Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimization of Akaike's Information Criterion in Linear Regression
  Analysis via Mixed Integer Nonlinear Program   Akaike's information criterion (AIC) is a measure of the quality of a
statistical model for a given set of data. We can determine the best
statistical model for a particular data set by the minimization of the AIC.
Since we need to evaluate exponentially many candidates of the model by the
minimization of the AIC, the minimization is unreasonable. Instead, stepwise
methods, which are local search algorithms, are commonly used to find a better
statistical model though it may not be the best.
  We propose a branch and bound search algorithm for a mixed integer nonlinear
programming formulation of the AIC minimization by Miyashiro and Takano (2015).
More concretely, we propose methods to find lower and upper bounds, and
branching rules for this minimization. We then combine them with SCIP, which is
a mathematical optimization software and a branch-and-bound framework. We show
that the proposed method can provide the best statistical model based on AIC
for small-sized or medium-sized benchmark data sets in UCI Machine Learning
Repository. Furthermore, we show that this method finds good quality solutions
for large-sized benchmark data sets.

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The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int