This paper addresses the problem of active learning of a multi-output Gaussian process (MOGP) model representing multiple types of coexisting correlated environmental phenomena. In contrast to existing works, our active learning problem involves selecting not just the most informative sampling locations to be observed but also the types of measurements at each selected location for minimizing the predictive uncertainty (i.e., posterior joint entropy) of a target phenomenon of interest given a sampling budget. Unfortunately, such an entropy criterion scales poorly in the numbers of candidate sampling locations and selected observations when optimized. To resolve this issue, we first exploit a structure common to sparse MOGP models for deriving a novel active learning criterion. Then, we exploit a relaxed form of submodularity property of our new criterion for devising a polynomial-time approximation algorithm that guarantees a constant-factor approximation of that achieved by the optimal set of selected observations. Empirical evaluation on real-world datasets shows that our proposed approach outperforms existing algorithms for active learning of MOGP and single-output GP models.
We consider the spatial sampling design problem for a random field X. This random field is in general assumed not to be directly observable, but sample information from a related variable Y is available. Our purpose in this paper is to present a state-space model approach to network design based on Shannon's definition of entropy, and describe its main points with regard to some of the most common practical problems in spatial sampling design. For applications, an adaptation of 's (1995) algorithm for maximum entropy sampling in this context is provided. We illustrate the methodology using piezometric data from the Velez aquifer (Malaga, Spain). © Rapid Science 1998 Recommender systems, especially the newly launched ones, have to deal with the data-sparsity issue, where little existing rating information is available. Recently, transfer learning has been proposed to address this problem by leveraging the knowledge from related recommender systems where rich collaborative data are available. However, most previous transfer learning models assume that entity-correspondences across different systems are given as input, which means that for any entity (e.g., a user or an item) in a target system, its corresponding entity in a source system is known. This assumption can hardly be satisfied in real-world scenarios where entity-correspondences across systems are usually unknown, and the cost of identifying them can be expensive. For example, it is extremely difficult to identify whether a user A from Facebook and a user B from Twitter are the same person. In this paper, we propose a framework to construct entity correspondence with limited budget by using active learning to facilitate knowledge transfer across recommender systems. Specifically, for the purpose of maximizing knowledge transfer, we first iteratively select entities in the target system based on our proposed criterion to query their correspondences in the source system. We then plug the actively constructed entity-correspondence mapping into a general transferred collaborative-filtering model to improve recommendation quality. We perform extensive experiments on real world datasets to verify the effectiveness of our proposed framework for this crosssystem recommendation problem. The problem of estimating a multivariate spatial random process from observations obtained by sampling a related multivariate spatial random process is considered. A method based on additive perturbation of the variables of interest is proposed for the assignment of degrees of relative importance to the variables and or locations of interest in the design of sampling strategies. In the case where the variables involved have a multivariate Gaussian distribution, some theoretical results are provided to justify the method proposed; in particular, it is proved that the amount of information contained in the data on the perturbed variables of interest is never higher than that contained in the original variables of interest. These results and the application of the method are illustrated with an empirical study, showing the variation of the effects of perturbation on spatial sampling design configurations and related ratios of information for different degrees of dependence according to the model specifications. Copyright © 2001 John Wiley & Sons, Ltd. In many complex machine learning applications there is a need to learn multiple interdependent output variables, where knowledge of these interdependencies can be exploited to improve the global performance. Typically, these structured output scenarios are also characterized by a high cost associated with obtaining supervised training data, motivating the study of active learning for these situations. Starting with active learning approaches for multiclass classification, we first design querying functions for selecting entire structured instances, exploring the tradeoff between selecting instances based on a global margin or a combination of the margin of local classifiers. We then look at the setting where subcomponents of the structured instance can be queried independently and examine the benefit of incorporating structural information in such scenarios. Empirical results on both synthetic data and the semantic role labeling task demonstrate a significant reduction in the need for supervised training data when using the proposed methods.