A Stochastic Model for the Inheritance of the Cancer Proneness Phenotype

1987 ◽  
Vol 26 (03) ◽  
pp. 117-123
Author(s):  
P. Tautu ◽  
G. Wagner
Keyword(s):  
Stochastic Model ◽  
Gaussian Process ◽  
Covariance Function ◽  
Neoplastic Disease ◽  
Disease Phenotype ◽  
Probabilistic Representation ◽  
Temporal Behaviour ◽  
Continuous Trait ◽  
Continuous Parameter ◽  
Level Zero

SummaryA continuous parameter, stationary Gaussian process is introduced as a first approach to the probabilistic representation of the phenotype inheritance process. With some specific assumptions about the components of the covariance function, it may describe the temporal behaviour of the “cancer-proneness phenotype” (CPF) as a quantitative continuous trait. Upcrossing a fixed level (“threshold”) u and reaching level zero are the extremes of the Gaussian process considered; it is assumed that they might be interpreted as the transformation of CPF into a “neoplastic disease phenotype” or as the non-proneness to cancer, respectively.

A Stochastic Model for the Inheritance of the Cancer Proneness Phenotype

1987 ◽  
Vol 26 (03) ◽  
pp. 117-123
Author(s):  
P. Tautu ◽  
G. Wagner
Keyword(s):  
Stochastic Model ◽  
Gaussian Process ◽  
Covariance Function ◽  
Neoplastic Disease ◽  
Disease Phenotype ◽  
Probabilistic Representation ◽  
Temporal Behaviour ◽  
Continuous Trait ◽  
Continuous Parameter ◽  
Level Zero

SummaryA continuous parameter, stationary Gaussian process is introduced as a first approach to the probabilistic representation of the phenotype inheritance process. With some specific assumptions about the components of the covariance function, it may describe the temporal behaviour of the “cancer-proneness phenotype” (CPF) as a quantitative continuous trait. Upcrossing a fixed level (“threshold”) u and reaching level zero are the extremes of the Gaussian process considered; it is assumed that they might be interpreted as the transformation of CPF into a “neoplastic disease phenotype” or as the non-proneness to cancer, respectively.

Visualizing State of Time-Series Data by Supervised Gaussian Process Dynamical Models

2015 ◽  
Vol 19 (5) ◽  
pp. 688-696
Author(s):  
Nobuhiko Yamaguchi ◽  
Keyword(s):  
Time Series ◽  
Gaussian Process ◽  
Time Series Data ◽  
Series Data ◽  
Nonlinear Dimensionality Reduction ◽  
Probabilistic Representation ◽  
Dynamical Models ◽  
Motion Data ◽  
Dimensionality Reduction Technique ◽  
Representation Of Time

Gaussian Process Dynamical Models (GPDMs) constitute a nonlinear dimensionality reduction technique that provides a probabilistic representation of time series data in terms of Gaussian process priors. In this paper, we report a method based on GPDMs to visualize the states of time-series data. Conventional GPDMs are unsupervised, and therefore, even when the labels of data are available, it is not possible to use this information. To overcome the problem, we propose a supervised GPDM (S-GPDM) that utilizes both the data and their corresponding labels. We demonstrate experimentally that the S-GPDM can locate related motion data closer together than conventional GPDMs.

Computation with Infinite Neural Networks

1998 ◽  
Vol 10 (5) ◽  
pp. 1203-1216 ◽  
Author(s):  
Christopher K. I. Williams
Keyword(s):  
Neural Networks ◽  
Gaussian Process ◽  
Infinite Number ◽  
Wide Class ◽  
Gaussian Processes ◽  
Covariance Function ◽  
Bayesian Prediction ◽  
Infinite Networks

For neural networks with a wide class of weight priors, it can be shown that in the limit of an infinite number of hidden units, the prior over functions tends to a gaussian process. In this article, analytic forms are derived for the covariance function of the gaussian processes corresponding to networks with sigmoidal and gaussian hidden units. This allows predictions to be made efficiently using networks with an infinite number of hidden units and shows, somewhat paradoxically, that it may be easier to carry out Bayesian prediction with infinite networks rather than finite ones.

Wave-length and amplitude in Gaussian noise

1972 ◽  
Vol 4 (1) ◽  
pp. 81-108 ◽  
Author(s):  
Georg Lindgren
Keyword(s):  
Gaussian Process ◽  
Density Function ◽  
Gaussian Noise ◽  
Covariance Function ◽  
Wave Length ◽  
Local Maximum ◽  
Stationary Gaussian Process ◽  
Numerical Examples ◽  
Vertical Distance

We give moment approximations to the density function of the wavelength, i. e., the time between “a randomly chosen” local maximum with height u and the following minimum in a stationary Gaussian process with a given covariance function. For certain processes we give similar approximations to the distribution of the amplitude, i. e., the vertical distance between the maximum and the minimum. Numerical examples and diagrams illustrate the results.

scholarly journals Detecting periodicities with Gaussian processes

2016 ◽  
Vol 2 ◽  
pp. e50 ◽  
Author(s):  
Nicolas Durrande ◽  
James Hensman ◽  
Magnus Rattray ◽  
Neil D. Lawrence
Keyword(s):  
Hilbert Space ◽  
Gaussian Process ◽  
Gaussian Processes ◽  
Covariance Function ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Gaussian Process Regression ◽  
Inner Product ◽  
Input Output ◽  
Periodic Data

We consider the problem of detecting and quantifying the periodic component of a function given noise-corrupted observations of a limited number of input/output tuples. Our approach is based on Gaussian process regression, which provides a flexible non-parametric framework for modelling periodic data. We introduce a novel decomposition of the covariance function as the sum of periodic and aperiodic kernels. This decomposition allows for the creation of sub-models which capture the periodic nature of the signal and its complement. To quantify the periodicity of the signal, we derive a periodicity ratio which reflects the uncertainty in the fitted sub-models. Although the method can be applied to many kernels, we give a special emphasis to the Matérn family, from the expression of the reproducing kernel Hilbert space inner product to the implementation of the associated periodic kernels in a Gaussian process toolkit. The proposed method is illustrated by considering the detection of periodically expressed genes in thearabidopsisgenome.

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