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.
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.
@cite_28
2011508070 2609455865 2949971467 2149273154
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. Gaussian processes (GPs) are powerful non-parametric function estimators. However, their applications are largely limited by the expensive computational cost of the inference procedures. Existing stochastic or distributed synchronous variational inferences, although have alleviated this issue by scaling up GPs to millions of samples, are still far from satisfactory for real-world large applications, where the data sizes are often orders of magnitudes larger, say, billions. To solve this problem, we propose ADVGP, the first Asynchronous Distributed Variational Gaussian Process inference for regression, on the recent large-scale machine learning platform, PARAMETERSERVER. ADVGP uses a novel, flexible variational framework based on a weight space augmentation, and implements the highly efficient, asynchronous proximal gradient optimization. While maintaining comparable or better predictive performance, ADVGP greatly improves upon the efficiency of the existing variational methods. With ADVGP, we effortlessly scale up GP regression to a real-world application with billions of samples and demonstrate an excellent, superior prediction accuracy to the popular linear models. Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates, robustness to over-fitting, and principled ways for tuning hyper-parameters. However the scalability of these models to big datasets remains an active topic of research. We introduce a novel re-parametrisation of variational inference for sparse GP regression and latent variable models that allows for an efficient distributed algorithm. This is done by exploiting the decoupling of the data given the inducing points to re-formulate the evidence lower bound in a Map-Reduce setting. We show that the inference scales well with data and computational resources, while preserving a balanced distribution of the load among the nodes. We further demonstrate the utility in scaling Gaussian processes to big data. We show that GP performance improves with increasing amounts of data in regression (on flight data with 2 million records) and latent variable modelling (on MNIST). The results show that GPs perform better than many common models often used for big data. Gaussian process (GP) models are very popular for machine learning and regression and they are widely used to account for spatial or temporal relationships between multivariate random variables. In this paper, we propose a general formulation of underdetermined source separation as a problem involving GP regression. The advantage of the proposed unified view is first to describe the different underdetermined source separation problems as particular cases of a more general framework. Second, it provides a flexible means to include a variety of prior information concerning the sources such as smoothness, local stationarity or periodicity through the use of adequate covariance functions. Third, given the model, it provides an optimal solution in the minimum mean squared error (MMSE) sense to the source separation problem. In order to make the GP models tractable for very large signals, we introduce framing as a GP approximation and we show that computations for regularly sampled and locally stationary GPs can be done very efficiently in the frequency domain. These findings establish a deep connection between GP and nonnegative tensor factorizations (NTF) with the Itakura-Saito distance and lead to effective methods to learn GP hyperparameters for very large and regularly sampled signals.