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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36 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 ...
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7 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 ...
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2answers
34 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 ...
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7 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?
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1answer
25 views

Stationary function

I am reading Karl Rasmussen's book on Gaussian processes and in the introductory chapter he has the following statement: ...
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41 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, ...
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61 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 ...
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15 views

Digit recognition using GPML package

Is there any code in GPML package (http://www.gaussianprocess.org/) using which I can execute 10-class digit recognition problem? Because I notices that this is for binary classification. For n-class ...
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1answer
44 views

R Bayesian prediction of a Gaussian process

I have a Gaussian model with mean zero, variance is arbitrary constant, and correlation function $e^{-\theta(x-x')^2}$ where $\theta$ is again an arbitrary constant. I've plotted some realizations of ...
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13 views

periodic covariance function

"Gaussian processes can be completely defined by their second-order statistics.Thus, if a Gaussian process is assumed to have mean zero, defining the covariance function completely defines the ...
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19 views

Determine a distribution of a gaussian stochastic with different time

I would like to determine the autocorrelation function of a Gaussian stochastic. Let see my problem So my solution is The distribution of $y=x(t_1)-x(t_2)$ is also a Gaussian stochastic with ...
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17 views

Gaussian Processes: 2-output [latitude longitude] as regression output

I'm trying to model a problem where inputs are 100-d vectors and outputs are 2-d vector [latitude, longitude]. I need to perform prediction on new unseen 100-d vectors and find out the latitude and ...
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25 views

Stochastic linearization by irregular waves of ship roll motion equation

I'm interested in finding some way for doing "stochastic linearisation by irregular waves of ship roll motion equation". I found some publications about it but its hard for me to understand, how to ...
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23 views

How many models I need?

I am doing an estimation using a bunch of sparse data. Suppose that I have a 100x100 grid and 20 data is available on this 2D grid. One solution is to use a determiastic method and estimate the other ...
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1answer
38 views

Jaynes' Derivation of Herschel-Maxwell for Normal Distribution

I am reading the following paper: http://www-biba.inrialpes.fr/Jaynes/cc07s.pdf and cannot seem to figure out how Jaynes is deriving (P2) and below (specifically the log arithmetic ...
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6 views

Can a kernel function for GP-regression use measurement information?

when building a kernel function for a Gaussian-Process-Regression I am asking myself whether the kernel function is allowed to contain information from the measurements. To ask a little more general, ...
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0answers
33 views

How to apply Gaussian kernel to smooth density of points on 2D (theoretically)

I have a set of discrete points on a 2D surface and need to build a heat map or a distribution of the density of the points. However, I also need to smooth out the density/distribution by applying ...
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1answer
51 views

Why we check the residuals of ARIMA model for white Gaussian?

I have problem about the assumptions and model verification of ARIMA models. I know that Gaussian distributed assumption is not necessary for fitting ARIMA models but I wonder why a lot of people ...
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24 views

issue in using GP_fit() of GPfit package in R

I am trying to work with Gaussian process through GPfit package of R but every time I use GP_fit() of this package, either it ...
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0answers
33 views

Gaussian Process Regression with additional Basis Functions

I'm working through Rasmussen's Gaussian Processes book, and I have a question about the possibility of optimizing additional basis function hyperparameters (in section 2.7 ...
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0answers
27 views

Low pass filter to maintain edge information

I am looking for a kernel as low pass filter that satisfy as:I must find a kernel that statisfies as follows: In the my reference paper, the author suggest gaussian kernel that is The gaussian ...
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1answer
72 views

How to find $E[x|y]$ when distributions of y and x are separately known,(p.s. they are both Gaussian)?

In detail, I have these relations (in order of causality): $u_1 = ax_0$ $x_1 = u_1 + x_0$ $y = x_1 + w$ where $w = N(0,1), x_0 = N(0,\sigma^2)$. This was my approach: I know the distribution of ...
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1answer
267 views

Which is kernel similar gaussian kernel?

I must find a kernel that statisfies as follows: In the my reference paper, the author suggest gaussian kernel that is The purpose of that kernel is that it will take a weight for each points ...
2
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1answer
79 views

How to understand the log marginal likelihood of a Gaussian Process?

I'm trying to understand Gaussian Processes. Could anyone tell me: Why we need to use the log marginal likelihood? Why using log, the marginal likelihood can be decomposed to 3 terms (including a ...
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0answers
24 views

Combining independent Gaussian probabilities

I am using three Gaussian distributions with which I generate random numbers to represent many candidate xyz points. I use some selection criteria (details not particularly relevant) to decide on ...
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16 views

Is my interpretation of a Hierarchical Gaussian Process model correct?

I'm learning about GPs in hopes that it'll be the tool I need to deal with the common scenario I encounter where I have a continuous predictor variable whose effect might not be linear. I think I ...
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0answers
7 views

How can one understand the projection of a general Gaussian onto the sphere?

Let $N(0,\Sigma)$ be a Gaussian distribution with mean $0$ and covariance $\Sigma$, a $p\times p$ matrix. Is there an understanding the distribution $\mathcal{P}_{\mathbb{S}^{p-1}} (N(0,\Sigma))$? Is ...
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25 views

Confusion related to derivation of a formula in gaussian process

I was reading this paper related to online Gaussian processes. I didn't get how equation set 2 was derived. Any suggestions?
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19 views

Confusion related to posterior gaussian process

I was reading this [paper][1] related to sparse online gaussian processes. However, I didn't get how the denominator in the equation 1 was derived? It was supposed ...
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1answer
243 views

Why is this likelihood function equal to the noise PDF?

