Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Almost Optimal Universal Lower Bound for Learning Causal DAGs with
  Atomic Interventions   A well-studied challenge that arises in the structure learning problem of
causal directed acyclic graphs (DAG) is that using observational data, one can
only learn the graph up to a "Markov equivalence class" (MEC). The remaining
undirected edges have to be oriented using interventions, which can be very
expensive to perform in applications. Thus, the problem of minimizing the
number of interventions needed to fully orient the MEC has received a lot of
recent attention, and is also the focus of this work. We prove two main
results. The first is a new universal lower bound on the number of atomic
interventions that any algorithm (whether active or passive) would need to
perform in order to orient a given MEC. Our second result shows that this bound
is, in fact, within a factor of two of the size of the smallest set of atomic
interventions that can orient the MEC. Our lower bound is provably better than
previously known lower bounds. The proof of our lower bound is based on the new
notion of clique-block shared-parents (CBSP) orderings, which are topological
orderings of DAGs without v-structures and satisfy certain special properties.
Further, using simulations on synthetic graphs and by giving examples of
special graph families, we show that our bound is often significantly better.

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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat