The gaussian-process tag has no wiki summary.
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How to test if two samples are distributed from the same Gaussian process
Given a sequence $\mathbf{x} = (x_1,x_2,\dots,x_n)$ which is sampled from some Gaussian process $GP(\mu_1,\Sigma_1)$ and a "target" sequence $\mathbf{y} = (y_1,y_2,\dots,y_n)$ sampled from another ...
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Degrees of freedom for Gaussian Process
I am reading this paper on Generalised Wishart Process (GWP). It is about modelling covariance matrix of D - dimensional gaussian processes (GP) as GWP. I fail to understand interpretation of "degrees ...
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Closed form Karhunen-Loeve/PCA expansion for gaussian/squared-exponential covariance
The Gaussian, or squared exponential covariance is $k_{SE}(s,t) = \exp \left\{ -\frac{1}{2l} (s - t)^2 \right\}$. It is a common covariance function used in Gaussian processes. The Karhunen-Loeve ...
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How to implement multiple GP submodels in PYMC
I'm hoping someone can give me some guidance on implementing
Gaussian processes (GP) with PYMC. In particular, I'm not sure how to use
multiple GP submodels properly within a single pymc model.
More ...
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58 views
Q: About the “a prior over the parameters” why always Gaussian distribution?
I have the following problem.
I'm reading through the Gaussian Process book http://www.gaussianprocess.org/gpml/chapters/RW2.pdf. In the bayesian linear regression it is suggested to use the Gaussian ...
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39 views
Confusion related to kriging
I was going through the wiki article related to kriging http://en.wikipedia.org/wiki/Kriging. However, I couldn't follow some derivations.
In the first figure for simple kriging, how come the ...
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1answer
64 views
Confusion related to difference of kriging and gaussian processes
I am having a hard time understanding what is the difference between kriging and gaussian processes. I mean wiki says they are the same but their formulas for prediction are so different.
I am a bit ...
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1answer
159 views
How can you detect if a Gaussian process is over-fitting?
I am training a Gaussian process with an ARD kernel with lots of parameters by maximizing the marginal lielihood of the data, instead of cross-validation.
I suspect that it is over-fitting. How can ...
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1answer
79 views
Calculation of posterior distribution of a GP
Suppose I have a set of points Y,X and I model them by using a GP(m,K). Let the noisy observations be given by
$y^i = f^i + \sigma^2$
p(f) gives the prior on the GP. Then what will be the posterior ...
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50 views
Confusion related to a derivation
I was reading this paper http://cs.ru.nl/~perry/publications/2011/ICANN2011/groot-icann2011.pdf and I am a bit confused how this was derived
$p(f|Y) \propto p(f)*p(Y|f) \propto ...
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51 views
Confusion related to calculation of likelihood
I was reading this paper related to Learning from multiple annotator using Gaussian processes. The idea is if we don't have the actual ground truth of a certain data, but only the labels from some ...
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167 views
Gaussian processes benefits
I have this confusion related to the benefits of Gaussian processes. I mean comparing it to simple linear regression, where we have defined that the linear function models the data.
However, in ...
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Confusion related to drawing samples from a gaussian process [closed]
I was going through this tutorial related to Gaussian processes
http://www.cs.ubc.ca/~hutter/EARG.shtml/earg/papers05/rasmussen_gps_in_ml.pdf. I came across this code given in the paper
...
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36 views
Confusion related to derivation of gaussian process regression
I was going through these slides related to gaussian process regression and I have a certain confusion
http://www.eurandom.tue.nl/events/workshops/2010/YESIV/Prog-Abstr_files/Ghahramani-lecture2.pdf
...
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2answers
173 views
Why are Gaussian process models called non-parametric?
I am a bit confused. Why are Gaussian processes called non parametric models?
They do assume that the functional values, or a subset of them, have a Gaussian prior with mean 0 and covariance function ...
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59 views
How can I generate data from a SVM?
I would like to generate samples from a support vector machine, with a Gaussian kernel and a fixed C and sigma? For examples ...
