Extensions to McDiarmid's inequality when dierences are bounded with high probability

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PAC-Bayesian Collective Stability (2014, methodology): “We can also recover (approximate) MAP inference by letting Ψ(s) , 0 and decoding the unary terms.”
Stability and Generalization in Structured Prediction (2016, result): “If the bad set BZ has measure D(BZ) ≤ ν, then (β,BZ)-local stability is similar to, though slightly weaker than, the strongly difference-bounded property proposed by Kutin (2002). If φ is strongly difference-bounded, then Equation 1 must hold for any z / ∈ BZ and z′ ∈ Zn (which could be in BZ).”
Improvability Through Semi-Supervised Learning: A Survey of Theoretical Results (2019, background): “The transductive bounds are an extension of the inductive bounds that use the notion of uniform stability (Bousquet and Elisseeff, 2002) and weak stability (Kutin and Niyogi, 2013; Kutin, 2002).”