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ai-content-maker/.venv/Lib/site-packages/sklearn/preprocessing/_polynomial.py

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2024-05-03 04:18:51 +03:00
"""
This file contains preprocessing tools based on polynomials.
"""
import collections
from itertools import chain, combinations
from itertools import combinations_with_replacement as combinations_w_r
from numbers import Integral
import numpy as np
from scipy import sparse
from scipy.interpolate import BSpline
from scipy.special import comb
from ..base import BaseEstimator, TransformerMixin, _fit_context
from ..utils import check_array
from ..utils._param_validation import Interval, StrOptions
from ..utils.fixes import parse_version, sp_version
from ..utils.stats import _weighted_percentile
from ..utils.validation import (
FLOAT_DTYPES,
_check_feature_names_in,
_check_sample_weight,
check_is_fitted,
)
from ._csr_polynomial_expansion import (
_calc_expanded_nnz,
_calc_total_nnz,
_csr_polynomial_expansion,
)
__all__ = [
"PolynomialFeatures",
"SplineTransformer",
]
def _create_expansion(X, interaction_only, deg, n_features, cumulative_size=0):
"""Helper function for creating and appending sparse expansion matrices"""
total_nnz = _calc_total_nnz(X.indptr, interaction_only, deg)
expanded_col = _calc_expanded_nnz(n_features, interaction_only, deg)
if expanded_col == 0:
return None
# This only checks whether each block needs 64bit integers upon
# expansion. We prefer to keep int32 indexing where we can,
# since currently SciPy's CSR construction downcasts when possible,
# so we prefer to avoid an unnecessary cast. The dtype may still
# change in the concatenation process if needed.
# See: https://github.com/scipy/scipy/issues/16569
max_indices = expanded_col - 1
max_indptr = total_nnz
max_int32 = np.iinfo(np.int32).max
needs_int64 = max(max_indices, max_indptr) > max_int32
index_dtype = np.int64 if needs_int64 else np.int32
# This is a pretty specific bug that is hard to work around by a user,
# hence we do not detail the entire bug and all possible avoidance
# mechnasisms. Instead we recommend upgrading scipy or shrinking their data.
cumulative_size += expanded_col
if (
sp_version < parse_version("1.8.0")
and cumulative_size - 1 > max_int32
and not needs_int64
):
raise ValueError(
"In scipy versions `<1.8.0`, the function `scipy.sparse.hstack`"
" sometimes produces negative columns when the output shape contains"
" `n_cols` too large to be represented by a 32bit signed"
" integer. To avoid this error, either use a version"
" of scipy `>=1.8.0` or alter the `PolynomialFeatures`"
" transformer to produce fewer than 2^31 output features."
)
# Result of the expansion, modified in place by the
# `_csr_polynomial_expansion` routine.
expanded_data = np.empty(shape=total_nnz, dtype=X.data.dtype)
expanded_indices = np.empty(shape=total_nnz, dtype=index_dtype)
expanded_indptr = np.empty(shape=X.indptr.shape[0], dtype=index_dtype)
_csr_polynomial_expansion(
X.data,
X.indices,
X.indptr,
X.shape[1],
expanded_data,
expanded_indices,
expanded_indptr,
interaction_only,
deg,
)
return sparse.csr_matrix(
(expanded_data, expanded_indices, expanded_indptr),
shape=(X.indptr.shape[0] - 1, expanded_col),
dtype=X.dtype,
)
class PolynomialFeatures(TransformerMixin, BaseEstimator):
"""Generate polynomial and interaction features.
Generate a new feature matrix consisting of all polynomial combinations
of the features with degree less than or equal to the specified degree.
For example, if an input sample is two dimensional and of the form
[a, b], the degree-2 polynomial features are [1, a, b, a^2, ab, b^2].
Read more in the :ref:`User Guide <polynomial_features>`.
