On measures of dependence

By A. Rényi. 1959

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Citations in the corpus

Invariant Causal Prediction for Nonlinear Models (2017, background): “There has been some progress towards nonparametric independence tests (Bergsma and Dassios, 2014; Hoeffding, 1948; Blum et al., 1961; Rényi, 1959; Székely et al., 2007; Zhang et al., 2011).”
On Brownian Distance Covariance and High Dimensional Data (2009, neutral): “An important example is maximal correlation, characterized by Rényi [22].”
Rényi Fair Inference (2019, background): “Unlike HSIC and Pearson correlation, Rényi correlation captures higher-order dependencies between random variables. Rényi correlation between two random variables is zero if and only if the random variables are independent, and it is one if there is a strict dependence between the variables Rényi (1”
LEEP: A New Measure to Evaluate Transferability of Learned Representations (2020, background): “Although, like us, their transferability measure can be applied to general settings, their measure is hard to interpret since it involves solving a Hirschfeld-Gebelein-R ´ enyi maximum correlation problem (Hirschfeld, 1935; Gebelein, 1941; R´enyi, 1959).”
Gaussian Bounds for Noise Correlation of Functions (2007, background): “lated Spaces and Markov Operators Here we derive properties of correlated spaces and Markov operators that will be repeatedly used below. We start with the following which was already known to R´enyi [27]. Lemma 2.8 Let (Ω(1) × Ω(2),P) be two correlated spaces. Let f be a Ω(2) measurable function wi”
Distribution-Free Consistent Independence Tests via Center-Outward Ranks and Signs (2019, unknown): “The second track to characterize nonlinear, nonmonotone dependence is based on the maximal correlation introduced in Hirschfeld (1935) and Gebelein (1941), reformulated and examined by Rényi (1959a, 1959b).”
A Minimax Approach to Supervised Learning (2016, methodology): “e [13–15]. The HGR maximal correlation of two random variables X;Yis deﬁned as ˆ m(X;Y) = sup f;g ˆ(f(X);g(Y)); (13) where the supremum is taken over all functions f;gwith ﬁnite non-zero variance. In [15], it has been shown the maximal correlation satisﬁes several interesting properties. Here, we co”
A measure of mutual complete dependence (2010, methodology): “We refer to [4, 5, 9, 12, 18] and the references therein for an exhaustive list.”
A New Coefficient of Correlation (2019, background): “ons that are not monotonic, even in the complete absence of noise. There have been many proposals to address this deciency of the classical coecients [23], such as the maximal correlation coecient [5, 15, 21, 33], various coecients based on joint cumulative distribution functions and ranks [3, 4, 8,”
Random Fields Simplified: Preserving Marginal Distributions, Correlations, and Intermittency, With Applications From Rainfall to Humidity (2020, result): “Yet similar results were proven even earlier in the works of Maung (1941) and Gebelein (1941); the topic was also extensively studied by Rényi (1959).”
Predicting the effect of interventions using invariance principles for nonlinear models (2016, background): “There has been some progress towards nonparametric independence tests [1, 7, 2, 12, 14, 16].”
Detecting Novel Associations in Large Datasets (2011, methodology): “We compared MIC to a wide range of methods – including methods formulated around the axiomatic framework for measures of dependence developed by Rényi (8), other state-ofthe-art measures of dependence, and several nonparametric curve estimation techniques that can be used to score pairs of variables”
Multivariate Rank-Based Distribution-Free Nonparametric Testing Using Measure Transportation (2019, methodology): “[122] Rényi, A.”
Copula-Based Measures of Multivariate Association (2010, background): “The works by Rényi [86], Scarsini [91] as well as Schweizer and Wolff [99] introduce various axioms to characterize bivariate measures of association.”
A Robust-Equitable Measure for Feature Ranking and Selection (2017, background): “Rényi (1959) proposed seven axioms for dependence measures D[X;Y ].”