Multivariate polynomial regression with numpy

Question

I have many samples (y_i, (a_i, b_i, c_i)) where y is presumed to vary as a polynomial in a,b,c up to a certain degree. For example f

Answer 1

sklearn has a nice example using their Pipeline here. Here's the core of their example:

polynomial_features = PolynomialFeatures(degree=degrees[i],
                                         include_bias=False)
linear_regression = LinearRegression()
pipeline = Pipeline([("polynomial_features", polynomial_features),
                     ("linear_regression", linear_regression)])
pipeline.fit(X[:, np.newaxis], y)

You don't need to transform your data yourself -- just pass it into the Pipeline.