Parameters
----------
degree : int or tuple (min_degree, max_degree), default=2
If a single int is given, it specifies the maximal degree of the
polynomial features. If a tuple `(min_degree, max_degree)` is passed,
then `min_degree` is the minimum and `max_degree` is the maximum
polynomial degree of the generated features. Note that `min_degree=0`
and `min_degree=1` are equivalent as outputting the degree zero term is
determined by `include_bias`.
interaction_only : bool, default=False
If `True`, only interaction features are produced: features that are
products of at most `degree` *distinct* input features, i.e. terms with
power of 2 or higher of the same input feature are excluded:
- included: `x[0]`, `x[1]`, `x[0] * x[1]`, etc.
- excluded: `x[0] ** 2`, `x[0] ** 2 * x[1]`, etc.
include_bias : bool, default=True
If `True` (default), then include a bias column, the feature in which
all polynomial powers are zero (i.e. a column of ones - acts as an
intercept term in a linear model).
order : {'C', 'F'}, default='C'
Order of output array in the dense case. `'F'` order is faster to
compute, but may slow down subsequent estimators.
.. versionadded:: 0.21
Attributes
----------
powers_ : ndarray of shape (`n_output_features_`, `n_features_in_`)
`powers_[i, j]` is the exponent of the jth input in the ith output.
n_features_in_ : int
Number of features seen during :term:`fit`.
.. versionadded:: 0.24
feature_names_in_ : ndarray of shape (`n_features_in_`,)
Names of features seen during :term:`fit`. Defined only when `X`
has feature names that are all strings.
.. versionadded:: 1.0
n_output_features_ : int
The total number of polynomial output features. The number of output
features is computed by iterating over all suitably sized combinations
of input features.
See Also
--------
SplineTransformer : Transformer that generates univariate B-spline bases
for features.
Notes
-----
Be aware that the number of features in the output array scales
polynomially in the number of features of the input array, and
exponentially in the degree. High degrees can cause overfitting.
See :ref:`examples/linear_model/plot_polynomial_interpolation.py
<sphx_glr_auto_examples_linear_model_plot_polynomial_interpolation.py>`
Examples
--------
>>> import numpy as np
>>> from sklearn.preprocessing import PolynomialFeatures
>>> X = np.arange(6).reshape(3, 2)
>>> X
array([[0, 1],
[2, 3],
[4, 5]])
>>> poly = PolynomialFeatures(2)
>>> poly.fit_transform(X)
array([[ 1., 0., 1., 0., 0., 1.],
[ 1., 2., 3., 4., 6., 9.],
[ 1., 4., 5., 16., 20., 25.]])
>>> poly = PolynomialFeatures(interaction_only=True)
>>> poly.fit_transform(X)
array([[ 1., 0., 1., 0.],
[ 1., 2., 3., 6.],
[ 1., 4., 5., 20.]])
"""
_parameter_constraints: dict = {
"degree": [Interval(Integral, 0, None, closed="left"), "array-like"],
"interaction_only": ["boolean"],
"include_bias": ["boolean"],
"order": [StrOptions({"C", "F"})],
}
def __init__(
self, degree=2, *, interaction_only=False, include_bias=True, order="C"
):
self.degree = degree
self.interaction_only = interaction_only
self.include_bias = include_bias
self.order = order
@staticmethod
def _combinations(
n_features, min_degree, max_degree, interaction_only, include_bias
):
comb = combinations if interaction_only else combinations_w_r
start = max(1, min_degree)
iter = chain.from_iterable(
comb(range(n_features), i) for i in range(start, max_degree + 1)
)
if include_bias:
iter = chain(comb(range(n_features), 0), iter)
return iter
@staticmethod
def _num_combinations(
n_features, min_degree, max_degree, interaction_only, include_bias
):
"""Calculate number of terms in polynomial expansion
This should be equivalent to counting the number of terms returned by
_combinations(...) but much faster.
"""
if interaction_only:
combinations = sum(
[
comb(n_features, i, exact=True)
for i in range(max(1, min_degree), min(max_degree, n_features) + 1)
]
)
else:
combinations = comb(n_features + max_degree, max_degree, exact=True) - 1
if min_degree > 0:
d = min_degree - 1
combinations -= comb(n_features + d, d, exact=True) - 1
if include_bias:
combinations += 1
return combinations
@property
def powers_(self):
"""Exponent for each of the inputs in the output."""
check_is_fitted(self)
combinations = self._combinations(
n_features=self.n_features_in_,
min_degree=self._min_degree,
max_degree=self._max_degree,
interaction_only=self.interaction_only,
include_bias=self.include_bias,
)
return np.vstack(
[np.bincount(c, minlength=self.n_features_in_) for c in combinations]
)
def get_feature_names_out(self, input_features=None):
"""Get output feature names for transformation.
Parameters
----------
input_features : array-like of str or None, default=None
Input features.
- If `input_features is None`, then `feature_names_in_` is
used as feature names in. If `feature_names_in_` is not defined,
then the following input feature names are generated:
`["x0", "x1", ..., "x(n_features_in_ - 1)"]`.
- If `input_features` is an array-like, then `input_features` must
match `feature_names_in_` if `feature_names_in_` is defined.
Returns
-------
feature_names_out : ndarray of str objects
Transformed feature names.
"""
powers = self.powers_
input_features = _check_feature_names_in(self, input_features)
feature_names = []
for row in powers:
inds = np.where(row)[0]
if len(inds):
name = " ".join(
(
"%s^%d" % (input_features[ind], exp)
if exp != 1
else input_features[ind]
)
for ind, exp in zip(inds, row[inds])
)
else:
name = "1"
feature_names.append(name)
return np.asarray(feature_names, dtype=object)
@_fit_context(prefer_skip_nested_validation=True)
def fit(self, X, y=None):
"""
Compute number of output features.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The data.
y : Ignored
Not used, present here for API consistency by convention.
Returns
-------
self : object
Fitted transformer.
"""
_, n_features = self._validate_data(X, accept_sparse=True).shape
if isinstance(self.degree, Integral):
if self.degree == 0 and not self.include_bias:
raise ValueError(
"Setting degree to zero and include_bias to False would result in"
" an empty output array."
)
self._min_degree = 0
self._max_degree = self.degree
elif (
isinstance(self.degree, collections.abc.Iterable) and len(self.degree) == 2
):
self._min_degree, self._max_degree = self.degree
if not (
isinstance(self._min_degree, Integral)
and isinstance(self._max_degree, Integral)
and self._min_degree >= 0
and self._min_degree <= self._max_degree
):
raise ValueError(
"degree=(min_degree, max_degree) must "
"be non-negative integers that fulfil "
"min_degree <= max_degree, got "
f"{self.degree}."
)
elif self._max_degree == 0 and not self.include_bias:
raise ValueError(
"Setting both min_degree and max_degree to zero and include_bias to"
" False would result in an empty output array."
)
else:
raise ValueError(
"degree must be a non-negative int or tuple "
"(min_degree, max_degree), got "
f"{self.degree}."
)
self.n_output_features_ = self._num_combinations(
n_features=n_features,
min_degree=self._min_degree,
max_degree=self._max_degree,
interaction_only=self.interaction_only,
include_bias=self.include_bias,
)
if self.n_output_features_ > np.iinfo(np.intp).max:
msg = (
"The output that would result from the current configuration would"
f" have {self.n_output_features_} features which is too large to be"
f" indexed by {np.intp().dtype.name}. Please change some or all of the"
" following:\n- The number of features in the input, currently"
f" {n_features=}\n- The range of degrees to calculate, currently"
f" [{self._min_degree}, {self._max_degree}]\n- Whether to include only"
f" interaction terms, currently {self.interaction_only}\n- Whether to"
f" include a bias term, currently {self.include_bias}."
)
if (
np.intp == np.int32
and self.n_output_features_ <= np.iinfo(np.int64).max
): # pragma: nocover
msg += (
"\nNote that the current Python runtime has a limited 32 bit "
"address space and that this configuration would have been "
"admissible if run on a 64 bit Python runtime."
)
raise ValueError(msg)
# We also record the number of output features for
# _max_degree = 0
self._n_out_full = self._num_combinations(
n_features=n_features,
min_degree=0,
max_degree=self._max_degree,
interaction_only=self.interaction_only,
include_bias=self.include_bias,
)
return self
def transform(self, X):
"""Transform data to polynomial features.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The data to transform, row by row.
