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_28: Building a model of large-scale terrain that can adequately handle uncertainty and incompleteness in a statistically sound way is a challenging problem. This work proposes the use of Gaussian processes as models of large-scale terrain. The proposed model naturally provides a multiresolution representation of space, incorporates and handles uncertainties aptly, and copes with incompleteness of sensory information. Gaussian process regression techniques are applied to estimate and interpolate (to fill gaps in occluded areas) elevation information across the field. The estimates obtained are the best linear unbiased estimates for the data under consideration. A single nonstationary (neural network) Gaussian process is shown to be powerful enough to model large and complex terrain, effectively handling issues relating to discontinuous data. A local approximation method based on a “moving window” methodology and implemented using k-dimensional (KD)-trees is also proposed. This enables the approach to handle extremely large data sets, thereby completely addressing its scalability issues. Experiments are performed on large-scale data sets taken from real mining applications. These data sets include sparse mine planning data, which are representative of a global positioning system–based survey, as well as dense laser scanner data taken at different mine sites. Further, extensive statistical performance evaluation and benchmarking of the technique has been performed through cross-validation experiments. They conclude that for dense and-or flat data, the proposed approach will perform very competitively with grid-based approaches using standard interpolation techniques and triangulated irregular networks using triangle-based interpolation techniques; for sparse and-or complex data, however, it would significantly outperform them. © 2009 Wiley Periodicals, Inc.
The work @cite_28 , modeled large scale terrain modeling using GPs. It proposed the use of non-stationary kernels (neural network) to model large scale discontinuous spatial data. A performance comparison between GPs based on stationary (squared exponential) and non-stationary (neural network) kernels as well as several other standard interpolation methods applicable to alternative representations of terrain data, was reported. The non-stationary neural network kernel was found to be superior to the stationary squared exponential kernel and at least as good as most standard interpolation techniques for a range of terrain (in terms of sparsity complexity discontinuities). The work presented in this paper builds on this GP representation. However, it addresses the problem of simultaneous modeling multiple heterogeneous quantities of interest, in the context of geological resource modeling. This requires the modeling and usage of the correlations between these quantities towards improving predictions of each of them - an instance of data fusion using Gaussian processes.