Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Data Structures & Algorithms for Exact Inference in Hierarchical
  Clustering   Hierarchical clustering is a fundamental task often used to discover
meaningful structures in data, such as phylogenetic trees, taxonomies of
concepts, subtypes of cancer, and cascades of particle decays in particle
physics. Typically approximate algorithms are used for inference due to the
combinatorial number of possible hierarchical clusterings. In contrast to
existing methods, we present novel dynamic-programming algorithms for
\emph{exact} inference in hierarchical clustering based on a novel trellis data
structure, and we prove that we can exactly compute the partition function,
maximum likelihood hierarchy, and marginal probabilities of sub-hierarchies and
clusters. Our algorithms scale in time and space proportional to the powerset
of $N$ elements which is super-exponentially more efficient than explicitly
considering each of the (2N-3)!! possible hierarchies. Also, for larger
datasets where our exact algorithms become infeasible, we introduce an
approximate algorithm based on a sparse trellis that compares well to other
benchmarks. Exact methods are relevant to data analyses in particle physics and
for finding correlations among gene expression in cancer genomics, and we give
examples in both areas, where our algorithms outperform greedy and beam search
baselines. In addition, we consider Dasgupta's cost with synthetic data.

35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat