  We show that the class of strongly connected graphical models with treewidth
at most k can be properly efficiently PAC-learnt with respect to the
Kullback-Leibler Divergence. Previous approaches to this problem, such as those
of Chow ([1]), and Ho gen ([7]) have shown that this class is PAC-learnable by
reducing it to a combinatorial optimization problem. However, for k > 1, this
problem is NP-complete ([15]), and so unless P=NP, these approaches will take
exponential amounts of time. Our approach differs significantly from these, in
that it first attempts to find approximate conditional independencies by
solving (polynomially many) submodular optimization problems, and then using a
dynamic programming formulation to combine the approximate conditional
independence information to derive a graphical model with underlying graph of
the tree-width specified. This gives us an efficient (polynomial time in the
number of random variables) PAC-learning algorithm which requires only
polynomial number of samples of the true distribution, and only polynomial
running time.
