A new class of metric divergences on probability spaces and its applicability in statistics

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On integral probability metrics, φ-divergences and binary classification (2009, unknown): “is Bπ = π ∧ (1 − π). The statistical information, Iπ(P,Q) in the model {(M,A),(P,Q),π} is deﬁned as the diﬀerence between the a priori and a posteriori Bayes loss given by Iπ(P,Q) = Bπ −Bπ(P,Q). (21) [23] showed that for P,Q ∈ P0, Iπ(P,Q) is the φ-divergence between P and Q for φ = φπ := π ∧(1−π)− π”
Practical and Consistent Estimation of f-Divergences (2019, background): “Of them, possibly the least well-known in the machine learning literature are f -divergences [32].”
On Divergences and Informations in Statistics and Information Theory (2006, methodology): “The Arimoto divergences were introduced for all by Österreicher and Vajda [42] who proved the triangle inequality (64) for all and found also the metric properties of these divergences for .”
Divergence for s-concave and log concave functions (2013, background): “Such divergences and their related inequalities are important tools in information theory, statistics, probability theory and machine learning [8, 13, 18, 24, 32, 33, 53, 55, 71].”