Quan Nguyen - But what is a Gaussian process? Regression while knowing how certain you are

Gaussian Processes (GPs) provide regression predictions with uncertainty quantification through error bars and confidence intervals

GPs are a generalization of multivariate Gaussian distributions to infinite dimensions, allowing modeling of correlations between variables

Key components of GPs include a mean function (often set to zero) and a covariance function that determines similarity between points

Uncertainty behaves differently for interpolation vs extrapolation:

• Lower uncertainty when interpolating between training points
• Higher uncertainty when extrapolating far from training data

Covariance functions determine how similarity is measured between points:

• Higher correlation for nearby points
• Lower correlation for distant points
• Common choice is radial basis function (RBF) kernel

GPs automatically handle the tradeoff between:

• Exploitation (using known information)
• Exploration (accounting for uncertainty)

Applications include:

• Bayesian optimization for expensive black-box functions
• Housing price prediction with uncertainty estimates
• Decision making under uncertainty

Implementation in Python possible through libraries like GPyTorch

GPs address limitations of traditional ML models that only provide point estimates without uncertainty quantification

Mathematical foundation based on properties of multivariate Gaussian distributions and their posterior updates with new observations