def natural_cubic_spline(*,
X: pd.Series,
y: pd.Series,
number_knots: int,
list_knots: List[int] = None) -> Pipeline:
"""
Piecewise natural cubic spline helper function
If number_knots is given, the calculated knots are equally-spaced
within minval and maxval. The endpoints are not included as knots.
The X series must be in increasing order.
The y series must not contain missing values.
Parameters
----------
X : pd.Series
The data series of the abscissa.
y : pd.Series
The data series of the ordinate.
number_knots : int
The number of knots for the spline.
list_knots : List[int] = None
A list of specific knots.
Returns
-------
p: Pipeline
The model object.
Example
-------
>>> import matplotlib.pyplot as plt
>>> import datasense as ds
>>> X = ds.random_data(distribution="uniform").sort_values()
>>> y = ds.random_data(distribution="norm")
>>> p = ds.natural_cubic_spline(
>>> X=X,
>>> y=y,
>>> number_knots=10
>>> )
>>> fig, ax = ds.plot_scatter_line_x_y1_y2(
>>> X=X,
>>> y1=y,
>>> y2=p.predict(X)
>>> )
>>> plt.show()
"""
if list_knots:
spline = NaturalCubicSpline(knots=list_knots)
else:
spline = NaturalCubicSpline(max=max(X),
min=min(X),
n_knots=number_knots)
p = Pipeline([("natural_cubic_spline", spline),
("linear_regression", LinearRegression(fit_intercept=True))])
p.fit(X, y)
return p
def simple_spline_specification(name, knots):
select_name = "{}_select".format(name)
spline_name = "{}_spline".format(name)
return Pipeline([
(select_name, ColumnSelector(name=name)),
(spline_name, NaturalCubicSpline(knots=knots))
])
def make_natural_cubic_regression(n_knots, knot_range=(-2, 2)):
"""A helper function for constructing a pipeline fiting a one dimensional
regression with a cubic spline feature."""
return Pipeline([
('standardizer', StandardScaler()),
('nat_cubic', NaturalCubicSpline(knot_range[0], knot_range[1], n_knots=n_knots)),
('regression', LinearRegression(fit_intercept=True))
])
def simple_spline_specification(name, knots):
'''
making a lot of these simple spline specifications, let's write a small function to make them for us.
income_spec = Pipeline([
('Income_select', ColumnSelector(name="Income")),
('Income_spline', NaturalCubicSpline(knots=[25, 50, 75, 100, 125]))
])
'''
select_name = "{}_select".format(name)
spline_name = "{}_spline".format(name)
return Pipeline([
(select_name, ColumnSelector(name=name)),
(spline_name, NaturalCubicSpline(knots=knots))
])
def make_natural_cubic_regression(n_knots):
return Pipeline([
('standardizer', StandardScaler()),
('nat_cubic', NaturalCubicSpline(-2, 2, n_knots=n_knots)),
('regression', LinearRegression(fit_intercept=True))
])
def make_natural_cubic_regression(n_knots):
return Pipeline([
('standardizer', StandardScaler()),
('nat_cubic', NaturalCubicSpline(-2, 2, n_knots=n_knots)),
('regression', HuberRegressor())
])