Local constancy and smoothness priors are commonly used methods to ensure that learned functions are locally constant or smooth. These priors rely on the assumption that a function should satisfy $f(x) \approx f(x+\epsilon)$ for a small $\epsilon$. For example, $k$-nearest neighbor algorithms directly copy output values from nearby data points, while most kernel methods interpolate between nearby data points.

Smoothness priors work best for functions with sufficient examples and low dimensionality. However, more complicated functions can be estimated and generalized effectively by dividing their domain into regions and using underlying assumptions to associate each region. For instance, a function with $O(2^k)$ regions can be defined by $O(k)$ examples if additional assumptions are used to connect these regions.