Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Learning and Testing Decision Tree   In this paper, we study learning and testing decision tree of size and depth
that are significantly smaller than the number of attributes $n$.
  Our main result addresses the problem of poly$(n,1/\epsilon)$ time algorithms
with poly$(s,1/\epsilon)$ query complexity (independent of $n$) that
distinguish between functions that are decision trees of size $s$ from
functions that are $\epsilon$-far from any decision tree of size
$\phi(s,1/\epsilon)$, for some function $\phi > s$. The best known result is
the recent one that follows from Blank, Lange and Tan,~\cite{BlancLT20}, that
gives $\phi(s,1/\epsilon)=2^{O((\log^3s)/\epsilon^3)}$. In this paper, we give
a new algorithm that achieves $\phi(s,1/\epsilon)=2^{O(\log^2 (s/\epsilon))}$.
  Moreover, we study the testability of depth-$d$ decision tree and give a {\it
distribution free} tester that distinguishes between depth-$d$ decision tree
and functions that are $\epsilon$-far from depth-$d^2$ decision tree. In
particular, for decision trees of size $s$, the above result holds in the
distribution-free model when the tree depth is $O(\log(s/\epsilon))$.
  We also give other new results in learning and testing of size-$s$ decision
trees and depth-$d$ decision trees that follow from results in the literature
and some results we prove in this paper.

26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
2
The categories of this paper are: math
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th