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1answer
107 views
Understanding the predictive distribution in gaussian linear regression
I'm reading through the Gaussian Process book http://www.gaussianprocess.org/gpml/chapters/RW2.pdf and there's one section here I don't quite understand (page 11). The author says:
"the predictive ...
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63 views
Time derivative of a gaussian process
I am currently working on biomass. I am trying to quantify how much the level of uncertainties in biomass estimations will affect the level of uncertainty in biomass fluxes.
For example, I know the ...
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1answer
101 views
How do I access or compute the posterior covariance matrix returned by kernlab::gausspr R function?
I am looking to compute the covariance matrix of an inferred Gaussian process in R. Below I outline how I would do this manually, but I realize that the kernlab ...
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1answer
142 views
Sum of normally distributed variables is a normally distributed variable?
Consider two Wiener processes:
$$
\begin{aligned}
X_a &\sim\mathcal N(0,a) \\
X_{a-b} &\sim\mathcal N(0,a-b)
\end{aligned}
$$
How do I show that:
$$
X_a - X_{a-b} \sim\mathcal N(.,.)
$$
That ...
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153 views
Combining normal distributions
Imagine that I take two separate measures and I get two separate normal distributions
N1(m1, s1^2)
N2(m2, s2^2)
How can I find a single normal distribution N3 ...
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1answer
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Gaussian process : function approximation properties
I'm learning about Gaussian Process and have heard only bits and pieces. Would really appreciate comments and answers.
For any set of data, is it true that a Gaussian Process function approximation ...
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2answers
132 views
Confusion regarding random walk model
I was referring to this book where it is given that
If we assume equally spaced nodes $i$ for $i=1,...,n$.
The first order random walk is constructed using independent increments
$$
\Delta{x_i} ...
6
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1answer
88 views
What is a stationary Gaussian field?
I know what a Gaussian field is. However, I am not quite sure what is meant by stationary. I have seen this stationary thing at lots of places like stationary autoregressive processes etc but don't ...
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2answers
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Gaussian Process goodness of fit
Let's say I got a Gaussian Process model $M$ based on some training data. Now I get a stream of sample data of a certain batch size coming in.
The GP does not model a time series, but it's trying to ...
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135 views
Queries regarding gaussian processes and kriging
I am confused how gaussian processes and kriging are related? Can anyone please give me some simple explanation. I tried to go through the wiki but I didn't get it
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4answers
352 views
How to increase variance in Gaussian Process regression?
I'm currently experimenting with Gaussian processes.
I decided to use matlab + gpml (http://www.gaussianprocess.org/gpml/code/) for playing around with Gaussian processes a bit.
I'd like to do ...
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133 views
Gaussian process - dimensionality reduction
Specific question on Gaussian Processes and dimensionality reduction. I saw a a method for dimensionality reduction for the squared exponential covariance function (not ARD) whereby one uses a GxD ...
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1answer
509 views
Gaussian Process regression for high dimensional data sets
Just wanted to see if anyone has any experience applying Gaussian process regression (GPR) to high dimensional data sets. I'm looking into some of the various sparse GPR methods (e.g. sparse ...
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56 views
With what probability the standard deviation of GP capture the measurement?
An interesting property of Gaussian Processes is estimating the uncertainty range. This uncertainty range of prediction can potentially capture the actual measurements.
I am wondering, how many times ...
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1answer
216 views
Computing time issues when using ordinary kriging
I am having time issues when using ordinary kriging. I have a spatial grid of 200x300 where I want to calculate the interpolated values. For that I am using ordinary kriging. Now for each point in the ...
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454 views
Hyperparameter estimation in gaussian process
Dear gaussian process experts,
i'm trying to optimize the hyperparameters for a gaussian process. As a starter i choose the squared exponential formula for covariance where i have to optimize 3 ...
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220 views
How adding covariance noise in Gaussian processes to prevent overfitting?
I am told, in Gaussian Processes, adding covariance function noise to others, say SEiso or Materns, cause a better result, since it prevents from over fitting. I appreciate if someone could put more ...
