Probabilistic Deep Ordinal Regression Based on Gaussian Processes

Abstract

With excellent representation power for complex data, deep neural networks (DNNs) based approaches are state-of-the-art for ordinal regression problem which aims to classify instances into ordinal categories. However, DNNs are not able to capture uncertainties and produce probabilistic interpretations. As a probabilistic model, Gaussian Processes (GPs) on the other hand offers uncertainty information, which is nonetheless lack of scalability for large datasets. This paper adapts traditional GPs regression for ordinal regression problem by using both conjugate and non-conjugate ordinal likelihood. Based on that, it proposes a deep neural network with a GPs layer on the top, which is trained end-to-end by the stochastic gradient descent method for both neural network parameters and GPs parameters. The parameters in the ordinal likelihood function are learned as neural network parameters so that the proposed framework is able to produce fitted likelihood functions for training sets and make probabilistic predictions for test points. Experimental results on three real-world benchmarks -- image aesthetics rating, historical image grading and age group estimation -- demonstrate that in terms of mean absolute error, the proposed approach outperforms state-of-the-art ordinal regression approaches and provides the confidence for predictions.