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 ...

learn more… | top users | synonyms

0
votes
1answer
11 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 ...
0
votes
1answer
18 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 ...
0
votes
1answer
16 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 ...
0
votes
0answers
1 view

Matlab GPML Super Resolution Using Gaussian Process Regression [migrated]

I was doing image super-resolution using a learning based approach using GPR. But I was having problems implementing gpr in my case. Basically, I am doing a patch based regression in which I have k ...
1
vote
2answers
83 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, ...
0
votes
0answers
57 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
votes
1answer
28 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 ...
1
vote
1answer
41 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 ...
1
vote
1answer
41 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. ...
0
votes
0answers
30 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 ...
0
votes
0answers
18 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 ...
7
votes
0answers
76 views

Why does inversion of a covariance matrix yield partial correlations between random variables?

I heard that partial correlations between random variables can be found by inverting the covariance matrix and taking appropriate cells from such resulting precision matrix (this fact is mentioned in ...
1
vote
0answers
30 views

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 ...
0
votes
0answers
9 views

Sub-space / latent-space covariance

I am not entirely sure what I should be googling for this in my present context. Basically I am working with a set of latent variable models such as the Gaussian Processes latent variable model ...
0
votes
1answer
21 views

Covariance function to draw an inverse function

In a Gaussian Process (GP), we know that choice of the covariance function determines the shape of function that can be drawn from the GP. eg. Constant : $\sigma _{o}^{2}$ Draws constant function ...
2
votes
0answers
33 views

How to prove that Radial Basis Function can be derived by mapping function?

How to prove the radial basis function $k(u,v) = \int_{\mathbb{R}^d} \phi_t(u)\phi_t(v)dt $ can be integrated out by mapping function? $$\phi_{t}(u) = \frac{1}{(2\pi\Sigma)^{d/2}} ...
0
votes
0answers
36 views

How to fit a Gaussian Mixture Model to data with correlated errors?

I'm restating this question in the hope of getting more interest. The usual function for scoring a Gaussian mixture model assumes independent measurements. But what if we have correlated measurements? ...
0
votes
1answer
54 views

How to estimate the noise variance of covSEiso covariance function for GPML code?

For the covariance function covSEiso: $$k(x^i,x^j)=\sigma_f^2\exp(-(x^i-x^j)^T{\rm diag}(l)^{-2}(x^i-x^j))+\sigma_n^2\delta_{ij}$$ in ...
0
votes
0answers
14 views

A binomial bandit v. a Gaussian process optimizer

I am reading about multi-armed bandits for web optimization, and I have come across a couple of options, two of which are the binomial bandit and the Gaussian process (an implementation here). Am I ...
1
vote
1answer
43 views

Determining whether time series is Gaussian from autocorrelations

Can one say anything about the "Gaussiness" of a time series merely by looking at its autocorrelations? I find this hard to reconcile. Let us say I find that there are significant autocorrelations in ...
0
votes
1answer
29 views

How to optimize Gaussian-process parameters for multiple tasks with GPML?

I have a lot of test curves and I want to optimize the length and scale parameters simultaneously for all curves. Is this possible?
0
votes
0answers
20 views

Does the curse of dimensionality apply to discriminative models?

I want to understand the curse of dimensionality better and where does/doesn't apply. I know about exponential volume growth and also the distances becoming not distinguishable from each other in ...
1
vote
0answers
67 views

How to reduce dimension of the sampling procedure?

I am stuck with this problem for a long time, hopefully I can get help here! Basically, I want to sample from a posterior distribution that looks like, \begin{align*} X &\sim ...
2
votes
2answers
30 views

How to implement Gaussian process using GPML toolbox with known output noise?

I want to implement a simple regression model using Gaussian process. I chose GPML toolbox of Rasmussen for simplicity. My question is how we can let the toolbox know that we already have a different ...
0
votes
0answers
30 views

Gaussian or Dirichlet Process from aggregated samples

For N individuals, I have the number of measurements taken per individual, the individual's mean measurement value, and the standard deviation of the individual's measurements, but I do not have ...
1
vote
1answer
57 views

Gaussian Process: Using partitions of a Cholesky decomposition solution for conditional deduction

If I define a GP over observed values, $y$, of a sensor reading over time, $t$, as (for simplicity assuming discrete time series e.g lets say readings after every 5 mins) : $y=f(t)+\epsilon$ where ...
0
votes
0answers
18 views

Find the bounding rectangle of a covariance matrix based on mahalanobis distance

I'm trying to develop an algorithm that makes use of the Mahalanobis distance from an arbitrary test point to assign a score to each observation in a dataset. I want to only consider observations ...
1
vote
1answer
28 views

Is derivative of a Gaussian Signal also Gaussian? How to find variance of signal that is obtained from differentiation of a Gaussian signal?

Could someone please let me know or give appropriate references for the question I have posed above. My main interest lies in applying Kalman filter for state estimation. The noise on sensor ...
1
vote
1answer
48 views

Posterior covariance from GPML toolbox

I am currently using the GPML toolbox to perform regression. Generally, after learning the hyperparameters we can extract the posterior mean and variance by using the function in the toolbox as ...
0
votes
1answer
44 views

What are the various basic kernels available?