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2answers
485 views
Simulating a Gaussian process with an exponentially decaying covariance function
I'm trying to generate many draws (i.e., realizations) of
a Gaussian process $e_i(t)$, $1\leq t \leq T$ with mean 0 and covariance
function $\gamma(s,t)=\exp(-|t-s|)$.
Is there an efficient way ...
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89 views
How to incorporate prior knowledge in GPML?
I am using the MATLAB code for Rasmussen & Williams' book Gaussian Processes for Machine Learning.
How can one incorporate prior knowledge in Gaussian process regression? Say, that the variance ...
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133 views
Guassian Process Regression - feature selection
I'm using guassian process regression to do some modeling. One issue I'm encountering is feature selection for some of my models, which often have many relevant features. I'm not sure what the best ...
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290 views
Using GPML in Matlab for MultiClass Classification
I am using Rasmussen's GPML code in Matlab R2011a_student. I have training data (2560x29707) w/ labels (6 classes), and test data (640x29707). To prep the data I have 1. converted from sparse to full, ...
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3answers
561 views
Simple introduction to MCMC with Dirichlet process prior?
I'm looking for a simple and easy to read introduction to using MCMC with a dirichlet process prior. Or perhaps using MCMC in any machine learning scenario, eg Gaussian Process.
I've been circling ...
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229 views
Gaussian process predictor
I am building GP regressor , my input data is 1-d column vector and so is my target. I have divided my data into training and testing sets. I trained the model to learn the hyper-paramters and then ...
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Estimating a 1-D Brownian motion process using noisy observations
This question is a follow-up on my previous question.
Suppose I have a Brownian motion process that is defined as follows: at time $i=1$ random variable $X_1\sim\mathbf{N}(\mu,\sigma^2)$, and, for ...
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192 views
How to perform Gaussian process regression when function being approximated changes over time?
What are good strategies for performing Gaussian process regression when the function I am trying to approximate changes over time? The naive approach that springs to my mind is to only use the N most ...
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763 views
Problem with singular covariance matrices when doing gaussian process regression
I'm working with gaussian process regression. Currently I start testing differnt covariance functions and compositions to see what type of data they could describe best. I made an own implementation ...
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1answer
97 views
Risk bounds for Gaussian regression
Does anyone know references for non-asymptotic risk bounds for Gaussian regression. Specifically, I am interested in Bayesian regression with a Gaussian prior on the estimator space, and a Gaussian ...
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2answers
490 views
Gaussian Process covariance matrix gets zero determinant
i have a gaussian process regression implementation and developed some example data to test the capabilities of those methods. In the posterior calculation one gets the covariance matrix K. For some ...
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1answer
101 views
Gaussian process scale targets
I currently play around with gaussian process regression. I discovered some confusing facts that I like to be answered or maybe has a good mailing list for this at hand:
When I optimize the ...
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1answer
645 views
Implementation of Gaussian process
i try to implement a simple gaussian process regression in java. I almost got every step from the book http://www.GaussianProcess.org/gpml .
With my implementation of algorithm 2.1 on page 19 i'm ...
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Resources about functional distributions
Is there a article/textbook that treats probability distributions on functions just like basic textbooks cover the classical distributions for scalar variables?
Suppose the random function $f$ has a ...
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Inferring a Gaussian from noisy data
Assume a noise comes from a specific point on a line, noise which I can detect but not completely accurately. My uncertainty we assume to be Gaussian.
I want to gather evidence about the real ...
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Fitting multivariate, natural cubic spline
note: with no correct answers after a month, I have reposted to SO
Background
I have a model, $f$, where $Y=f(\textbf{X})$
$\textbf{X}$ is an $n \times m$ matrix of samples from $m$ parameters and ...
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Similarity matrix and multiple-regression
Let, $S_{n*n}$ represent a similarity matrix, among $n$ observation, my case n = 215. and $Y=\{y_1, y_2, ...,y_n\}$ contains a response value for each $x_n$ observation. For each observation we have ...
