Gaussian process

About: Gaussian process is a research topic. Over the lifetime, 18944 publications have been published within this topic receiving 486645 citations. The topic is also known as: Gaussian stochastic process.

Multi-Information Source Optimization

Abstract: We consider Bayesian methods for multi-information source optimization (MISO), in which we seek to optimize an expensive-to-evaluate black-box objective function while also accessing cheaper but biased and noisy approximations ("information sources"). We present a novel algorithm that outperforms the state of the art for this problem by using a Gaussian process covariance kernel better suited to MISO than those used by previous approaches, and an acquisition function based on a one-step optimality analysis supported by efficient parallelization. We also provide a novel technique to guarantee the asymptotic quality of the solution provided by this algorithm. Experimental evaluations demonstrate that this algorithm consistently finds designs of higher value at less cost than previous approaches.

Linear Problems in Linear Problems in pth Order and Stable Processes

Abstract: This work extends to processes with finite moments of order $p,1 < p < 2$ and to symmetric $\alpha $-stable processes, $1 < \alpha < 2$, some of the basic linear theory known for processes with finite second moments $(p = 2)$ and for Gaussian processes $(\alpha = 2)$. Here the “covariation” plays a role analogous to the covariance. Specifically, stochastic integrals of two types are introduced and studied for pth order processes and in particular for symmetric stable processes. Regression estimates and linear estimates on certain symmetric stable processes are evaluated, including regression and linear filtering of signal in noise. Also, for certain symmetric stable inputs, the identification of a linear system from the input covariation and the input–output cross covariation is considered, and the way the distribution of the output depends on the linear system is studied.

Texture segmentation using Gaussian-Markov random fields and neural oscillator networks

Abstract: We propose an image segmentation method based on texture analysis. Our method is composed of two parts. The first part determines a novel set of texture features derived from a Gaussian-Markov random fields (GMRF) model. Unlike a GMRF-based approach, our method does not employ model parameters as features or require the extraction of features for a fixed set of texture types a priori. The second part is a 2D array of locally excitatory globally inhibitory oscillator networks (LEGION). After being filtered for noise suppression, features are used to determine the local couplings in the network. When LEGION runs, the oscillators corresponding to the same texture tend to synchronize, whereas different texture regions tend to correspond to distinct phases. In simulations, a large system of differential equations is solved for the first time using a recently proposed method for integrating relaxation oscillator networks. We provide results on real texture images to demonstrate the performance of our method.

Continuity properties of Gaussian processes with multidimensional time parameter

Abstract: In this paper we shall present a strengthening and generalization to higher dimensions of the real variable lemma presented in [4]. As a consequence we shall obtain a criterion for the continuity of sample functions of Gaussian processes with a multidimensional time parameter. Remarkably enough, the difficulty ofthe arguments here is almost independent of dimensions, indeed the proofs in this paper are considerably simpler and yield stronger results than those in [4]. As in [4] our point of departure is a real variable lemma giving an a priori modulus of continuity for functions satisfying certain integral inequalities. As in [4], the basic ingredients are two functions p(u), defined in [-1, 1] and T(u), defined in (o, + oo). However here, in addition to the conditions

An extended class of scale-invariant and recursive scale space filters

Abstract: Explores how the functional form of scale space filters is determined by a number of a priori conditions. In particular, if one assumes scale space filters to be linear, isotropic convolution filters, then two conditions (viz. recursivity and scale-invariance) suffice to narrow down the collection of possible filters to a family that essentially depends on one parameter which determines the qualitative shape of the filter. Gaussian filters correspond to one particular value of this shape-parameter. For other values the filters exhibit a more complicated pattern of excitatory and inhibitory regions. This might well be relevant to the study of the neurophysiology of biological visual systems, for recent research shows the existence of extensive disinhibitory regions outside the periphery of the classical center-surround receptive field of LGN and retinal ganglion cells (in cats). Such regions cannot be accounted for by models based on the second order derivative of the Gaussian. Finally, the authors investigate how this work ties in with another axiomatic approach of scale space operators which focuses on the semigroup properties of the operator family. The authors show that only a discrete subset of filters gives rise to an evolution which can be characterized by means of a partial differential equation. >