Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A probabilistic and multi-objective analysis of lexicase selection and
  epsilon-lexicase selection   Lexicase selection is a parent selection method that considers training cases
individually, rather than in aggregate, when performing parent selection.
Whereas previous work has demonstrated the ability of lexicase selection to
solve difficult problems in program synthesis and symbolic regression, the
central goal of this paper is to develop the theoretical underpinnings that
explain its performance. To this end, we derive an analytical formula that
gives the expected probabilities of selection under lexicase selection, given a
population and its behavior. In addition, we expand upon the relation of
lexicase selection to many-objective optimization methods to describe the
behavior of lexicase selection, which is to select individuals on the
boundaries of Pareto fronts in high-dimensional space. We show analytically why
lexicase selection performs more poorly for certain sizes of population and
training cases, and show why it has been shown to perform more poorly in
continuous error spaces. To address this last concern, we propose new variants
of epsilon-lexicase selection, a method that modifies the pass condition in
lexicase selection to allow near-elite individuals to pass cases, thereby
improving selection performance with continuous errors. We show that
epsilon-lexicase outperforms several diversity-maintenance strategies on a
number of real-world and synthetic regression problems.

22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph