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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Gaussian processes ordinal regression in R [on hold]

Is there any ordinal regression using gaussian processes implemented in R? I made a research in the Internet, but I didn't find anything.
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41 views

Multi Armed Bandit for Continuous Rewards - Extended Question

This question is an extension to A continuous generalization of the binary bandit The Multi-Armed Bandit (MAB) Problem in general is described here: https://en.wikipedia.org/wiki/Multi-armed_bandit ...
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36 views

Covariance Matrix with all equal entries

by training a Gaussian Process Regression Model I'm finding the weird result where the resulting covariance matrix has all the entries equal between each others. I'm using a Gaussian kernel with ...
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55 views

Can you use a gaussian process to model the smoothness of residuals?

I see a lot of use of Gaussian Processes for regression - fitting a GP model to data points, with a prior specifying the smoothness of the function, and using it to predict new values. However, I'm ...
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47 views

How to invert a sparse covariance matrix for spatial data on a grid?

Say we have some gaussian random variables that can be indexed on a grid. A convolution was applied to this grid, so now there is covariance between the grid points. The covariance is given by (see ...
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19 views

Theoretical properties of Gaussian Process Emulator

I am studying Guassian Prcess Emulator (GPE) to approximate computationally expensive computer models. Basically, we suppose the computer model, or simulator, is denoted by $f(x)$, where $x$ is the ...
2
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38 views

Hierarchical (multilevel, random-effects) Gaussian process regression

If we have a $J$ groups of predictor, outcome (univariate) variable pairs, $$ \{(y_{j1}, x_{j1}) \ldots (y_{jn_j}, x_{jn_j})\}, \quad\text{for $j \in 1\cdots J$}, $$ a hiearchical linear regression ...
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21 views

Relative speed of gaussian process classification

I used gaussian process classification implemented in Matlab gpml toolbox and also in R kernlab. For my problem - 600*14 matrix with two classes - it trains order of magnitude slower than other ...
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58 views

Understanding Gaussian Process Regression via infinite dimensional basis function view

It is often said that gaussian process regression corresponds (GPR) to bayesian linear regression with a (possibly) infinite amount of basis functions. I am currently trying to understand this in ...
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50 views

Preference learning with Bayesian optimization

I want to learn parameter preferences of users for different algorithms. The users are queried for their preference for one of the visualizations generated from a pair of parameter configurations for ...
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13 views

Simulating a Brownian Excursion using a Brownian Bridge?

I would like to simulate a Brownian excursion process (a Brownian motion that is conditioned always be positive when $0 \lt t \lt 1$ to $0$ at $t=1$). Since a Brownian excursion process is a Brownian ...
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1answer
14 views

Gaussian Mixture Model: bandwidth parameter versus variogram fitting?

I'm estimating a stationary, spatially random variable over a 2-dimensional domain. I have ground-truth measurements in several locations, over time. I need some way of spatially-interpolating ...
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51 views

The squared-norm of the projection of a Gaussian vector onto an independent $d$-dimensional subspace is a $\chi^2_{2d}$

How we can prove that: The squared-norm of the projection of a $N$-dimensional complex vector with i.i.d. unit-variance and zero mean Gaussian components onto an independent $d$-dimensional subspace ...
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gaussian process - missing data

One approach to deal with missing data is be to define a joint gaussian distribution / Gaussian process, and then define the (conditional) distribution of the unknown values on the known values. (e.g. ...
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29 views

interpolation of noisy data

Kevin Murphy discusses an approach to interpolate 1D data in his book "Machine Learning - a Probabilistic Approach". I have been staring at the page below for a while -- but am struggling to see the ...
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268 views

How can I predict Stock Market using Gaussian Process with the help of GPML?

I'm reading this paper and I would like to implement it. It gives me a matrix in this way: $$ \begin{array}{lcr} \mbox{Year} & \mbox{day 1} & \mbox{day 2} & \dots & \mbox{day 250} ...
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20 views

Gaussian Process for periodic data?

