# Tagged Questions

Gaussian processes refer to stochastic processes whose realization consists of normally distributed random variables, with the additional property that any finite collection of these random variables have a multivariate normal distribution. The machinery of Gaussian processes can be employed in ...

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### What is the conceptual difference between the marginal variance and the range in the Matérn covariance?

The MatÃ©rn covariance kernel is given by: $$C_\nu(d) = \sigma^2 \frac{2^{1-\nu}}{\Gamma(\nu)}\left(\sqrt{2\nu}\frac{d}{p}\right)^\nu K_\nu\left(\sqrt{2\nu}\frac{d}{p}\right)$$ My question is, what ...
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### Splitting Gaussian into N beta distributions [on hold]

Suppose we have a standard,symmetrical Gaussian distribution. The extreme values are not very likely, the central values most likely. Is there a method to split this gaussian distribution into $N$ ...
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### Sampling from Gaussian Process Posterior

Anyone know of a Python package that both fits a Gaussian Process to data, and also lets you sample paths from the posterior? I'm interested in sampling the colorful lines on right (b) of the ...
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### Gaussian Process Regression in R

I'm not sure this is the right Stack Exchange Community for the question: in case I'm wrong, please let me know. I would like to try using GP for regression: here is an example of data I need to fit ...
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### Multiplication of two normals Gaussian Processes

I am working with Bayesian statistics for gaussian processes and I want to derive the posterior distribution. In general, I am clear about how to derive a posterior using Bayes rule. However in this ...
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### Gaussian Process FITC approximation

I'm reading up on Gaussian Processes and trying to understand sparse Gaussian processes; in particular the FITC approximation (http://papers.nips.cc/paper/3351-the-generalized-fitc-approximation.pdf) ...
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### Implementation of FITC approximation for Gaussian Processes [closed]

I'm attempting to use Gaussian processes for classification. When using a large number of observations, sparse approaches are used to deal with the scalability issue of O(N^3). Sparse approaches ...
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### Corresponding RKHS of Common Kernels

A kernel, $k(x_1, x_2)$, has the interesting property that it may be represented as the dot product in a reproducing kernel hilbert space (RKHS), $\phi(x_0)\phi(x_1)$. I know that for the gaussian ...
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### practical implementation detail of Bayesian Optimization

I'm giving Bayesian Optimization a go, following Snoek, Larochelle, and Adams [http://arxiv.org/pdf/1206.2944.pdf], using GPML [http://www.gaussianprocess.org/gpml/code/matlab/doc/]. I've implemented ...
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### Diagonal linear discriminant analysis

On p110 of Murphy's machine learning book, he derives the discriminant function for the diagonal LDA model by simplifying the full linear discriminant analysis equation (4.33): It seems that he's ...
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### What does surrogate mean in this context?

I'm trying to learn about Gaussian Processes and ran into an interesting example on the scikit-learn documentation but am having trouble interpreting the line below. Say we want to surrogate the ...
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### Stochastic Differential Equation Interpretation of Squared Exponential Kernel

As far as I understand, many Gaussian Processes can be either described by their corresponding mean and kernel functions or by a stochastic differential equation (SDE). For my purposes it is ...
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### Estimate mean and variance from multiple realizations of Gaussian process

I have a certain number of realizations of the same Gaussian process. I want to get the mean and the variance of this process. How can I do that? To better explain the question lets suppose I have my ...
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### Ill-conditioned covariance matrix in GP regression for Bayesian optimization

Background and problem I am using Gaussian Processes (GP) for regression and subsequent Bayesian optimization (BO). For regression I use the gpml package for MATLAB with several custom-made ...
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### Calculating the expression for the derivative of a Gaussian process

I know based on the answers to this question Derivative of a Gaussian Process that the derivative of a Gaussian process is another Gaussian process, but I was wondering if someone could tell (or show) ...
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### Gaussian-Process (scikit-learn) Prediction Confidence Interval Oddities - Stats Question

I'm doing some particle physics analysis and was hoping someone out there could give me some insight on a Gaussian-Process fit I'm trying to use to extrapolate some data. I have data with ...
When performing Gaussian process regression, the variance at a prediction point is given by $\operatorname{var}[f_*] = k(x_*,x_*) - k_*^T(K+\sigma_n^2I)^{-1}k_*$ (Equation 2.26 from GPML) Basic ...