  In recent years, there are many attempts to understand popular heuristics. An
example of such a heuristic algorithm is the ID3 algorithm for learning
decision trees. This algorithm is commonly used in practice, but there are very
few theoretical works studying its behavior. In this paper, we analyze the ID3
algorithm, when the target function is a $k$-Junta, a function that depends on
$k$ out of $n$ variables of the input. We prove that when $k = \log n$, the ID3
algorithm learns in polynomial time $k$-Juntas, in the smoothed analysis model
of Kalai & Teng. That is, we show a learnability result when the observed
distribution is a "noisy" variant of the original distribution.
