  The task of dialog management is commonly decomposed into two sequential
subtasks: dialog state tracking and dialog policy learning. In an end-to-end
dialog system, the aim of dialog state tracking is to accurately estimate the
true dialog state from noisy observations produced by the speech recognition
and the natural language understanding modules. The state tracking task is
primarily meant to support a dialog policy. From a probabilistic perspective,
this is achieved by maintaining a posterior distribution over hidden dialog
states composed of a set of context dependent variables. Once a dialog policy
is learned, it strives to select an optimal dialog act given the estimated
dialog state and a defined reward function. This paper introduces a novel
method of dialog state tracking based on a bilinear algebric decomposition
model that provides an efficient inference schema through collective matrix
factorization. We evaluate the proposed approach on the second Dialog State
Tracking Challenge (DSTC-2) dataset and we show that the proposed tracker gives
encouraging results compared to the state-of-the-art trackers that participated
in this standard benchmark. Finally, we show that the prediction schema is
computationally efficient in comparison to the previous approaches.