Assuming that I have data with repeated measures (or, in other words, multiple time series of different realizations of the same process), can I train a Gaussian Process on this data? In fact, is ...
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1answer
28 views

Regression on multiple independent (noisy) inputs [closed]

I have a data set that is highly variable and made up of 17 different inputs and 1 output. I'm currently using a Gaussian Process Regression toolbox. However I'm curious to see if they're other types ...
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19 views

What is the integrand in a Gaussian process covariance function?

I have a very basic question about Gaussian process covariance functions. When I specify a covariance function like $k(x,y)$, what exactly is assumed to be co-varying? Is it correlated noise at the ...
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Fitting of non-linear GP-LVM

I'm trying to perform dimension reduction using the Gaussian process latent variable model. I read the paper from N. Lawrence http://jmlr.org/papers/volume6/lawrence05a/lawrence05a.pdf and there are ...
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1answer
32 views

GP regression - Matern kernel gradient issue

I'm trying to use a Matern 5/2 kernel for GP regression, so my kernel function is $ K(x,x')\triangleq\theta_0(1+\sqrt{5r(x,x')}+5/3r)\exp(-\sqrt{5r}), $ where $r(x,x')\triangleq\sum_{d=1}^D ...
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How to select a subset of variables from a large dimensional dataset for Gaussian Process Regression?

I am currently working on GPR(gaussian process regression) on a large dimensional input dataset(around 300). I am pretty sure that some of these variables have weak correlation with target output. If ...
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38 views

optimal sequential sampling in gaussian process models

Let's say we have a one dimensional dataset of 24 points along with their responses. I am reserving three boundary points for testing (i=1,23,24) and i am fitting a Gaussian process model based on a ...
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1answer
57 views

Gaussian Process Regression for piecewise linear response functions

I am performing Gaussian Process Regression (without noise) for response functions which are piecewise linear. My question: Does there exist a covariance function, such that sample paths from a ...
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1answer
37 views

Meaning of syntax $N(\mathbf{y} \mid \mathbf{0}, \mathbf{K})$ (multivariate normal distribution)

So I'm reading notes on Gaussian Processses, and came across syntax $p(\mathbf{y} \mid \text{stuff}) = N(\mathbf{y} \mid \mathbf{0}, \mathbf{K})$ for multivariate normal distribution, and I'm not ...
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Gaussian process regression implementaion

I am using the GPML matlab code found here. I have been using a squared exponential cov function with ARD. I am finding that if I use the minimise function to train the process I get uniform large ...
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35 views

Gaussian Process Regression

After implementing a Gaussian process regression model I am getting a negative log marginal likelihood figure that is very high (~100). What does this mean?
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85 views

Gaussian process regression: leave-one-out prediction

According to Dubrule's Cross validation of kriging in a unique neighborhood, it is possible to compute leave-one-out the gaussian process prediction $\hat{Y}_{-i}(x_i)$ at a point $x_i$ from the ...
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72 views

Hyperparameter tuning in Gaussian Process Regression

I am trying to tune the hyperparameters of the gaussian process regression algorithm I've implemented. I simply want to maximize the log marginal likelihood given by the formula ...
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28 views

What is the shape of the decision surface of a Gaussian Process classifier?

I've got a binary classification problem, which I am trying to solve using a generative classifier. If I use Gaussian Discriminant Analysis, and fit two Gaussian distributions to my two classes, the ...
2
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42 views

Incremental Gaussian Process Regression

I want to implement an incremental gaussian process regression using a sliding window over the data points which arrives one by one through a stream. Let $d$ denote the dimensionality of the input ...
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31 views

Bayesian multivariate extrapolation

I'm not sure "Bayesian multivariate extrapolation " is the right formulation of what I want to do but here is my problem: I have a set of observations in a state $k$ (having a multivariate Gaussian ...
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1answer
186 views

Unscented Kalman Filter with Gaussian Process regression for time series prediction

I've trained a gaussian process which will take X (x1:5) and predict Y (x6). I'm trying to do 1step ahead prediction with Unscented Kalman filter with this GP as my state transition funtion. The ...
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1answer
20 views

GPML producing wrong output using correct target labels

I am using the GPML code found here. The key function in the aforementioned library is the gp function described below: Two modes are possible: training or ...
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An example for Gaussian Process: Singular covariance matrix?

