A new metric for probability distributions

By Dominik M. Endres, Johannes E. Schindelin. IEEE Transactions on Information Theory, 2003

1,244 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/475e0371a1b1c903eeff45c328d825f4537ab746

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Citations in the corpus

Aspect-Aware Latent Factor Model: Rating Prediction with Ratings and Reviews (2018, positive): “su,i,a ∈ [0,1] is then computed as : su,i,a = 1 − JSD (θu,a ,ψi,a ) (2) where JSD (θu,a ,ψi,a ) denotes the Jensen–Shannon divergence [13] between θu,a andψi,a .”
NetCoMi: network construction and comparison for microbiome data in R (2020, neutral): “The length of a path is the sum of edge weights, where the weight of an edge is a real non-negative number associated with this edge [78].”
Linear Algebra and its Applications (2010, neutral): “So we require The number of iterations k i , i = 1,2, is now chosen as follows.”
Geometry of Quantum States: Index (2007, background): “2 This was shown in 2003 by Endres and Schindelin [295], and the result is expected to generalise to the quantum case [175, 570].”
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 2 Applications and Future Perspectives (2017, background): “An alternative simple divergence is the symmetric Jensen-Shannon (JS) 69 divergence [Chan et al., 2004, Cichocki et al., 2011, Endres and Schindelin, 2003], given by DJS(p}q) = 1 2 KL(p}r) + 1 2 KL(q}r), (2.46) where KL(¨}¨) denotes the Kullback-Leibler divergence and r(x) = p(x)+q(x) 2 .”
Unsupervised learning of dynamical and molecular similarity using variance minimization (2017, background): “…1991] is a related symmetric formulation that utilizes M , the elementwise mean of P and Q , Since it has been shown that the square root of (4) obeys the triangle inequality [Endres and Schindelin, 2003], we can write the following distance metric, div √ JS ( P i || Q i ) ≡ div JS ( P i || Q i ) .”
Nonextensive Information Theoretic Kernels on Measures (2009, background): “It has been shown that √ JS satisfies the triangle inequality (hence being a metric) and that, moreover, it is a Hilbertian metric1 (Endres and Schindelin, 2003; Topsøe, 2000), which has motivated its use in kernel-based machine learning (Cuturi et al., 2005; Hein and Bousquet, 2005) (see Section…”
On integral probability metrics, φ-divergences and binary classification (2009, background): “wn to be metrics on P0, for example, the square root of variational distance, the square root of Hellinger’s distance, the square root of Jensen-Shannon divergence etc., are shown to be metrics on P0 [8, 11, 17]. Similarly, [23, Theorem 1] has shown that certain powers of Dφ is a metric on P0. So, o”
On Learning Invariant Representations for Domain Adaptation (2019, background): “Additionally, from the JS divergence, we can define a distance metric between two distributions as well, known as the JS distance (Endres & Schindelin, 2003): dJS(D,D′) := √ DJS(D || D′).”
Properties of Classical and Quantum Jensen-Shannon Divergence (2008, background): “We extend the results of Endres and Schindelin, concerning the metric property of JD, and those of Lamberti et al., concerning the metric property of QJD, as follows: • Denoting the set of probability distributions on a set X by M1+(X), we prove that for α ∈ (0, 2], the pair ( M1+(X), JD 1/2 α ) is ”
The dimensionality of discourse (2010, methodology): “Because this measure has been shown tomeet metric criteria (25, 26), it is more appropriate for the correlation dimension analysis than other measures of divergence that do not meet these criteria, such as the Kullback-Leibler divergence.”
On f-Divergences: Integral Representations, Local Behavior, and Inequalities (2018, background): “ical tools for maximizing or minimizing an f-divergence subject to a ﬁnite number of constraints on other f-divergences [31]; 5) Inequalities which rely on powers of f-divergences deﬁning a distance ([24], [36], [47], [71]); 6) Vajda and Pinsker-type inequalities for f-divergences ([12]–[15], [30], ”
Semigroup Kernels on Measures (2005, methodology): “Following (Rao, 1987) we consider the quantity J(f, f ′) = h( f + f ′ 2 )− h(f) + h(f ′) 2 , (2) known as the Jensen divergence (or Jensen-Shannon divergence) between f and f ′, which as noted by Fuglede and Topse (2004) can be seen as a symmetrized version of the KullbackLeibler (KL) divergence D, ”
Causal Intervention for Leveraging Popularity Bias in Recommendation (2021, methodology): “Then, we use the Jensen-Shannon Divergence (JSD) [15] to measure the similarity between two stages: where 𝑡 and 𝑠 are the two stages.”