7 1 Feature Expansions | Machine Learning

FEATURE EXPANSIONS AND DOT PRODUCTS
What expansion should I use?
This is not obvious. The illustrations required knowledge about the data that
we likely won’t have (especially if it’s in high dimensions).
One approach is to use the “kitchen sink”: If you can think of it, then use it.
Select the useful features with an ‘1 penalty
w‘1 = arg min
w
nXi=1
f(yi; φ(xi); w) + λkwk1:
We know that this will find a sparse subset of the dimensions of φ(x) to use.
Often we only need to work with dot products φ(xi)Tφ(xj) ≡ K(xi; xj). This
is called a kernel and can produce some interesting results.
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