  We consider the problem of enumerating relevant features hidden in other
irrelevant information for multi-labeled data, which is formalized as learning
juntas.
  A $k$-junta function is a function which depends on only $k$ coordinates of
the input. For relatively small $k$ w.r.t. the input size $n$, learning
$k$-junta functions is one of fundamental problems both theoretically and
practically in machine learning. For the last two decades, much effort has been
made to design efficient learning algorithms for Boolean junta functions, and
some novel techniques have been developed. However, in real world,
multi-labeled data seem to be obtained in much more often than binary-labeled
one. Thus, it is a natural question whether these techniques can be applied to
more general cases about the alphabet size.
  In this paper, we expand the Fourier detection techniques for the binary
alphabet to any finite field $\mathbb{F}_q$, and give, roughly speaking, an
$O(n^{0.8k})$-time learning algorithm for $k$-juntas over $\mathbb{F}_q$. Note
that our algorithm is the first non-trivial (i.e., non-brute force) algorithm
for such a class even in the case where $q=3$ and we give an affirmative answer
to the question posed by Mossel et al.
  Our algorithm consists of two reductions: (1) from learning juntas to LDME
which is a variant of the learning with errors (LWE) problems introduced by
Regev, and (2) from LDME to the light bulb problem (LBP) introduced by
L.Valiant. Since the reduced problem (i.e., LBP) is a kind of binary problem
regardless of the alphabet size of the original problem (i.e., learning
juntas), we can directly apply the techniques for the binary case in the
previous work.
