Before revision:  For instance, Ban et . al.'s algorithm can only learn a mixture of O(\log n/\log \log n) strings with a subexponential number of queries, whereas we are able to learn a mixture of up to n^{o(1)} strings in subexponential queries\big(}\big)  and time.
After revision:  For instance, Ban et . al.'s algorithm can only learn a mixture of O(\log n/\log \log n) strings with a subexponential number of queries, whereas we are able to learn a mixture of up to n^{o(1)} strings in subexponential queries\big(n^{1/3 + o(1)}\big) and time.