Viterbi training in PRISM
  VT (Viterbi training), or hard EM, is an efficient way of parameter learning
for probabilistic models with hidden variables. Given an observation $y$, it
searches for a state of hidden variables $x$ that maximizes $p(x,y \mid
\theta)$ by coordinate ascent on parameters $\theta$ and $x$. In this paper we
introduce VT to PRISM, a logic-based probabilistic modeling system for
generative models. VT improves PRISM in three ways. First VT in PRISM converges
faster than EM in PRISM due to the VT's termination condition. Second,
parameters learned by VT often show good prediction performance compared to
those learned by EM. We conducted two parsing experiments with probabilistic
grammars while learning parameters by a variety of inference methods, i.e.\ VT,
EM, MAP and VB. The result is that VT achieved the best parsing accuracy among
them in both experiments. Also we conducted a similar experiment for
classification tasks where a hidden variable is not a prediction target unlike
probabilistic grammars. We found that in such a case VT does not necessarily
yield superior performance. Third since VT always deals with a single
probability of a single explanation, Viterbi explanation, the exclusiveness
condition that is imposed on PRISM programs is no more required if we learn
parameters by VT.
  Last but not least we can say that as VT in PRISM is general and applicable
to any PRISM program, it largely reduces the need for the user to develop a
specific VT algorithm for a specific model. Furthermore since VT in PRISM can
be used just by setting a PRISM flag appropriately, it makes VT easily
accessible to (probabilistic) logic programmers. To appear in Theory and
Practice of Logic Programming (TPLP).
