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

A Faster Algorithm Enumerating Relevant Features over Finite Fields