- #1

- 46

- 1

**y**=

**w**

^{T}xyou then define your loss function as

1/n Σ

^{n}(w

_{i}*x

_{i}-y

_{i})

^{2}

then you take the partial derivatives with respect to

**w**set it equal to zero and solve.

So now I want to use a non-linear basis functions, lets say I want to use m gaussians basis functions, φ

_{i}, the procedure is the same but I am not sure exactly on the construction of the model. Lets say I have L features is the model equation of the form

y

_{n}=Σ

^{m}Σ

^{L}w

_{i}φ

_{i}(x

_{j})

in other words I have created a linear combination of M new features, φ(

**x**), which are constructed with all L of the previous features for each data point n:

y

_{n}=w

_{0}+w

_{1}(φ

_{1}(x

_{1})+φ

_{1}(x

_{2})...+...φ

_{1}(x

_{L}) ......+......w

_{m}(φ

_{1}(x

_{1})+φ

_{2}(x

_{2})...+...φ

_{m}(x

_{L}))

where x

_{i}are features / variables for my model and not data values? I hope this makes sense. Thanks in advance.