 
Summary: Fast Algorithms for Robust Classification with
Bayesian Nets
Alessandro Antonucci and Marco Zaffalon
IDSIA, Istituto Dalle Molle di Studi sull'Intelligenza Artificiale, Galleria 2,
CH6928 Manno (Lugano), Switzerland
Abstract
We focus on a wellknown classification task with expert systems based on Bayesian
networks: predicting the state of a target variable given an incomplete observation
of the other variables in the network, i.e., an observation of a subset of all the pos
sible variables. To provide conclusions robust to nearignorance about the process
that prevents some of the variables from being observed, it has recently been derived
a new rule, called conservative updating. With this paper we address the problem
to efficiently compute the conservative updating rule for robust classification with
Bayesian networks. We show first that the general problem is NPhard, thus estab
lishing a fundamental limit to the possibility to do robust classification efficiently.
Then we define a wide subclass of Bayesian networks that does admit efficient com
putation. We show this by developing a new classification algorithm for such a class,
which extends substantially the limits of efficient computation with respect to the
previously existing algorithm. The algorithm is formulated as a variable elimination
procedure, whose computation time is linear in the input size.
