`tags: [AI/Tasks/Regression, AI/Regression ]`

Gaussian Process Regression (GPR) is a non-parametric probabilistic model used for Regression tasks. Unlike traditional Regression methods that define a fixed functional form for the relationship between inputs and outputs, GPR treats the relationship as a distribution over functions. This distribution is defined by a mean function and a covariance function, which captures the uncertainty or confidence associated with predictions at different input points.

**Notes**

- GPR is particularly useful for tasks where uncertainty estimation is crucial, as it provides not only predictions but also confidence intervals around those predictions.
- GPR is a flexible and powerful tool, capable of capturing complex nonlinear relationships in the data.
- The choice of covariance function, often referred to as the kernel function, significantly influences the behavior of the Gaussian process and its ability to model different types of data.
- GPR inherently provides measures of uncertainty, making it valuable in scenarios where understanding prediction confidence is essential, such as in financial forecasting, healthcare, or physics-based simulations.
- The main drawbacks of GPR lie in its computational complexity, especially for large datasets, and its scalability with respect to the number of input features.
- Despite its computational demands, GPR is a valuable technique in situations where high-fidelity predictions and uncertainty quantification are required.

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