Running your code and then plotting
plt.plot(x, lasso_predict)
plt.plot(x, y)
shows a pretty good correspondence (r^2 = .97)!
I think the problem is that Xpoly does not contain raw polynomials as you
use for prediction.
If you do
p_lasso = a[0] + a[1] * Xpoly[:, 1] + a[2] * Xpoly[:, 2] + a[3] * Xpoly[:,
3]
then it works. The polynomials in Xpoly are actually not pure monomials,
and they are scaled with a certain rule in order not to explode.
On Sun, Jun 29, 2014 at 6:53 AM, 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)')
>
> n = 3
> lasso_model = LassoCV(cv=15, copy_X=True, normalize=True)
> lasso_fit = lasso_model.fit(Xpoly[:,1:n+1], y)
> 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?
>
> Thank you,
> -fernando
>
> PS: If this is mentioned in any documentation, I couldn't find it.
>
>
>
> --
> Fernando Paolo
> Institute of Geophysics & Planetary Physics
> Scripps Institution of Oceanography
> University of California, San Diego
> 9500 Gilman Drive
> La Jolla, CA 92093-0225
>
>
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http://p.sf.net/sfu/Bonitasoft
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