  We study a fundamental problem in Bayesian learning, where the goal is to
select a set of data sources with minimum cost while achieving a certain
learning performance based on the data streams provided by the selected data
sources. First, we show that the data source selection problem for Bayesian
learning is NP-hard. We then show that the data source selection problem can be
transformed into an instance of the submodular set covering problem studied in
the literature, and provide a standard greedy algorithm to solve the data
source selection problem with provable performance guarantees. Next, we propose
a fast greedy algorithm that improves the running times of the standard greedy
algorithm, while achieving performance guarantees that are comparable to those
of the standard greedy algorithm. The fast greedy algorithm can also be applied
to solve the general submodular set covering problem with performance
guarantees. Finally, we validate the theoretical results using numerical
examples, and show that the greedy algorithms work well in practice.
