Minimizing Negative Transfer of Knowledge in Multivariate Gaussian Processes: A Scalable and Regularized Approach

Recently there has been an increasing interest in the multivariate Gaussian process (MGP) which extends the Gaussian process (GP) to deal with multiple outputs. One approach to construct the MGP and account for non-trivial commonalities amongst outputs employs a convolution process (CP). The CP is based on the idea of sharing latent functions across several convolutions. Despite the elegance of the CP construction, it provides new challenges that need yet to be tackled. First, even with a moderate number of outputs, model building is extremely prohibitive due to the huge increase in computational demands and number of parameters to be estimated. Second, the negative transfer of knowledge may occur when some outputs do not share commonalities. In this paper we address these issues. We propose a regularized pairwise modeling approach for the MGP established using CP. The key feature of our approach is to distribute the estimation of the full multivariate model into a group of bivariate GPs which are individually built. Interestingly pairwise modeling turns out to possess unique characteristics, which allows us to tackle the challenge of negative transfer through penalizing the latent function that facilitates information sharing in each bivariate model. Predictions are then made through combining predictions from the bivariate models within a Bayesian framework. The proposed method has excellent scalability when the number of outputs is large and minimizes the negative transfer of knowledge between uncorrelated outputs. Statistical guarantees for the proposed method are studied and its advantageous features are demonstrated through numerical studies

A review of domain adaptation without target labels

Domain adaptation has become a prominent problem setting in machine learning and related fields. This review asks the question: how can a classifier learn from a source domain and generalize to a target domain? We present a categorization of approaches, divided into, what we refer to as, sample-based, feature-based and inference-based methods. Sample-based methods focus on weighting individual observations during training based on their importance to the target domain. Feature-based methods revolve around on mapping, projecting and representing features such that a source classifier performs well on the target domain and inference-based methods incorporate adaptation into the parameter estimation procedure, for instance through constraints on the optimization procedure. Additionally, we review a number of conditions that allow for formulating bounds on the cross-domain generalization error. Our categorization highlights recurring ideas and raises questions important to further research.Comment: 20 pages, 5 figure