Energy statistics: A class of statistics based on distances

By G'abor J. Sz'ekely, Maria L. Rizzo. 2013

825 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics

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Citations in the corpus

NoPeek: Information leakage reduction to share activations in distributed deep learning (2020, methodology): “Our approach is based on minimizing a statistical dependency measure called distance correlation [10, 11, 12, 13, 14] between raw data and any intermediary communications across the clients or server participating in distributed deep learning.”
On the (Statistical) Detection of Adversarial Examples (2017, background): “This validates Hypothesis 1 from Section 3: adversarial examples exhibit statistical properties significantly different from legitimate data.”
Prototypal Analysis and Prototypal Regression (2017, neutral): “The energy distance DED (Székely and Rizzo, 2013; Rizzo and Székely, 2016): D2ED(µ1(·), µ2(·)) =2 ∫ X×X ‖x1 − x2‖ dµ1(x1)dµ2(x2)− ∫ X×X ‖x1 − x2‖ dµ1(x1)dµ1(x2) − ∫ X×X ‖x1 − x2‖ dµ2(x1)dµ2(x2) is proved in Klebanov (2002) to yield a metric, implying that the energy distance kernel induces an inje”
Distance covariance in metric spaces (2011, background): “See Székely and Rizzo (2013) for an invited review paper on statistics that are functions of distances between observations.”
A Probabilistic U-Net for Segmentation of Ambiguous Images (2018, methodology): “ only want to compare a deterministic prediction with a unique ground truth, but rather we are interested in comparing distributions of segmentations. To do so, we use the generalized energy distance [26,27,28], which leverages distances between observations: D2 GED (P gt;P out) = 2E h d(S;Y) i E h ”
Sphere Generative Adversarial Network Based on Geometric Moment Matching (2019, methodology): “The critic function was parameterized by neural networks, and then, the energy distance was maximized [30, 41].”
Partial Distance Correlation with Methods for Dissimilarities (2013, neutral): “For theory, background and further properties of the population and sample co-efﬁcients, see Székely et al. [34], Székely and Rizzo [30, 33] and Lyons [16] and the references therein.”
Multivariate Rank-Based Distribution-Free Nonparametric Testing Using Measure Transportation (2019, methodology): “, problem (II)) and propose a test for this goodness-of-fit using the rank energy statistic which is based on the usual energy statistic (as in [141], also see [8, 139] for definitions and motivation).”
Support points (2016, methodology): “1 of [68] (this is a duality result connecting the energy distance with c.”
Measuring Association on Topological Spaces Using Kernels and Geometric Graphs (2020, neutral): “[101] Székely, G.”
Multivariate quantile mapping bias correction: an N-dimensional probability density function transform for climate model simulations of multiple variables (2017, background): “(2011), Vrac and Friederichs (2015), Mehrotra and Sharma (2016), and Cannon (2016), MBCn is not restricted to correcting a specified measure of joint dependence, such as Pearson or Spearman rank correlation, nor does it make strong stationarity assumptions about climate model temporal sequencing.”
Trend-preserving bias adjustment and statistical downscaling with ISIMIP3BASD (v1.0) (2019, neutral): “Panel (b) shows the energy distance (Székely and Rizzo, 2013) between observation and simulation data over iterations for 30 random data samples (thin dashed lines) and on average over these 30 samples (thick solid lines).”
Multivariate nonparametric test of independence (2017, background): “More details on the properties of this distance correlation, the issue of testing independence of two random vectors, and uniqueness are discussed in [29, 30, 31].”