Gaussian Process Regression
A model that places a prior directly over the space of possible functions, defined by a kernel, and predicts by conditioning that prior on observed data.
A kernel function measures how correlated two points' outputs should be based purely on their inputs, and predicting at a new point is conditioning a joint normal distribution on the training data — pure probability algebra, with predictive uncertainty falling directly out of the same calculation as the mean prediction.
The kernel-matrix inversion this requires costs O(n cubed), which is why Gaussian processes stay confined to small or medium-sized datasets rather than large-scale ones.