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...Cluster trellis data structures algorithms for exact inference in hierarchical clustering craig s greenberg sebastian macaluso nicholas monath ji ah lee patrick flaherty kyle cranmer andrew mcgregor mccallum university of massachusetts amherst national institute standards and technology new york abstract is a fundamental task often used to discover meaningful due the combinatorial number figure schematic representation possible clusterings approximate h denotes x are typically dataset contrast existing methods we present novel natural generated by dynamic programming markov tree i e shaped model where state based on variables dependent only their parent or children structure prove wedene as recursive split that can exactly compute partition n ting elements xi into function maximum likelihood hierarchy marginal probabilities sub hierarchies subsets until reaching singletons this equivalently clusters our scale time be viewed starting with set space proportional powerset el repeatedly ta...