# Questions tagged [gaussian-process]

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 regression and classification problems.

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### Why functions sampled from a linear kernel Gaussian Process are guaranteed to be a linear function?

It's well known that a linear kernel Guassian Process regression is equivalent to Bayesian Linear Regression, because the functions sampled from a linear kernel GP is bound to be a linear function. ...
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### Gaussian process - what am I doing wrong?

I have recently started to delve into Gaussian processes. During my review, I have found a book which states that one can interpret the mean of a Gaussian process as a combination of basis functions, ...
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### Regression:how to deal with known observation error?

I try to reproduce an experiment of a paper. If I known observation error ,how can I build my model ? Is this the case Heteroscedastic Regression? What's the difference between this case and error-in-...
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### Kernel ridge regression and Gaussian Process Regression

One knows that through the both methods mentioned in the title, in regression setting, with the same kernel $K$, the result is the same. It may be a very naive question but why? To me, they are quite ...
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### reference source for multivariate gaussian processes

I'm studying Gaussian processes and currently reading the standard reference Gaussian Processes for Machine Learning. However, so far I didn't see any example of a multivariate Gaussian process nor ...
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### How to ensure inequality constraints on surrogate model from Bayesian optimization?

I am using bayesian optimization as a sequential strategy to globally optimize my objective function on a Simplex. Currently I am using Gaussian Process Regression for my surrogate model. Gaussian ...
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### Why prior distribution is not conditioned on X?

I would like to know why in the below formula the prior distribution of theta is not conditioned on X (observations): In my understanding, the correct formula should be: P(theta | X, y) = P(y| X, ...
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### Computing posterior variance at noisy training samples using Gaussian Process regression

Sorry for a possible naive question but this has been unclear to me for awhile... Consider the data model $y = f(x) + \epsilon, \;\; \epsilon \sim \mathcal{N}(0, \sigma_v^2)$. They show in Rasmussen ...
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### How is length scale calculated in ARD matern kernel functions?

I am new to machine learning and I have a question regarding ARD Matern 5/2 kernel functions. How is the characteristic length scale calculated? Is it a constant value or it varies in each iteration (...
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### Proof (requested) of sample sizes in multivariate distribution

My team has been asked to build a predictive model. We have a very limited dataset, but using a number of rationalizations about bounds on the data and the current behavior (54 data points) I have ...
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### Differences between Kriging and Gaussian Process Regression

I am having quite difficult time to clearly understand the differences between Kriging and Gaussian Process Regression. Here is what I have understood so far: For simple kriging (mean value known), ...
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