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Across various sectors such as healthcare, criminal justice, national security, finance, and technology, large-scale machine learning (ML) and artificial intelligence (AI) systems are being deployed to make critical data-driven decisions.…

Machine Learning · Statistics 2023-10-09 Camille Olivia Little , Debolina Halder Lina , Genevera I. Allen

Given a model $f$ that predicts a target $y$ from a vector of input features $\pmb{x} = x_1, x_2, \ldots, x_M$, we seek to measure the importance of each feature with respect to the model's ability to make a good prediction. To this end, we…

Machine Learning · Computer Science 2019-10-03 Luke Merrick

Shapley values, a game theoretic concept, has been one of the most popular tools for explaining Machine Learning (ML) models in recent years. Unfortunately, the two most common approaches, conditional and marginal, to calculating Shapley…

Computer Science and Game Theory · Computer Science 2024-09-11 Ilya Rozenfeld

Shapley values are one of the main tools used to explain predictions of tree ensemble models. The main alternative to Shapley values are Banzhaf values that have not been understood equally well. In this paper we make a step towards filling…

Machine Learning · Computer Science 2021-08-10 Adam Karczmarz , Anish Mukherjee , Piotr Sankowski , Piotr Wygocki

Healthy urban forests comprising of diverse trees and shrubs play a crucial role in mitigating climate change. They provide several key advantages such as providing shade for energy conservation, and intercepting rainfall to reduce flood…

Computer Vision and Pattern Recognition · Computer Science 2025-04-22 Akshit Gupta , Remko Uijlenhoet

Entropy measures of probability distributions are widely used measures in ecology, biology, genetics, and in other fields, to quantify species diversity of a community. Unfortunately, entropy-based diversity indices, or diversity indices…

Populations and Evolution · Quantitative Biology 2014-08-14 Karim T. Abou-Moustafa

Motivated by the problem of utility allocation in a portfolio under a Markowitz mean-variance choice paradigm, we propose an allocation criterion for the variance of the sum of $n$ possibly dependent random variables. This criterion, the…

Probability · Mathematics 2017-04-04 Riccardo Colini-Baldeschi , Marco Scarsini , Stefano Vaccari

In anomaly detection, the degree of irregularity is often summarized as a real-valued anomaly score. We address the problem of attributing such anomaly scores to input features for interpreting the results of anomaly detection. We…

Machine Learning · Computer Science 2023-07-24 Naoya Takeishi , Yoshinobu Kawahara

Efforts are needed to identify and measure both communities' exposure to climate hazards and the social vulnerabilities that interact with these hazards, but the science of validating hazard vulnerability indicators is still in its infancy.…

Econometrics · Economics 2024-11-19 Lidia Cano Pecharroman , Melissa O. Tier , Elke U. Weber

Random forests are a statistical learning method widely used in many areas of scientific research because of its ability to learn complex relationships between input and output variables and also its capacity to handle high-dimensional…

Machine Learning · Statistics 2024-02-19 Louis Capitaine , Jérémie Bigot , Rodolphe Thiébaut , Robin Genuer

This paper is about variable selection with the random forests algorithm in presence of correlated predictors. In high-dimensional regression or classification frameworks, variable selection is a difficult task, that becomes even more…

Methodology · Statistics 2016-04-19 Baptiste Gregorutti , Bertrand Michel , Philippe Saint-Pierre

Many existing approaches for estimating feature importance are problematic because they ignore or hide dependencies among features. A causal graph, which encodes the relationships among input variables, can aid in assigning feature…

Machine Learning · Computer Science 2021-03-01 Jiaxuan Wang , Jenna Wiens , Scott Lundberg

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

Random forests are popular methods for regression and classification analysis, and many different variants have been proposed in recent years. One interesting example is the Mondrian random forest, in which the underlying constituent trees…

Statistics Theory · Mathematics 2025-11-10 Matias D. Cattaneo , Jason M. Klusowski , William G. Underwood

Decision trees and their ensembles are endowed with a rich set of diagnostic tools for ranking and screening variables in a predictive model. Despite the widespread use of tree based variable importance measures, pinning down their…

Machine Learning · Statistics 2020-12-14 Jason M. Klusowski , Peter M. Tian

Random forest is a classification algorithm well suited for microarray data: it shows excellent performance even when most predictive variables are noise, can be used when the number of variables is much larger than the number of…

Quantitative Methods · Quantitative Biology 2007-05-23 Ramon Diaz-Uriarte , Sara Alvarez de Andres

Explaining AI systems is fundamental both to the development of high performing models and to the trust placed in them by their users. The Shapley framework for explainability has strength in its general applicability combined with its…

Machine Learning · Statistics 2021-12-21 Christopher Frye , Colin Rowat , Ilya Feige

Throughout the last decade, random forests have established themselves as among the most accurate and popular supervised learning methods. While their black-box nature has made their mathematical analysis difficult, recent work has…

Methodology · Statistics 2019-12-10 Tim Coleman , Wei Peng , Lucas Mentch

Importance sampling is a popular method for efficient computation of various properties of a distribution such as probabilities, expectations, quantiles etc. The output of an importance sampling algorithm can be represented as a weighted…

Probability · Mathematics 2016-04-18 Henrik Hult , Pierre Nyquist

Random Forests have become a widely used tool in machine learning since their introduction in 2001, known for their strong performance in classification and regression tasks. One key feature of Random Forests is the Random Forest…

Statistics Theory · Mathematics 2025-12-18 Nico Föge , Lena Schmid , Marc Ditzhaus , Markus Pauly