Prefer CSR over CSC for sparse input (for speed), but CSC is
required if the degree is 4 or higher. If the degree is less than
4 and the input format is CSC, it will be converted to CSR, have
its polynomial features generated, then converted back to CSC.
If the degree is 2 or 3, the method described in "Leveraging
Sparsity to Speed Up Polynomial Feature Expansions of CSR Matrices
Using K-Simplex Numbers" by Andrew Nystrom and John Hughes is
used, which is much faster than the method used on CSC input. For
this reason, a CSC input will be converted to CSR, and the output
will be converted back to CSC prior to being returned, hence the
preference of CSR.
Returns
-------
XP : {ndarray, sparse matrix} of shape (n_samples, NP)
The matrix of features, where `NP` is the number of polynomial
features generated from the combination of inputs. If a sparse
matrix is provided, it will be converted into a sparse
`csr_matrix`.
"""
check_is_fitted(self)
X = self._validate_data(
X, order="F", dtype=FLOAT_DTYPES, reset=False, accept_sparse=("csr", "csc")
)
n_samples, n_features = X.shape
max_int32 = np.iinfo(np.int32).max
if sparse.issparse(X) and X.format == "csr":
if self._max_degree > 3:
return self.transform(X.tocsc()).tocsr()
to_stack = []
if self.include_bias:
to_stack.append(
sparse.csr_matrix(np.ones(shape=(n_samples, 1), dtype=X.dtype))
)
if self._min_degree <= 1 and self._max_degree > 0:
to_stack.append(X)
cumulative_size = sum(mat.shape[1] for mat in to_stack)
for deg in range(max(2, self._min_degree), self._max_degree + 1):
expanded = _create_expansion(
X=X,
interaction_only=self.interaction_only,
deg=deg,
n_features=n_features,
cumulative_size=cumulative_size,
)
if expanded is not None:
to_stack.append(expanded)
cumulative_size += expanded.shape[1]
if len(to_stack) == 0:
# edge case: deal with empty matrix
XP = sparse.csr_matrix((n_samples, 0), dtype=X.dtype)
else:
# `scipy.sparse.hstack` breaks in scipy<1.9.2
# when `n_output_features_ > max_int32`
all_int32 = all(mat.indices.dtype == np.int32 for mat in to_stack)
if (
sp_version < parse_version("1.9.2")
and self.n_output_features_ > max_int32
and all_int32
):
raise ValueError( # pragma: no cover
"In scipy versions `<1.9.2`, the function `scipy.sparse.hstack`"
" produces negative columns when:\n1. The output shape contains"
" `n_cols` too large to be represented by a 32bit signed"
" integer.\n2. All sub-matrices to be stacked have indices of"
" dtype `np.int32`.\nTo avoid this error, either use a version"
" of scipy `>=1.9.2` or alter the `PolynomialFeatures`"
" transformer to produce fewer than 2^31 output features"
)
XP = sparse.hstack(to_stack, dtype=X.dtype, format="csr")
elif sparse.issparse(X) and X.format == "csc" and self._max_degree < 4:
return self.transform(X.tocsr()).tocsc()
elif sparse.issparse(X):
combinations = self._combinations(
n_features=n_features,
min_degree=self._min_degree,
max_degree=self._max_degree,
interaction_only=self.interaction_only,
include_bias=self.include_bias,
)
columns = []
for combi in combinations:
if combi:
out_col = 1
for col_idx in combi:
out_col = X[:, [col_idx]].multiply(out_col)
columns.append(out_col)
else:
bias = sparse.csc_matrix(np.ones((X.shape[0], 1)))
columns.append(bias)
XP = sparse.hstack(columns, dtype=X.dtype).tocsc()
else:
# Do as if _min_degree = 0 and cut down array after the
# computation, i.e. use _n_out_full instead of n_output_features_.
XP = np.empty(
shape=(n_samples, self._n_out_full), dtype=X.dtype, order=self.order
)
