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Efficient training of Gaussian processes with tensor product structure
No full textAbstract To determine the optimal set of hyperparameters of a Gaussian process based on a large number of training data, both a linear system and a trace estimation problem must be solved. In this paper, we focus on establishing numerical methods for the case where the covariance matrix is given as the sum of possibly multiple Kronecker products, i.e., can be identified as a tensor. As such, we will represent this operator and the training data in the tensor train format. Based on the AME n method and Krylov subspace methods, we derive an efficient scheme for computing the matrix functions required for evaluating the gradient and the objective function in hyperparameter optimization
Greedy adaptive local recovery of functions in Sobolev spaces
No full textAbstract There are many ways to upsample functions from multivariate scattered data locally, using only a few neighbouring data points of the evaluation point. The position and number of the actually used data points is not trivial, and many cases like Moving Least Squares require point selections that guarantee local recovery of polynomials up to a specified order. This paper suggests a kernel-based greedy local algorithm for point selection that has no such constraints. It realizes the optimal L ∞ convergence rates in Sobolev spaces using the minimal number of points necessary for that purpose. On the downside, it does not care for smoothness, relying on fast L ∞ convergence to a smooth function. The algorithm ignores near-duplicate points automatically and works for quite irregularly distributed point sets by proper selection of points. Its computational complexity is constant for each evaluation point, being dependent only on smoothness and scale parameters of the kernel. Various numerical examples are provided. As a byproduct, it turns out that the well-known instability of global kernel-based interpolation in the standard basis of kernel translates arises already locally, independent of global kernel matrices and small separation distances
Conceptualizing hybrid intelligent service ecosystems
No full textAbstract With the proliferation of artificial intelligence (AI) technologies, the collaboration of human and AI actors in value co-creation processes permeates various application domains. In this conceptual paper, we integrate concepts from human-AI collaboration and service research and present a conceptual framework for hybrid intelligent service ecosystems (HISE). The framework extends the existing conceptualizations of service ecosystems as put forward by the service-dominant logic (S-D logic) by emphasizing how actors deliberately configure human and artificial agencies to co-create value via hybrid intelligent service exchange and how this impacts ecosystem formation and evolution. Our conceptualization highlights that value co-creation in HISE is guided and facilitated by shared resources and institutional arrangements, which differ from previous service ecosystems through the emergence of hybrid agency. We demonstrate the applicability of our framework with five illustrative HISE scenarios and provide five theoretical propositions. Our findings extend existing knowledge by theorizing on how to incorporate hybrid intelligence into value co-creation processes. Thereby, we provide a foundation for future interdisciplinary research on human-AI collaboration at the intersection of information systems, human–computer interaction, and service research with S-D logic as a unifying theoretical lens
Surgical indications and techniques in ischemic cerebellar stroke – results from an international survey
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The number of vertebral fractures in indolent systemic mastocytosis is influenced by presence of the KIT-mutation
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