This paper proposes a deep convolutional neural network model for ordinal regression by considering a family of probabilistic ordinal link functions in the output layer. The link functions are those used for cumulative link models, which are traditional statistical linear models based on projecting each pattern into a 1-dimensional space. A set of ordered thresholds splits this space into the different classes of the problem. In our case, the projections are estimated by a non-linear deep neural network. To further improve the results, we combine these ordinal models with a loss function that takes into account the distance between the categories, based on the weighted Kappa index. Three different link functions are studied in the experimental study, and the results are contrasted with statistical analysis. The experiments run over two different ordinal classification problems and the statistical tests confirm that these models improve the results of a nominal model and outperform other robust proposals considered in the literature.
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