Questions tagged [gaussian-process]
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 regression and classification problems.
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Preventing Shrinking towards the mean in Bayesian Modelling
I am working on a model where I am aiming to predict influenza in geographic regions. In my case I aiming to predict influenza cases in high resolution regions using low resolution data. I am using a ...
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Defining epistemic and aleatoric uncertainty in GPR
Gaussian Process Regression (GPR) enables uncertainty quantification by modeling the posterior distribution of functions. Given observed data, the latent function is the mean of the posterior ...
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Gaussian order statistics
Let $X=(X_1, X_2, \dots, X_n)$ a centered gaussian vector with a positive covariance matrix and $X_{(1)} < X_{(2)} < \dots < X_{(n)}$ his increasing rearrangement. Let $k\in \{2, 3, \dots, n-...
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Gaussian process regression when the function output is not directly observable
I have a situation where I have a number of entities, and wish to model a function which maps the feature of each entity to an output value ($f(\mathbf{x}_i) = \hat{y}_i$). However, I do not have the ...
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Theory of the conditional distribution on continuous observations for Gaussian processes
This topic arises from my study concerning Gaussian processes. Given a zero-mean Gaussian process with covariance function $k(x,x')$, i.e. $f(x)\sim\mathcal{GP}(0,k(x,x'))$, with finite observations $(...
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Mechanistic parameter inference via emulator / surrogate model
$\def\X{\vec X}\def\Y{\vec Y}$
We have a semi-expensive stochastic model $M: \X \mapsto \Y$ having ~10 continuous-valued parameters $\X$ (e.g. mean rates of state change) and producing ~10 continuous-...
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High-Dimensional Function Approximation with Uncertainty Quantification
Gaussian Processes are considered the gold-standard for regression with formal uncertainty guarantees. For this reason, they are used extensively to model system dynamics by researchers in the domain ...
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How to model both clustering and inhibition between marks in multitype point patterns (spatial transcriptomics)?
I have a large dataset from spatial transcriptomics. This is essentially a dense (>c.75million) multitype (~500) marked point pattern dataset where each mark is a gene label, and each point is ...
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Am I doing uncertainty quantification for Gaussian Processes incorrectly or are my predictions just that bad? (GPyTorch)
Quick overview of my data; I have nearly 300 samples and around 40 features (33 numerical, 7 are encoded as 0's and 1's because they were categorical), so definitely a high dimensional dataset. I use ...
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Quantification of departure from gaussianity in residuals of inhomogeneous time series model
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I applied a Gaussian process regression on several inhomogeneous time series. The GP kernels were motivated by a physical understanding of the phenomenon; the posteriors are well-sampled and ...
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Large errors with log-transformed Gaussian process regression?
I am working with some data in which the output target values $(Y)$ are all strictly positive values, essentially in the range of 0.001 to 100. Since these values can inherently never be negative or ...
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Modifying Gaussian Processes and/or using transformations for dealing with positive-only output values? [closed]
I've been reading into different Gaussian processes recently to better fit some data that I'm working with. My data clearly does not follow a multivariate Gaussian as required for a standard exact ...
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On the condition number of Gaussian sample-covariance matrices
The Gaussian kernel is special as discussed in $\text{Kostinski & Koivunen}^{\color{magenta}{\dagger}}$. The solution of the corresponding linear system is highly sensitive, and there are "...
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Difference between the posterior and posterior predictive of a Gaussian process
There is a similar question that was asked here: Gaussian processes: posterior vs. predictive distributions but it never received any attention and so I am re-asking the question although the emphasis ...
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Fit symmetrical Gaussian Mixture with small sample size?
How to fit symmetrical ($\mu_i=0$) gaussian mixture model? When the sample size is very small.
We assume that sample generated by Symmetrical Gaussian Model of 3 components (stock log returns).
How to ...
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