Questions tagged [gaussian-process]
The gaussian-process tag has no usage guidance.
30 questions
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Gaussian process binary classification: why are all latent function samples crossing 0 at the same location?
I am using a Gaussian process binary classifier on a multi-dimensional dataset with binary labels. The probability generally increases or decreases monotonically along each feature/dimension. For the ...
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Numpy implementation of Matern covariance kernel derivative
For my research, I'm making use of the Numpy implementation of the Matern covariance kernel.
To make sure I'm understanding what's happening, I try to derive the formulas inside the Numpy ...
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Gaussian Process not fitting well // nearly constant predictions
I am a PhD student trying to optimize a chemical engineering process with Bayesian Optimization. I have 5 variables and 3 objectives/responses I want to optimize, so I chose Botorch with the qneHVi ...
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Literature suggestions: Guarantees for GPs with subset of data
I am currently trying to solve the following problem:
Given a fixed set of query points (or if possible even better: a region where I want to obtain accurate predictions), approximate the GP such that ...
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Gaussian process regression not working in GPytorch and Scikit-learn, can't find suitable hyperparameters
This is a MWE of my problem, basically I want to find out the map between qin and qout using a Gaussian process and with that ...
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Performance difference between two equivalent ML codes
Using the two Python libraries GPyTorch and scikit-learn to perform Gaussian Process Regression (GPR) for a machine learning task, I have encountered a problem I failed to solve during the last days. ...
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Variational Learning of Inducing Variables in Sparse Gaussian Processes
In this paper - Variational Learning of Inducing Variables in Sparse Gaussian Processes
After equation (5), the statement:
Here, $p(\textbf{f}|\textbf{f}_m) = p(\textbf{f}|\textbf{f}_m, \textbf{y})$ ...
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Understanding the uncertainty in gaussian processes
Consider the following image:
which is an fitted GP. Note how $0 <= x <= 2$ yield a much higher uncertainty than e.g $5 <= x <= 8$.
Thus gps are good when dealing with the exploration vs ...
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How to improve computational performances in GaussianProcessRegressor?
I need to fit my GaussianProcessRegressor with a lot of data. In particular, I start fitting the GP with few data, and I add more at each step. Since I need to ...
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293
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On the time complexity of Bayesian linear regression and Gaussian process
By drawing analogy, I believe that Bayesian linear regression has a time complexity same to standard linear regression $𝑂(𝑛𝑝^2+𝑝^3)$ which is dominated by the number of features $p$ (What is the ...
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Can a simple distance to a few nearest data points be used a measure of the uncertainty of a prediction?
One of the 'selling points' of the Gaussian process regression is that it provides not only the model but also the uncertainty estimate of a prediction. Then usually a picture is shown with a curve ...
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How can I plot the covariance matrix of scikit-learn's Gaussian process kernel?
How can I plot the covariance matrix of a Gaussian process kernel built with scikit-learn?
This is my code
...
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Why GP posterior variance is the worst-case error?(exact proof)
I am reading this paper, which explains the connecting idea Gaussian Process and Kernel methods in detail. I am impressed by the insightful explanation in this paper, but am stuck on one part in ...
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How does bayesian optimization with gaussian processes work?
Could someone explain in simple words
what are gaussian processes
how does bayesian optimization work
and their combination?
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VC dimension for Gaussian Process Regression [closed]
In neural networks, the VC dimension $d_{VC}$ equals approximately the number of parameters (weights) of the network. The rule of thump for good generalization is then $N \geq 10 d_{VC} \approx 10 * (\...
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How do you choose a kernel for a discontinuous function in Gaussian Process Regression? [closed]
I'm doing Gaussian Process Regression and created a series of functions by gluing other functions together on random places. Here's an example:
Perhaps this one is to complicated, but all the ...
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Multivariate noise variance in Gaussian process prediction
In GP regression, we predict using $\mu^* = ... (K(X,X)+\sigma^2I)^{-1}...$
This is fine when the noise $\sigma$ is a scalar, but I am confused about what happens when $\sigma$ is Multivariate/...
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Sequential sampling from Gaussian conditional not working
I'm trying to sequentially sample from a Gaussian Process prior.
The problem is that the samples eventually converge to zero or diverge to infinity.
I'm using the basic conditionals described e.g. ...
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Data model with more outputs than inputs?
I am working on parametric studies in physics simulations, i.e. I vary some real input parameters (e.g. x0,x1,x2,x3) and get an output with a larger size (e.g. y0,y1 ... y100). Assuming that I have a ...
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Derivative of multi-output Gaussian Process
I am working on a project where I estimate transition and measurements models for a kalman filter using Gaussian Processes.
In order to linearize the models I require the Jacobian of the estimated ...
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GP derivative in GpyTorch
I am working on a project using GP-regression models to model transition and measurements models in a Kalman Filter. This means I need to be able to sample from the derivative of the original GP model....
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Hyperparameter tuning of neural networks using Bayesian Optimization
One of the assumptions for finding good hyperparameters using Bayesian optimization (GP) is that the unknown function is smooth. Is this assumption valid for neural networks or at least for most of ...
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Gaussian process regressor returns almost identical std for all datapoints
I am using a Gaussian process regressor as the regressor for active learning and I use its standard deviation to choose the next training inctance (the one with the highest std is chosen). However, ...
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Gaussian Process for Classification: How to do predictions using MCMC methods
Problem
I was reading about Gaussian Processes for regression in the "Gaussian Processes for Classification" textbook and in a few other online resources. Everywhere I look people seem to avoid ...
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Using a trained classifier in an Android app
As the title suggests, I'm attempting to train some different classifiers into an android app. The main question I have is how to represent the different models in a neat and effective way, from ...
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Advice on machine learning for small inputs and outputs
I am planning on using a machine learning algorithm to learn the mapping between sets of four coordinates (x,y,z + a distance d ...
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46
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What is a "variable index" in the Gaussian perspective?
I was going through this article about Gaussian processes, in which the author explains about the "variable index" in the form of a plot while writing about 2D Gaussian.
The explanation and plot are ...
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Is it possible to train probabilistic model to return several distributions?
I have nonlinear data of function y(x), which is let's say parabolic. At some points of x there are several y's (look at the picture).
Is it possible to train a probabilistic model to return several ...
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How exactly do Gaussian Processes (square dist kernel) enforce smoothness? (Aka how are they computed to do so?)
From:
http://www.cs.cmu.edu/~16831-f12/notes/F10/16831_lecture22_jlisee/16831_lecture22.jlisee.pdf
"Gaussian Processes artificially introduce correlation between close samples in that vector in order ...
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How to combine different kernels for Gaussian process in GPyTorch?
I am trying to learn gaussian process by using GPyTorch to fit a Gaussian Process Regression model. However, I can't figure out ...
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