So I am currently learning some regression techniques for my research and have been reading a text that describes linear regression in terms of basis functions. I got linear basis functions down and no exactly how to get there because I saw this a lot in my undergrad basically, in matrix notation(adsbygoogle = window.adsbygoogle || []).push({});

y=w^{T}x

you 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 towset 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.

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# A Linear Regression with Non Linear Basis Functions

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