This paper evaluates heterogeneous information fusion using multi-task Gaussian processes in the context of geological resource modeling. Specifically, it empirically demonstrates that information integration across heterogeneous information sources leads to superior estimates of all the quantities being modeled, compared to modeling them individually. Multi-task Gaussian processes provide a powerful approach for simultaneous modeling of multiple quantities of interest while taking correlations between these quantities into consideration. Experiments are performed on large scale real sensor data.
@cite_5: Kernel methods are among the most popular techniques in machine learning. From a frequentist discriminative perspective they play a central role in regularization theory as they provide a natural choice for the hypotheses space and the regularization functional through the notion of reproducing kernel Hilbert spaces. From a Bayesian generative perspective they are the key in the context of Gaussian processes, where the kernel function is also known as the covariance function. Traditionally, kernel methods have been used in supervised learning problem with scalar outputs and indeed there has been a considerable amount of work devoted to designing and learning kernels. More recently there has been an increasing interest in methods that deal with multiple outputs, motivated partly by frameworks like multitask learning. In this paper, we review different methods to design or learn valid kernel functions for multiple outputs, paying particular attention to the connection between probabilistic and functional methods.
An extensive review of kernel methods applied in modeling vector valued functions was presented in a recent survey paper @cite_5 . The paper discusses different approaches to develop kernels for multi-task applications and draws parallels between regularization perspective of this problem and a Bayesian one. The latter perspective is discussed through Gaussian processes. The work presented in this paper focuses on one of the approaches reviewed in @cite_5 ; specifically, it addresses modeling and information fusion of multi-task geological data using Gaussian processes developed using the process convolution approach. The paper presents a detailed empirical study of the approach applied to a large scale real world problem in order to evaluate its efficacy for information fusion, to understand the modeling capabilities of different kernels (chosen apriori) with such data and to understand broader approach-related questions from an application perspective. The paper also ties together past works of the authors within the process convolution theme.