My professor has this slide up here: Here, $y$ is an observed signal. $H$ is a deterministic transformation, which is assumed known. $f$ is the original signal (which we dont know), and $w$ is ...
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0answers
22 views

Deviation from Gaussian smoothed curve and relation of its derivatives to the results [closed]

I was plotting a deviation of my data points from a Gaussian smoothed curve depending on different properties of this Gaussian curve that smooths the series. So I had a series of: ...
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1answer
38 views

Differential Entropy of Gaussian Process

I have $N$ datapoints that have $d$ features in a GP and their covariance matrix $K$ and I want to calculate the differential entropy of that GP. Is this formula right? $E(I)= \frac{1}{2} ...
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1answer
63 views

Random forest ML algorithm suitable for use on cluster based HPC?

I have developed a script using pythons scipy package to analyse a rather large model that I wish to solve, the model contains over 12gb of data, including over 500 parameters. Now running small ...
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2answers
73 views

Likelihood vs. noise kernel hyperparameter in GPML Toolbox

I'm using GPML toolbox by C.E.Rasmussen to solve the basic GP regression problem (presented in the book) with noisy observations. That is to say, estimate the underlying function $f$ of a static noisy ...
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2answers
51 views

Gaussian sampling in high dimension

I have a covariance function $f(x)$, where $x = (x_1, x_2, x_3)$ is a point in three-dimensional space. I need to generate a Gaussian field with given covariance function on a 3D grid of points, that ...
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1answer
30 views

Gaussian Process and Expectation Propagation time complexity?

What's the time complexity of training a Gaussian process and its Expectation Propagation approximation? (Before studying them, I'd like to understand if they are even feasible for my application)
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46 views

How to create a new covariance function using GPML toolbox in Matlab?

I want to create my own covariance function based on squared exponential or Matern that treats each dimension differently i.e. having a hyperparameter for each dimension, not just ell. How do I need ...
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1answer
33 views

Gaussian Process for Closed Curves

A Gaussian process gives a probability distribution over functions that pass through the data points. Is there a way to parameterize the Gaussian process to give a probability distribution over closed ...
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1answer
46 views

Glm gaussian Vs Glm Binomial Vs s log-linked GLM Gaussian

I am trying to do a study on death of malaria in certain in order to estimate the best way to predict how dangerous is this disease. I don't have a strong background in statistics, I am auto-learner ...
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0answers
29 views

What Gaussian process covariance function captures an affine mean?

In the documentation for GPML, the author trained a GP with an affine mean function and isotropic squared exponential covariance function. Then there is an exercise to the reader: Try training a ...
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1answer
63 views

Linear Kernel in Baysian Linear Regression

I came up with http://mlg.eng.cam.ac.uk/duvenaud/cookbook/index.html and it is actually very useful. At some point it says If you use just a linear kernel in a GP, you're simply doing Bayesian ...
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0answers
70 views

Derive squared exponential covariance function

In Gaussian Processes, SVMs, kernels are used (as to my understanding) as similarity measure. However, they have the constraint that any kernel has to be represented as a dot product. i.e. ...
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0answers
110 views

Gaussian Process , selecting the hyperparameters

I am using Gaussian Process regression toolbox from the site http://www.gaussianprocess.org/gpml/code/matlab/doc/ I was able to use implement the code in matlab easily, following the guide lines. ...
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0answers
37 views

Difference between summing and multiplying covariance matrices?

Say we have an RBF covariance matrix A and some periodic covariance matrix B for a given dataset. Covariance matrix A says that you believe that points that are close together are somewhat similar, ...
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0answers
25 views

Variance estimation from two gaussian distributions

Assume a stochastic process with observation $r$, and two hypotheses : $X \sim (0, \sigma^2)$ and $Y \sim (0, \sigma^2 + \tau^2)$. When we observe/receive $r$ we don't know which hypothesis $X$ or ...
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0answers
15 views

Neighborhood in Gaussian graphical models

A gaussian random vector $X$ can be represented using a graph where two nodes $a$ and $b$ are connected $\Leftrightarrow X_a$ is dependent on $X_b$ given all the remaining random variables. I have two ...
2
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1answer
242 views

Gaussian Process Kernel and Ridge Regression

Can a Dual Ridge Regression produce the same prediction results as a Gaussian Process with a polynomial kernel $K(x,x')=(x^Tx'+1)^2$ in less time complexity (GP is $O(n^3)$ ) using Cholesky ...
1
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1answer
103 views

Gaussian Regression With Multiple Inputs?

Is it possible to use a Gaussian Process to relate multiple independent input variables (X1, X2, X3) to an output variable (Y)? More specifically, I would like to produce a regression graph like the ...
1
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2answers
365 views

Multi-target Tracking: calculate the association gate from Kalman filter

I'm trying to implement a multi target tracking with Kalman filter. Each object has an instance of Kalman Filter. The true position of the objects $(x,Y)$ are the corrected state out of the KF after ...
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2answers
431 views

Is it possible to convert a Rayleigh distribution into a Gaussian distribution?

...and how might we do this? If possible, I am curious if outliers in the Rayleigh distributed data would also remain outliers in the new Gaussian distributed data. Thanks.