  Almost 10 years ago, Impagliazzo and Kabanets (2010) gave a new combinatorial
proof of Chernoff's bound for sums of bounded independent random variables.
Unlike previous methods, their proof is constructive. This means that it
provides an efficient randomized algorithm for the following task: given a set
of Boolean random variables whose sum is not concentrated around its
expectation, find a subset of statistically dependent variables. However, the
algorithm of Impagliazzo and Kabanets (2010) is given only for the Boolean
case. On the other hand, the general proof technique works also for real-valued
random variables, even though for this case, Impagliazzo and Kabanets (2010)
obtain a concentration bound that is slightly suboptimal.
  Herein, we revisit both these issues and show that it is relatively easy to
extend the Impagliazzo-Kabanets algorithm to real-valued random variables and
to improve the corresponding concentration bound by a constant factor.
