Measures of Dependence

By Reza Modarres. 2011

Subfields: Statistics and Probability, Information Theory

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “More detailed accounts on this topic can be found in Schölkopf and Smola (2002), Berlinet and Thomas-Agnan (2004), and Hofmann et al.”
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; R´enyi, 1959; Sz´ekely et al., 2007; Zhang et al., 2011).”
CAM: Causal Additive Models, high-dimensional order search and penalized regression (2013, neutral): “The question of closedness of additive models has also been studied in [1], for example; see also [29].”
Testing conditional independence using maximal nonlinear conditional correlation (2010, background): “The above properties are adapted from some of the conditions for a good measure of association proposed by Rényi [9].”
Measuring Association on Topological Spaces Using Kernels and Geometric Graphs (2020, background): “, [81, 15, 86, 38, 103, 102, 41, 106, 47, 76, 82, 67, 53, 88, 61, 14, 10] and the references therein, however none of them satisfy (II).”
Copula Theory: An Introduction (2010, unknown): “See [165] for Rényi’s paper.”
Discussion of: Brownian distance covariance (2009, methodology): “…in a spline-based RKHS as a dependence measure, using projection on a finite basis to regularize: this dependence measure follows the suggestion of Rényi (1959), but with a more restrictive pair of function classes used to compute the correlation (rather than the set of all square integrable…”
From Dependence to Causation (2016, methodology): “1) imposed by Rényi’s axiomatic framework for measures of dependence (Rényi, 1959).”
Extra Samples can Reduce the Communication for Independence Testing (2018, unknown): “[18]) and defined as”
Non-interactive simulation of joint distributions: The Hirschfeld-Gebelein-Rényi maximal correlation and the hypercontractivity ribbon (2012, background): “Let ( x ) be an arbitrary probability distribution on .”
A consistent test of independence based on a sign covariance related to Kendall's tau (2010, unknown): “Alternatively, Rényi [19] proposed maximal correlation, defined as ρ+ = sup g,h ρ ( g(X),h(Y ) ) ,”
Rényi Fair Inference (2019, methodology): “In this paper, we suggest to use Hirschfeld-Gebelein-R ´ enyi correlation R ´ enyi (1959); Hirschfeld (1935); Gebelein (1941) as a dependence measure between random variables to impose fairness.”
Consistent Nonparametric Tests of Independence (2010, methodology): “…correlation between variables in a spline-based RKHS as a statistic for an independence test: this dependence measure follows the suggestion of Rényi (1959), but with a more restrictive pair of function classes used to compute the correlation (rather than the set of all square integrable…”
Kernel Methods in Computer Vision (2009, background): “g(y) are uncorrelated, where f and g range over all bounded continuous functions f : X → R and g : Y → R [Rényi, 1959].”
On the Direction of Discrimination: An Information-Theoretic Analysis of Disparate Impact in Machine Learning (2018, background): “, [25]) between X and Y given S = 0 is defined as”
Statistical Dependence: Beyond Pearson’s ρ (2018, methodology): “Rényi (1959) gave a characterization of attainability.”