Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Model Assisted Variable Clustering: Minimax-optimal Recovery and
  Algorithms   Model-based clustering defines population level clusters relative to a model
that embeds notions of similarity. Algorithms tailored to such models yield
estimated clusters with a clear statistical interpretation. We take this view
here and introduce the class of G-block covariance models as a background model
for variable clustering. In such models, two variables in a cluster are deemed
similar if they have similar associations will all other variables. This can
arise, for instance, when groups of variables are noise corrupted versions of
the same latent factor. We quantify the difficulty of clustering data generated
from a G-block covariance model in terms of cluster proximity, measured with
respect to two related, but different, cluster separation metrics. We derive
minimax cluster separation thresholds, which are the metric values below which
no algorithm can recover the model-defined clusters exactly, and show that they
are different for the two metrics. We therefore develop two algorithms, COD and
PECOK, tailored to G-block covariance models, and study their
minimax-optimality with respect to each metric. Of independent interest is the
fact that the analysis of the PECOK algorithm, which is based on a corrected
convex relaxation of the popular K-means algorithm, provides the first
statistical analysis of such algorithms for variable clustering. Additionally,
we contrast our methods with another popular clustering method, spectral
clustering, specialized to variable clustering, and show that ensuring exact
cluster recovery via this method requires clusters to have a higher separation,
relative to the minimax threshold. Extensive simulation studies, as well as our
data analyses, confirm the applicability of our approach.

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The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat