# Non-linear Regression

For example suppose I've data set which looks like:

[[x,y,z],
[1,2,5],
[2,3,8],
[4,5,14]]


It's easy to find the theta parameters from those tiny data set. Which is theta = [1,2,0]

z = 1*x + 2*y + 0


But if my data set are non linear. Suppose:

[[x,y,z],
[1,2,6],
[2,3,15]]]


If i choose the mapping function to be of: z = xy+yy

It would return the theta parameter :

theta = [1,1,0]


So my deal is how to choose such mapping function for data sets which varies over time. As in recommender system the user rating varies as per the time, to reduce the cost. I've recently gone through regularization. Is there any other ideas for reducing the cost.

I believe your problem of choosing mapping function for non linear regression can be solved by using Support Vector Machines.

SVMs can learn non linear mapping functions in a kernel-induced feature space. What this means is in svms , the basic idea is to map the input data X into some high dimensional feature space f using a non linear mapping (kernel) and then doing linear regression in this feature space.