  We consider the question of learning the natural parameters of a $k$
parameter minimal exponential family from i.i.d. samples in a computationally
and statistically efficient manner. We focus on the setting where the support
as well as the natural parameters are appropriately bounded. While the
traditional maximum likelihood estimator for this class of exponential family
is consistent, asymptotically normal, and asymptotically efficient, evaluating
it is computationally hard. In this work, we propose a computationally
efficient estimator that is consistent as well as asymptotically normal under
mild conditions. We provide finite sample guarantees to achieve an ($\ell_2$)
error of $\alpha$ in the parameter estimation with sample complexity
$O(\mathrm{poly}(k/\alpha))$ and computational complexity
${O}(\mathrm{poly}(k/\alpha))$. To establish these results, we show that, at
the population level, our method can be viewed as the maximum likelihood
estimation of a re-parameterized distribution belonging to the same class of
exponential family.
