Hi Fernando,
On Sun, Jun 29, 2014 at 1:53 PM, Fernando Paolo <fpa...@ucsd.edu> wrote:
> Hello,
>
> I must be missing something obvious because I can't find the "actual"
> coefficients of the polynomial fitted using LassoCV. That is, for a 3rd
> degree polynomial
>
> p = a0 + a1 * x + a2 * x^2 + a3 * x^3
>
> I want the a0, a1, a2 and a3 coefficients (as those returned by
> numpy.polyfit()). Here is an example code of what I'm after
>
> import numpy as np
> import matplotlib.pyplot as plt
> from pandas import *
> from math import *
> from patsy import dmatrix
> from sklearn.linear_model import LassoCV
>
> sin_data = DataFrame({'x' : np.linspace(0, 1, 101)})
> sin_data['y'] = np.sin(2 * pi * sin_data['x']) + np.random.normal(0, 0.1,
> 101)
> x = sin_data['x']
> y = sin_data['y']
> Xpoly = dmatrix('C(x, Poly)')
>
The development version of scikit-learn contains a transformer to do
exactly this:
http://scikit-learn.org/dev/modules/generated/sklearn.preprocessing.PolynomialFeatures.html
> n = 3
> lasso_model = LassoCV(cv=15, copy_X=True, normalize=True)
> lasso_fit = lasso_model.fit(Xpoly[:,1:n+1], y)
>
In scikit-learn, "fit" always returns the model itself so here
"lasso_model" and "lasso_fit" refer to the same thing.
lasso_predict = lasso_model.predict(Xpoly[:,1:n+1])
>
> a = np.r_[lasso_fit.intercept_, lasso_fit.coef_]
>
> b = np.polyfit(x, y, n)[::-1]
>
> p_lasso = a[0] + a[1] * x + a[2] * x**2 + a[3] * x**3
> p_polyfit = b[0] + b[1] * x + b[2] * x**2 + b[3] * x**3
>
> print 'coef. lasso:', a
> print 'coef. polyfit:', b
>
>
> The returned coefficients 'a' and 'b' are completely different, and while
> 'p_polyfit' is indeed the fitted polynomial of degree 3, 'p_lasso' makes no
> sense (plot to see). Unless 'b' is something else... If so, what actually
> are the coefficients returned by fit()? And how can I get the coefficients
> that reconstruct the fitted polynomial?
>
>
Why are you expecting a and b to be the same? np.polyfit returns a
least-squares fit so the model is different from a lasso.
You should use LinearRegression or Ridge with light regularization instead.
HTH,
Mathieu
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