Distributed Gaussian Processes

The Rate of Entropy for Gaussian Processes

In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates. Using that we can obtain Tsallis entropy rate for stationary Gaussian processes. Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian proc...

Complete convergence of moving-average processes under negative dependence sub-Gaussian assumptions

The complete convergence is investigated for moving-average processes of doubly infinite sequence of negative dependence sub-gaussian random variables with zero means, finite variances and absolutely summable coefficients. As a corollary, the rate of complete convergence is obtained under some suitable conditions on the coefficients.

ADK Entropy and ADK Entropy Rate in Irreducible- Aperiodic Markov Chain and Gaussian Processes

In this paper, the two parameter ADK entropy, as a generalized of Re'nyi entropy, is considered and some properties of it, are investigated. We will see that the ADK entropy for continuous random variables is invariant under a location and is not invariant under a scale transformation of the random variable. Furthermore, the joint ADK entropy, conditional ADK entropy, and chain rule of this ent...

Autoregressive Gaussian Random Vectors of First Order

Spatial prediction with mobile sensor networks using Gaussian processes with built-in Gaussian Markov random fields

In this paper, a new class of Gaussian processes is proposed for resource-constrained mobile sensor networks. Such a Gaussian process builds on a GMRFwith respect to a proximity graph over a surveillance region. The main advantages of using this class of Gaussian processes over standard Gaussian processes defined by mean and covariance functions are its numerical efficiency and scalability due ...

Beyond Gaussian Processes: On the Distributions of Infinite Networks

A general analysis of the limiting distribution of neural network functions is performed, with emphasis on non-Gaussian limits. We show that with i.i.d. symmetric stable output weights, and more generally with weights distributed from the normal domain of attraction of a stable variable, that the neural functions converge in distribution to stable processes. Conditions are also investigated und...