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.
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.
@cite_5
2673818281 2740620254 2185932763 2951681657
In this paper, we analyze the spatial information of deep features, and propose two complementary regressions for robust visual tracking. First, we propose a kernelized ridge regression model wherein the kernel value is defined as the weighted sum of similarity scores of all pairs of patches between two samples. We show that this model can be formulated as a neural network and thus can be efficiently solved. Second, we propose a fully convolutional neural network with spatially regularized kernels, through which the filter kernel corresponding to each output channel is forced to focus on a specific region of the target. Distance transform pooling is further exploited to determine the effectiveness of each output channel of the convolution layer. The outputs from the kernelized ridge regression model and the fully convolutional neural network are combined to obtain the ultimate response. Experimental results on two benchmark datasets validate the effectiveness of the proposed method. Convolutional Neural Networks (CNNs) with Bilinear Pooling, initially in their full form and later using compact representations, have yielded impressive performance gains on a wide range of visual tasks, including fine-grained visual categorization, visual question answering, face recognition, and description of texture and style. The key to their success lies in the spatially invariant modeling of pairwise (2nd order) feature interactions. In this work, we propose a general pooling framework that captures higher order interactions of features in the form of kernels. We demonstrate how to approximate kernels such as Gaussian RBF up to a given order using compact explicit feature maps in a parameter-free manner. Combined with CNNs, the composition of the kernel can be learned from data in an end-to-end fashion via error back-propagation. The proposed kernel pooling scheme is evaluated in terms of both kernel approximation error and visual recognition accuracy. Experimental evaluations demonstrate state-of-the-art performance on commonly used fine-grained recognition datasets. One approach to improving the running time of kernel-based methods is to build a small sketch of the kernel matrix and use it in lieu of the full matrix in the machine learning task of interest. Here, we describe a version of this approach that comes with running time guarantees as well as improved guarantees on its statistical performance. By extending the notion of statistical leverage scores to the setting of kernel ridge regression, we are able to identify a sampling distribution that reduces the size of the sketch (i.e., the required number of columns to be sampled) to the effective dimensionality of the problem. This latter quantity is often much smaller than previous bounds that depend on the maximal degrees of freedom. We give an empirical evidence supporting this fact. Our second contribution is to present a fast algorithm to quickly compute coarse approximations to these scores in time linear in the number of samples. More precisely, the running time of the algorithm is O(np2) with p only depending on the trace of the kernel matrix and the regularization parameter. This is obtained via a variant of squared length sampling that we adapt to the kernel setting. Lastly, we discuss how this new notion of the leverage of a data point captures a fine notion of the difficulty of the learning problem. 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.