# What follows is a faster implementation of:
# for i, comb in enumerate(combinations):
# XP[:, i] = X[:, comb].prod(1)
# This implementation uses two optimisations.
# First one is broadcasting,
# multiply ([X1, ..., Xn], X1) -> [X1 X1, ..., Xn X1]
# multiply ([X2, ..., Xn], X2) -> [X2 X2, ..., Xn X2]
# ...
# multiply ([X[:, start:end], X[:, start]) -> ...
# Second optimisation happens for degrees >= 3.
# Xi^3 is computed reusing previous computation:
# Xi^3 = Xi^2 * Xi.
# degree 0 term
if self.include_bias:
XP[:, 0] = 1
current_col = 1
else:
current_col = 0
if self._max_degree == 0:
return XP
# degree 1 term
XP[:, current_col : current_col + n_features] = X
index = list(range(current_col, current_col + n_features))
current_col += n_features
index.append(current_col)
# loop over degree >= 2 terms
for _ in range(2, self._max_degree + 1):
new_index = []
end = index[-1]
for feature_idx in range(n_features):
start = index[feature_idx]
new_index.append(current_col)
if self.interaction_only:
start += index[feature_idx + 1] - index[feature_idx]
next_col = current_col + end - start
if next_col <= current_col:
break
# XP[:, start:end] are terms of degree d - 1
# that exclude feature #feature_idx.
np.multiply(
XP[:, start:end],
X[:, feature_idx : feature_idx + 1],
out=XP[:, current_col:next_col],
casting="no",
)
current_col = next_col
new_index.append(current_col)
index = new_index
if self._min_degree > 1:
n_XP, n_Xout = self._n_out_full, self.n_output_features_
if self.include_bias:
Xout = np.empty(
shape=(n_samples, n_Xout), dtype=XP.dtype, order=self.order
)
Xout[:, 0] = 1
Xout[:, 1:] = XP[:, n_XP - n_Xout + 1 :]
else:
Xout = XP[:, n_XP - n_Xout :].copy()
XP = Xout
return XP
class SplineTransformer(TransformerMixin, BaseEstimator):
"""Generate univariate B-spline bases for features.
Generate a new feature matrix consisting of
`n_splines=n_knots + degree - 1` (`n_knots - 1` for
`extrapolation="periodic"`) spline basis functions
(B-splines) of polynomial order=`degree` for each feature.
In order to learn more about the SplineTransformer class go to:
:ref:`sphx_glr_auto_examples_applications_plot_cyclical_feature_engineering.py`
Read more in the :ref:`User Guide <spline_transformer>`.
.. versionadded:: 1.0
Parameters
----------
n_knots : int, default=5
Number of knots of the splines if `knots` equals one of
{'uniform', 'quantile'}. Must be larger or equal 2. Ignored if `knots`
is array-like.
degree : int, default=3
The polynomial degree of the spline basis. Must be a non-negative
integer.
knots : {'uniform', 'quantile'} or array-like of shape \
(n_knots, n_features), default='uniform'
Set knot positions such that first knot <= features <= last knot.
- If 'uniform', `n_knots` number of knots are distributed uniformly
from min to max values of the features.
- If 'quantile', they are distributed uniformly along the quantiles of
the features.
- If an array-like is given, it directly specifies the sorted knot
positions including the boundary knots. Note that, internally,
`degree` number of knots are added before the first knot, the same
after the last knot.
extrapolation : {'error', 'constant', 'linear', 'continue', 'periodic'}, \
default='constant'
If 'error', values outside the min and max values of the training
features raises a `ValueError`. If 'constant', the value of the
splines at minimum and maximum value of the features is used as
constant extrapolation. If 'linear', a linear extrapolation is used.
If 'continue', the splines are extrapolated as is, i.e. option
`extrapolate=True` in :class:`scipy.interpolate.BSpline`. If
'periodic', periodic splines with a periodicity equal to the distance
between the first and last knot are used. Periodic splines enforce
equal function values and derivatives at the first and last knot.
