Is there a threshold for the amount of data that Gaussian process regression can reproduce?

I am working with a GPR model, however, with a shorter amount of data it work very well, and develop the metamodel very fast. Nevertheless, I need to test a larger dataset, and it has been running for several hours without success. Hence, I want to know if there are any limitations on GPR concerning the amount of data capable to be reproduced.

Thanks

Answer 1

[Vaibhav]

Hi Rafael,

It is my understanding that clarification is sought concerning the extended runtime of Gaussian Process Regression (GPR) when comparing a large dataset to the shorter runtime observed with a smaller dataset.

In MATLAB, Gaussian Process Regression (GPR) does not have any specific limitations on the amount of data that can be used for training the model. However, the computational complexity of GPR can increase with the size of the dataset, which can lead to longer training times for larger datasets.

The time complexity of GPR is “O(n^3)”, where “n” is the number of data points in the training set. This means that as the number of data points increases, the computational cost of training the GPR model grows significantly. Therefore, training a GPR model on a larger dataset can take more time and computational resources compared to a smaller dataset.

To address this issue, consider the following strategies:

1. Feature selection or dimensionality reduction: If the dataset has a large number of features or dimensions, try reducing the dimensionality by selecting relevant features or applying dimensionality reduction techniques. This can help reduce the computational burden and improve training times.

2. Subset sampling: Instead of using the entire dataset, consider sampling a subset of the data for training the GPR model. By selecting a representative subset, this can still obtain reasonable results while reducing the computational requirements.

3. Parallel processing: leverage parallel processing to distribute the computational workload across multiple cores or machines. This can help speed up the training process for larger datasets.

4. Optimization techniques: Consider using optimization techniques to improve the efficiency of the GPR model training process. This may involve selecting appropriate hyperparameters, using sparse approximations, or employing specialized algorithms designed for large-scale GPR.

Please refer to the following documentations for more information:

https://in.mathworks.com/help/stats/fitrgp.html

https://in.mathworks.com/help/stats/gaussian-process-regression-models.html

https://in.mathworks.com/help/stats/gaussian-process-regression.html

Hope this help!

Regards,

Vaibhav