeret

Despite their ubiquitous use, Shapley value feature attributions can be misleading due to feature interaction in both model and data. We propose an alternative attribution approach, Shapley Sets, which awards value to sets of features.…

Machine Learning · Computer Science 2023-07-06 Torty Sivill , Peter Flach

We introduce a variable importance measure to quantify the impact of individual input variables to a black box function. Our measure is based on the Shapley value from cooperative game theory. Many measures of variable importance operate by…

Machine Learning · Computer Science 2020-10-05 Masayoshi Mase , Art B. Owen , Benjamin Seiler

In clinical prediction settings the importance of a high-dimensional feature like genomics is often assessed by evaluating the change in predictive performance when adding it to a set of traditional clinical variables. This approach is…

Machine Learning · Statistics 2026-03-06 Mark A. van de Wiel , Jeroen Goedhart , Martin Jullum , Kjersti Aas

The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is discussed. A wide set of measurable quantities ("invariant moments") whose expectation value…

Data Analysis, Statistics and Probability · Physics 2015-06-15 Paolo Rossi

Identifying strategies to more broadly distribute the economic winnings of AI technologies is a growing priority in HCI and other fields. One idea gaining prominence centers on "data dividends", or sharing the profits of AI technologies…

Computers and Society · Computer Science 2019-12-03 Nicholas Vincent , Yichun Li , Renee Zha , Brent Hecht