For example, this makes it possible to avoid introducing an arbitrary
jump between Dec 31st and Jan 1st in spline features derived from a
naturally periodic "day-of-year" input feature. In this case it is
recommended to manually set the knot values to control the period.
include_bias : bool, default=True
If False, then the last spline element inside the data range
of a feature is dropped. As B-splines sum to one over the spline basis
functions for each data point, they implicitly include a bias term,
i.e. a column of ones. It acts as an intercept term in a linear models.
order : {'C', 'F'}, default='C'
Order of output array in the dense case. `'F'` order is faster to compute, but
may slow down subsequent estimators.
sparse_output : bool, default=False
Will return sparse CSR matrix if set True else will return an array. This
option is only available with `scipy>=1.8`.
.. versionadded:: 1.2
Attributes
----------
bsplines_ : list of shape (n_features,)
List of BSplines objects, one for each feature.
n_features_in_ : int
The total number of input features.
feature_names_in_ : ndarray of shape (`n_features_in_`,)
Names of features seen during :term:`fit`. Defined only when `X`
has feature names that are all strings.
.. versionadded:: 1.0
n_features_out_ : int
The total number of output features, which is computed as
`n_features * n_splines`, where `n_splines` is
the number of bases elements of the B-splines,
`n_knots + degree - 1` for non-periodic splines and
`n_knots - 1` for periodic ones.
If `include_bias=False`, then it is only
`n_features * (n_splines - 1)`.
See Also
--------
KBinsDiscretizer : Transformer that bins continuous data into intervals.
PolynomialFeatures : Transformer that generates polynomial and interaction
features.
Notes
-----
High degrees and a high number of knots can cause overfitting.
See :ref:`examples/linear_model/plot_polynomial_interpolation.py
<sphx_glr_auto_examples_linear_model_plot_polynomial_interpolation.py>`.
Examples
--------
>>> import numpy as np
>>> from sklearn.preprocessing import SplineTransformer
>>> X = np.arange(6).reshape(6, 1)
>>> spline = SplineTransformer(degree=2, n_knots=3)
>>> spline.fit_transform(X)
array([[0.5 , 0.5 , 0. , 0. ],
[0.18, 0.74, 0.08, 0. ],
[0.02, 0.66, 0.32, 0. ],
[0. , 0.32, 0.66, 0.02],
[0. , 0.08, 0.74, 0.18],
[0. , 0. , 0.5 , 0.5 ]])
"""
_parameter_constraints: dict = {
"n_knots": [Interval(Integral, 2, None, closed="left")],
"degree": [Interval(Integral, 0, None, closed="left")],
"knots": [StrOptions({"uniform", "quantile"}), "array-like"],
"extrapolation": [
StrOptions({"error", "constant", "linear", "continue", "periodic"})
],
"include_bias": ["boolean"],
"order": [StrOptions({"C", "F"})],
"sparse_output": ["boolean"],
}
def __init__(
self,
n_knots=5,
degree=3,
*,
knots="uniform",
extrapolation="constant",
include_bias=True,
order="C",
sparse_output=False,
):
self.n_knots = n_knots
self.degree = degree
self.knots = knots
self.extrapolation = extrapolation
self.include_bias = include_bias
self.order = order
self.sparse_output = sparse_output
@staticmethod
def _get_base_knot_positions(X, n_knots=10, knots="uniform", sample_weight=None):
"""Calculate base knot positions.
Base knots such that first knot <= feature <= last knot. For the
B-spline construction with scipy.interpolate.BSpline, 2*degree knots
beyond the base interval are added.
Returns
-------
knots : ndarray of shape (n_knots, n_features), dtype=np.float64
Knot positions (points) of base interval.
"""
if knots == "quantile":
percentiles = 100 * np.linspace(
start=0, stop=1, num=n_knots, dtype=np.float64
)
if sample_weight is None:
knots = np.percentile(X, percentiles, axis=0)
else:
knots = np.array(
[
_weighted_percentile(X, sample_weight, percentile)
for percentile in percentiles
]
)
else:
# knots == 'uniform':
# Note that the variable `knots` has already been validated and
# `else` is therefore safe.
# Disregard observations with zero weight.
mask = slice(None, None, 1) if sample_weight is None else sample_weight > 0
x_min = np.amin(X[mask], axis=0)
x_max = np.amax(X[mask], axis=0)
knots = np.linspace(
start=x_min,
stop=x_max,
num=n_knots,
endpoint=True,
dtype=np.float64,
)
return knots
def get_feature_names_out(self, input_features=None):
"""Get output feature names for transformation.
