def select_penweight_kfold(self,
alphas=None,
cv_iterator=None,
cost=None,
k_folds=5,
k_grid=11):
"""find alphas by k-fold cross-validation
Warning: This estimates ``k_folds`` models for each point in the
grid of alphas.
Parameters
----------
alphas : None or list of arrays
cv_iterator : instance
instance of a cross-validation iterator, by default this is a
KFold instance
cost : function
default is mean squared error. The cost function to evaluate the
prediction error for the left out sample. This should take two
arrays as argument and return one float.
k_folds : int
number of folds if default Kfold iterator is used.
This is ignored if ``cv_iterator`` is not None.
Returns
-------
alpha_cv : list of float
Best alpha in grid according to cross-validation
res_cv : instance of MultivariateGAMCVPath
The instance was used for cross-validation and holds the results
Notes
-----
The default alphas are defined as
``alphas = [np.logspace(0, 7, k_grid) for _ in range(k_smooths)]``
"""
if cost is None:
def cost(x1, x2):
return np.linalg.norm(x1 - x2) / len(x1)
if alphas is None:
alphas = [np.logspace(0, 7, k_grid) for _ in range(self.k_smooths)]
if cv_iterator is None:
cv_iterator = KFold(k_folds=k_folds, shuffle=True)
gam_cv = MultivariateGAMCVPath(smoother=self.smoother,
alphas=alphas,
gam=GLMGam,
cost=cost,
endog=self.endog,
exog=self.exog_linear,
cv_iterator=cv_iterator)
gam_cv_res = gam_cv.fit()
return gam_cv_res.alpha_cv, gam_cv_res
def test_multivariate_gam_cv():
# SMOKE test
# no test is performed. It only checks that there isn't any runtime error
def cost(x1, x2):
return np.linalg.norm(x1 - x2) / len(x1)
cur_dir = os.path.dirname(os.path.abspath(__file__))
file_path = os.path.join(cur_dir, "results", "prediction_from_mgcv.csv")
data_from_r = pd.read_csv(file_path)
# dataset used to train the R model
x = data_from_r.x.values
y = data_from_r.y.values
df = [10]
degree = [5]
bsplines = BSplines(x, degree=degree, df=df)
# y_mgcv is obtained from R with the following code
# g = gam(y~s(x, k = 10, bs = "cr"), data = data, scale = 80)
alphas = [0.0251]
alphas = [2]
cv = KFold(3)
gp = MultivariateGamPenalty(bsplines, alpha=alphas) # noqa: F841
gam_cv = MultivariateGAMCV(smoother=bsplines,
alphas=alphas,
gam=GLMGam,
cost=cost,
endog=y,
exog=None,
cv_iterator=cv)
gam_cv_res = gam_cv.fit() # noqa: F841
def test_multivariate_gam_cv_path():
def sample_metric(y1, y2):
return np.linalg.norm(y1 - y2) / len(y1)
cur_dir = os.path.dirname(os.path.abspath(__file__))
file_path = os.path.join(cur_dir, "results", "prediction_from_mgcv.csv")
data_from_r = pd.read_csv(file_path)
# dataset used to train the R model
x = data_from_r.x.values
y = data_from_r.y.values
se_from_mgcv = data_from_r.y_est_se # noqa: F841
y_mgcv = data_from_r.y_mgcv_gcv # noqa: F841
df = [10]
degree = [6]
bsplines = BSplines(x, degree=degree, df=df, include_intercept=True)
gam = GLMGam
alphas = [np.linspace(0, 2, 10)]
k = 3
cv = KFold(k_folds=k, shuffle=True)
# Note: kfold cv uses random shuffle
np.random.seed(123)
gam_cv = MultivariateGAMCVPath(smoother=bsplines,
alphas=alphas,
gam=gam,
cost=sample_metric,
endog=y,
exog=None,
cv_iterator=cv)
gam_cv_res = gam_cv.fit() # noqa: F841
glm_gam = GLMGam(y, smoother=bsplines, alpha=gam_cv.alpha_cv)
res_glm_gam = glm_gam.fit(method='irls',
max_start_irls=0,
disp=1,
maxiter=10000)
y_est = res_glm_gam.predict(bsplines.basis)
# plt.plot(x, y, '.', label='y')
# plt.plot(x, y_est, '.', label='y est')
# plt.plot(x, y_mgcv, '.', label='y mgcv')
# plt.legend()
# plt.show()
# The test compares to result obtained with GCV and not KFOLDS CV.
# This is because MGCV does not support KFOLD CV
assert_allclose(data_from_r.y_mgcv_gcv, y_est, atol=1.e-1, rtol=1.e-1)
# Note: kfold cv uses random shuffle
np.random.seed(123)
alpha_cv, res_cv = glm_gam.select_penweight_kfold(alphas=alphas, k_folds=3)
assert_allclose(alpha_cv, gam_cv.alpha_cv, rtol=1e-12)