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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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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11 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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18 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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35 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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27 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
46 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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19 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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23 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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24 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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266 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 ...
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1answer
68 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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22 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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14 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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6 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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24 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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18 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
241 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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18 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
36 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
58 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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63 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
50 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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38 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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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
38 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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27 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
60 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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59 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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103 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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35 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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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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14 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 ...
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1answer
211 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 ...
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1answer
87 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 ...
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2answers
302 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
391 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.
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304 views

Kalman filter equation derivation

I'm studying the Kalman Filter for tracking and smoothing. Even if I have understood the Bayesian filter concept, and I can efficiently use some of Kalman Filter implementation I'm stucked on ...
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1answer
37 views

Why X-process is called a process?

I have recently learnt about kernels in machine learning. And I have been introduced to many different processes e.g. Gaussian process, Wiener process. Now my question is why a set of functions has ...
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2answers
496 views

Is expectation the same as mean?

I am doing ML at my university, and the professor mentioned the term Expectation (E), while he was trying to explain us some things on Gaussian processes. But from the way he explained it, I ...
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52 views

Shouldn't a function of data from a PDF repeated over and over on new data eventually yield a Gaussian PDF?

I got into an interesting discussion with a co-worker today and we are not sure what the answer is: We have $N=1000$ samples from a Rayleigh PDF. We take those $N$ samples, and compute their ...
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1answer
98 views

Is Gaussian process regression a Bayesian method?

Actually I thought Gaussian Process is a kind of Bayesian method, since I read many tutorials in which GP is presented in Bayesian context, for example, in this tutorial, just pay attention to page ...
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56 views

derivation of predictive distribution of Gaussian Process

There is a duplicate, and the reason why I still ask this question is that, the answer to that duplicate doesn't answer the question well. The Gaussian Process prior is $$u\sim GP(0,k(x,x'))$$, I ...
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25 views

Large scale 1-Dimensional Gaussian Process Classification

I have a dataset with a small number of input points (e.g. +- 300), but millions of boolean outcomes. ...
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17 views

generating covariance matrices from multiple priors

In many optimisation problems, one typically uses many forms of regularisations over the parameters that is being estimated. For example, a typical cost function (to maximise) may look like this: $$ ...
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1answer
140 views

Trying to understand Gaussian Process

I'm reading the GPML book and in Chapter 2 (page 15), it tells how to do regression using Gaussian Process(GP), but I'm having a hard time figuring how it works. In Bayesian inference for parametric ...
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1answer
87 views

What's the point of estimating the posterior distribution $Y | X $ using a Gaussian Process?

So classic regression methods (ridge regression, LASSO) only predict the posterior mean $E[ Y | X ]$, while Gaussian Processes give you the full posterior distribution $Y | X$. It would be very ...