  We consider the problem of identifying the subset
$\mathcal{S}^{\gamma}_{\mathcal{P}}$ of elements in the support of an
underlying distribution $\mathcal{P}$ whose probability value is larger than a
given threshold $\gamma$, by actively querying an oracle to gain information
about a sequence $X_1, X_2, \ldots$ of $i.i.d.$ samples drawn from
$\mathcal{P}$. We consider two query models: $(a)$ each query is an index $i$
and the oracle return the value $X_i$ and $(b)$ each query is a pair $(i,j)$
and the oracle gives a binary answer confirming if $X_i = X_j$ or not. For each
of these query models, we design sequential estimation algorithms which at each
round, either decide what query to send to the oracle depending on the entire
history of responses or decide to stop and output an estimate of
$\mathcal{S}^{\gamma}_{\mathcal{P}}$, which is required to be correct with some
pre-specified large probability. We provide upper bounds on the query
complexity of the algorithms for any distribution $\mathcal{P}$ and also derive
lower bounds on the optimal query complexity under the two query models. We
also consider noisy versions of the two query models and propose robust
estimators which can effectively counter the noise in the oracle responses.
