
CMUCS05107
Computer Science Department
School of Computer Science, Carnegie Mellon University
CMUCS05107
Optimal Nonmyopic Value of Information in Graphical Models 
Efficient Algorithms and Theoretical Limits
Andreas Krause, Carlos Guestrin
February 2005
Also appears as Center for Automated Learning and Discovery
Technical Report CMUCALD05100.
CMUCS05107.ps
CMUCS05107.pdf
Keywords: Uncertainty, probabilistic reasoning, decision theory,
graphical models, value of information, complexity theory
Many realworld decision making tasks require us to choose among
several expensive observations. In a sensor network, for example,
it is important to select the subset of sensors that is expected
to provide the highest reduction in uncertainty. It has been
general practice to use heuristicguided procedures for selecting
observations. In this paper, we present the first efficient optimal
algorithms for selecting observations for a class of graphical
models containing Hidden Markov Models (HMMs). We provide results
for both selecting the optimal subset of observations, and for
obtaining an optimal conditional observation plan. We also prove a
surprising result: In most graphical models tasks, if one designs
an efficient algorithm for chain graphs, such as HMMs, this procedure
can be generalized to polytrees. We prove that the value of
information problem is NP^{PP}hard even for discrete polytrees. It also
follows from our results that even computing conditional entropies,
which are widely used to measure value of information, is a
#Pcomplete problem on polytrees. Finally, we
demonstrate the effectiveness of our approach on several realworld datasets.
8 pages