I am currently following the book Gaussian Processes for Machine Learning by C.E. Rasmussen and C.K.I. Williams and I have come across various kernels in their Chapter 4 I have also gone through the ...
1
vote
2answers
72 views

Product of two gaussian processes

Given, $\ {y}_{i} = N({\mu}_{i}, {\Sigma }_{i}) $ If we go by the link http://www.tina-vision.net/docs/memos/2003-003.pdf then we can understand that the product of many multivariate gaussians can ...
1
vote
0answers
65 views

Polynomial transform of a Gaussian Random Variable

I have been trying to find how the PDF of a polynomial transform of a Gaussian Random Variable could be found. Eg: If \begin{equation} \ X\sim N(\mu,\sigma^2) \end{equation} Then what would be the ...
1
vote
0answers
20 views

If $E[X(t)X(s)]=t \land s $.Show that this process has independent increments

Let $X(t), t\ge0$ be a real-valued Gaussian process with mean zero and covariance function $E[X(t)X(s)]=t \land s $.Show that this process has independent increments.
2
votes
0answers
26 views

I want Find finite dimensional densities for an $\mathbb R^d-$ valued Gaussian process $X$with specified mean and covariance functions

Write the finite dimensional densities for an $\mathbb R^d-$ valued Gaussian process $X$with specified mean and covariance functions.
6
votes
1answer
109 views

What is the probability of observing some function given a gaussian process?

I would like to compare a parametric function to a Gaussian Process. This may sound weird, but read on: Data description. I am looking at projections of a 3D object. However I expect a certain amount ...
1
vote
0answers
20 views

Detecting mean difference between two observed stochastic processes

Suppose to collect real time two set of samples coming from two sources so defined: S1: gaussian(m1, s1) S2: gaussian(m1+m2, s1+s2) with probability p S2: gaussian(m1, s1) with probability ...
2
votes
1answer
70 views

Gaussian Process Prediction Uncertainty

I am using Gaussian Process Regression to interpolate my input points. I would like to measure the total uncertainty of my prediction thus I sum up the GPR prediction variances at all the testing ...
2
votes
2answers
45 views

Gaussian Process Regression with positive prediction weights

I want to do Gaussian Process Regression for a density function $f(x)$ with a gaussian kernel function $k(x, x')$. Given the training data $\mathbf{x} = (x_1, x_2, \dots, x_N)$ and $\mathbf{f} = ...
0
votes
2answers
108 views

Why does the density function has product of variance and covariance for higher model order time series

In my previous question Density function for AR model, the density function of AR model has the covariance-variance matrix given as $\sigma^2 *V_p$. In multivariate Gaussian distribution, the pdf ...
0
votes
1answer
93 views

Gradients of marginal likelihood of Gaussian Process with squared exponential covariance, for learning hyper-parameters

The derivation of gradient of the marginal likelihood is given in this pdf, equation 5.9. But the gradient for the most commonly used covariance function, squared exponential covariance, is not ...
0
votes
0answers
19 views

Gaussian based clustering/partitioning, does it make sense with not much data?

I have a dataset about hourly aggregated mobile phone usage (#calls, #sms, #internetConnections) in one mobile cell. For example I have this data about activity at 8:00am: ...
0
votes
1answer
15 views

Is it posible to find a derivative of the mean function of Gaussian process regression?

The mean function $\hat{\mu}(x_*)$ of GPR is $k(x_*, X)(k(X, X) + \sigma^2_w I)^{-1}Y$ where $k(\cdot, \cdot)$ is a kernel matrix or vector of appropriate size and is parametrized by some ...
0
votes
0answers
55 views

How to measure goodness of fit in a simple quadratic Gaussian GLM?

I hope this question will be specific enough, I went through many of the other questions about GLM but now I am even more confused because my sample size is small and it seems that R square (or pseudo ...
2
votes
1answer
105 views

Gaussian mixture vs. Gaussian process

As far as I know, both Gaussian mixtures as well as Gaussian processes can be used for regression. My question is: what is better and why? The answers might contain theoretic insights, practical ...
0
votes
0answers
57 views

meanZero error when trying to use GPML gp function to perform regression to predict y

I've trying to learn how to use Gaussian Process for Machine learning (GPML)to do some prediction stuff. My goal is to get the returned output ...
0
votes
2answers
56 views

overfit gaussian regression

I have recently read a lot of posts about how maximizing the marginal likelihood in Gaussian Regression can cause overfitting. What is the best way out then? If we let the hyperparameters take values ...
1
vote
1answer
26 views

Gaussian Process Regression Variance

While doing regression using Gaussian Processes, isn't the variance of the posterior supposed to be low where training data has already been observed?
2
votes
1answer
41 views

Stationary function

I am reading Karl Rasmussen's book on Gaussian processes and in the introductory chapter he has the following statement: ...
0
votes
1answer
96 views

Estimating correlation hyperparameters of a Gaussian Process

I have an actual function that I need to simulate using a GP model. I've not done this before so I'm unclear of the steps. I have used the true function at different values of the inputs ($\vec X1, ...
1
vote
1answer
102 views

Gaussian Process Regression/ Classification

How do we estimate parameters of the model while performing Gaussian Process Regression or Classification? While performing regression, we estimate parameters such that the model is the best fit to ...