  We present a structured inference approach in deep neural networks for
multiple attribute prediction. In attribute prediction, a common approach is to
learn independent classifiers on top of a good feature representation. However,
such classifiers assume conditional independence on features and do not
explicitly consider the dependency between attributes in the inference process.
We propose to formulate attribute prediction in terms of marginal inference in
the conditional random field. We model potential functions by deep neural
networks and apply the sum-product algorithm to solve for the approximate
marginal distribution in feed-forward networks. Our message passing layer
implements sparse pairwise potentials by a softplus-linear function that is
equivalent to a higher-order classifier, and learns all the model parameters by
end-to-end back propagation. The experimental results using SUN attributes and
CelebA datasets suggest that the structured inference improves the attribute
prediction performance, and possibly uncovers the hidden relationship between
attributes.
