  The design of methods for inference from time sequences has traditionally
relied on statistical models that describe the relation between a latent
desired sequence and the observed one. A broad family of model-based algorithms
have been derived to carry out inference at controllable complexity using
recursive computations over the factor graph representing the underlying
distribution. An alternative model-agnostic approach utilizes machine learning
(ML) methods. Here we propose a framework that combines model-based algorithms
and data-driven ML tools for stationary time sequences. In the proposed
approach, neural networks are developed to separately learn specific components
of a factor graph describing the distribution of the time sequence, rather than
the complete inference task. By exploiting stationary properties of this
distribution, the resulting approach can be applied to sequences of varying
temporal duration. Learned factor graph can be realized using compact neural
networks that are trainable using small training sets, or alternatively, be
used to improve upon existing deep inference systems. We present an inference
algorithm based on learned stationary factor graphs, which learns to implement
the sum-product scheme from labeled data, and can be applied to sequences of
different lengths. Our experimental results demonstrate the ability of the
proposed learned factor graphs to learn to carry out accurate inference from
small training sets for sleep stage detection using the Sleep-EDF dataset, as
well as for symbol detection in digital communications with unknown channels.
