$\bullet$ Local constancy and smoothness priors are mostly used "priors". they are the methods to ensure the learned functions are locally constant or smooth. They need to be f(x)=f(x+c). For example, k-nearest neighbor copy directly data from nearby while most kernel interpolate between nearby data.

$\bullet$ The smoothness works best for function with enough examples and do not have lots of dimensions. However, there are methods to represent and estimate complicated functions.

$\bullet$ Complicated functions can be estimated and generalized well- by dividing regions and use underlying assumption to associate each regions. For example, a function with O(2^k) regions can be defined by O(k) examples and use additional assumptions to connect these regions(Chapter 2.5.11).