A Visual Exploration of Gaussian Processes (2019)
8 days ago
- #Machine Learning
- #Regression
- #Gaussian Processes
- Gaussian processes (GPs) are a powerful tool in machine learning for solving regression problems.
- GPs are based on the mathematical foundation of multivariate Gaussian distributions, defined by a mean vector and covariance matrix.
- Key operations for GPs include marginalization and conditioning, which are closed under Gaussian distributions.
- Marginalization allows extracting partial information, while conditioning enables Bayesian inference by updating probabilities based on new data.
- GPs use kernels (covariance functions) to define the covariance matrix, influencing the shape and characteristics of the predicted function.
- Kernels can be stationary (e.g., RBF, periodic) or non-stationary (e.g., linear), and can be combined to model complex data trends.
- The prior distribution in GPs assumes a mean of zero, and the posterior distribution is derived by conditioning on observed training data.
- GPs can model measurement errors by adding an error term to training points, leading to more realistic predictions.
- Combining kernels (e.g., linear + periodic) can capture both global trends and local patterns in the data.
- GPs are flexible and can be extended, such as by learning specialized kernels using deep learning.