I follow Christopher Bishop's book "Pattern Recognition and Machine Learning" and I am studying the section on Gaussian Processes. As an introduction, a simple model is given with the following ...
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281 views

How does the mean function work for a Gaussian Process?

I was reading the notes on Gaussian Processes by Choung B. Do (stanford course CS229) however was unsure of how the mean function worked and what a random variable was on the Gaussian Process So ...
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1answer
36 views

What is the realization value of f(x) in Gaussian process regression?

This is related to the Gaussian process regression. We propose the model as $y_i = f(\mathbf{x}_i) + \epsilon_i$ with $i = 1 \ldots n$ and $\epsilon_i \sim \mathcal{N}(0, \sigma^2)$. Here ...
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1answer
58 views

How to compare the relative importance of features in GP regression?

Kernel function with different length scales, such as the squared exponential function, is said to be able to quantify the relative importance among the input (predictor) features. The idea is to ...
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1answer
32 views

Reference for definition of multiple-output Gaussian process

Does anyone know any good reference that has a clear and precise definition of multiple-output Gaussian process? Something like the definition of the Gaussian process in the third page of this set of ...
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28 views

Marginal Likelihood of a Gaussian Process Model, Duplicate entries in kernel matrix

I am trying to fit a Gaussian process model using the toolbox and I got stuck in the following problem. Assuming that I have some duplicated data points in my training data, then those will map to ...
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1answer
72 views

Estimating the variance of the noise in Gaussian Process prediction

I've been trying to use leave-one-out cross-validation to estimate the $\sigma_n$, the variance of the signal noise when doing prediction according to $E[f_*] = k_*^T(K+\sigma_n^2I)^{-1}y$ (GPML ...
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1answer
35 views

scale of variance in Gaussian process

When performing Gaussian process regression, the variance at a prediction point is given by $var[f_*] = k(x_*,x_*) - k_*^T(k+\sigma_n^2I)^{-1}k_*$ (Equation 2.26 from GPML) The variance is not ...
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2answers
107 views

What mathematical background do I need for the Gaussian Process book by Rasmussen and Williams?

I started reading the book today, but right off the bat, he mentions infinite Hilbert spaces in the notation, so I feel that it might be out of my league. I am familiar with linear algebra, ...
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354 views

Calculate PLS Xscores for predicting new data

I wish to extract Partial Least Squares (PLS) components to apply non-linear regression (Gaussian Process Regression (GPR)) on the scores of the predictors (Xscores). The reason is my data is very ...
2
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1answer
110 views

Splines vs Gaussian Process Regression

I'm know that Gaussian Process Regression (GPR) is an alternative to using splines for fitting flexible nonlinear models. I would like to know in which situations would one be more suitable than the ...
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1answer
102 views

Kernel methods in machine learning?

I am beginning to tackle geostatistics problems where I tried to apply kriging(gaussian processes) to interpolate demographical water drop. According to my understanding, kernel methods are something ...
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1answer
58 views

How could the predictive mean in a GP become negative when both the prior and the training target values are non-negative?

I am training a Gaussian process regression where the training target values are between 0 and 1 and the prior mean is the fixed zero function. The predictive mean sometimes becomes negative e.g. ...
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92 views

Handling missing data in Gaussian Process Regression

I am trying to handle missing data in a model using Gaussian Processes. I have two spatial dimensions sharing the same length hyper-parameter, one dimension for time. Additionally I have split one ...
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33 views

Kriging, Gaussian Processes with categorical data

Theoretically it is possible to use Kriging also for categorical features by using a kernel function which supports factors. Does anybody know some references on this topic or whether they are ...
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How to reduce the number of features for Gaussian Process regression?

Ridge regression reduces complexity of the model by scaling down the coefficient. Lasso reduces the complexity of the model by selecting the features used. For Gaussian Process, is there similar way ...