Gaussian conditional random fields (GCRF) are a well-known used structured
model for continuous outputs that uses multiple unstructured predictors to form
its features and at the same time exploits dependence structure among outputs,
which is provided by a similarity measure. In this paper, a Gaussian
conditional random fields model for structured binary classification (GCRFBC)
is proposed. The model is applicable to classification problems with undirected
graphs, intractable for standard classification CRFs. The model representation
of GCRFBC is extended by latent variables which yield some appealing
properties. Thanks to the GCRF latent structure, the model becomes tractable,
efficient and open to improvements previously applied to GCRF regression
models. In addition, the model allows for reduction of noise, that might appear
if structures were defined directly between discrete outputs. Additionally, two
different forms of the algorithm are presented: GCRFBCb (GCRGBC – Bayesian) and
GCRFBCnb (GCRFBC – non Bayesian). The extended method of local variational
approximation of sigmoid function is used for solving empirical Bayes in
Bayesian GCRFBCb variant, whereas MAP value of latent variables is the basis
for learning and inference in the GCRFBCnb variant. The inference in GCRFBCb is
solved by Newton-Cotes formulas for one-dimensional integration. Both models
are evaluated on synthetic data and real-world data. It was shown that both
models achieve better prediction performance than unstructured predictors.
Furthermore, computational and memory complexity is evaluated. Advantages and
disadvantages of the proposed GCRFBCb and GCRFBCnb are discussed in detail.

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