Convolved Multi-output Gaussian Processes for Semi-Supervised Learning

Multi-output learning has become in a strong field of research in machine learning community during the last years. This setup considers the occurrence of multiple and related tasks in real-world problems. Another approach called semi-supervised learning (SSL) is the middle point between the case where all training samples are labeled (supervised learning) and the case where all training samples are unlabeled (unsupervised learning). In many applications it is difficult or impossible to access to fully labeled data. At these scenarios, SSL becomes a very useful methodology to achieve successful results, either for regression or for classification. In this paper, we propose the use of kernels for vector-valued functions for Gaussian process multi-output regression in the context of semi-supervised learning. We combine a Gaussian process with process convolution (PC) type of covariance function with techniques commonly used in semi-supervised learning like the Expectation-Maximization (EM) algorithm, and Graph-based regularization. We test our proposed method in two widely used databases for multi-output regression. Results obtained by our method exhibit a better performance compared to supervised methods based on Gaussian processes in scenarios where there are not available a good amount of labeled data.