Parameters
----------
input_features : array-like of str or None, default=None
Input features.
- If `input_features` is `None`, then `feature_names_in_` is
used as feature names in. If `feature_names_in_` is not defined,
then the following input feature names are generated:
`["x0", "x1", ..., "x(n_features_in_ - 1)"]`.
- If `input_features` is an array-like, then `input_features` must
match `feature_names_in_` if `feature_names_in_` is defined.
Returns
-------
feature_names_out : ndarray of str objects
Transformed feature names.
"""
check_is_fitted(self, "n_features_in_")
n_splines = self.bsplines_[0].c.shape[1]
input_features = _check_feature_names_in(self, input_features)
feature_names = []
for i in range(self.n_features_in_):
for j in range(n_splines - 1 + self.include_bias):
feature_names.append(f"{input_features[i]}_sp_{j}")
return np.asarray(feature_names, dtype=object)
@_fit_context(prefer_skip_nested_validation=True)
def fit(self, X, y=None, sample_weight=None):
"""Compute knot positions of splines.
Parameters
----------
X : array-like of shape (n_samples, n_features)
The data.
y : None
Ignored.
sample_weight : array-like of shape (n_samples,), default = None
Individual weights for each sample. Used to calculate quantiles if
`knots="quantile"`. For `knots="uniform"`, zero weighted
observations are ignored for finding the min and max of `X`.
Returns
-------
self : object
Fitted transformer.
"""
X = self._validate_data(
X,
reset=True,
accept_sparse=False,
ensure_min_samples=2,
ensure_2d=True,
)
if sample_weight is not None:
sample_weight = _check_sample_weight(sample_weight, X, dtype=X.dtype)
_, n_features = X.shape
if isinstance(self.knots, str):
base_knots = self._get_base_knot_positions(
X, n_knots=self.n_knots, knots=self.knots, sample_weight=sample_weight
)
else:
base_knots = check_array(self.knots, dtype=np.float64)
if base_knots.shape[0] < 2:
raise ValueError("Number of knots, knots.shape[0], must be >= 2.")
elif base_knots.shape[1] != n_features:
raise ValueError("knots.shape[1] == n_features is violated.")
elif not np.all(np.diff(base_knots, axis=0) > 0):
raise ValueError("knots must be sorted without duplicates.")
if self.sparse_output and sp_version < parse_version("1.8.0"):
raise ValueError(
"Option sparse_output=True is only available with scipy>=1.8.0, "
f"but here scipy=={sp_version} is used."
)
# number of knots for base interval
n_knots = base_knots.shape[0]
if self.extrapolation == "periodic" and n_knots <= self.degree:
raise ValueError(
"Periodic splines require degree < n_knots. Got n_knots="
f"{n_knots} and degree={self.degree}."
)
# number of splines basis functions
if self.extrapolation != "periodic":
n_splines = n_knots + self.degree - 1
else:
# periodic splines have self.degree less degrees of freedom
n_splines = n_knots - 1
degree = self.degree
n_out = n_features * n_splines
# We have to add degree number of knots below, and degree number knots
# above the base knots in order to make the spline basis complete.
if self.extrapolation == "periodic":
# For periodic splines the spacing of the first / last degree knots
# needs to be a continuation of the spacing of the last / first
# base knots.
period = base_knots[-1] - base_knots[0]
knots = np.r_[
base_knots[-(degree + 1) : -1] - period,
base_knots,
base_knots[1 : (degree + 1)] + period,
]
else:
# Eilers & Marx in "Flexible smoothing with B-splines and
# penalties" https://doi.org/10.1214/ss/1038425655 advice
# against repeating first and last knot several times, which
# would have inferior behaviour at boundaries if combined with
# a penalty (hence P-Spline). We follow this advice even if our
# splines are unpenalized. Meaning we do not:
# knots = np.r_[
# np.tile(base_knots.min(axis=0), reps=[degree, 1]),
# base_knots,
# np.tile(base_knots.max(axis=0), reps=[degree, 1])
# ]
# Instead, we reuse the distance of the 2 fist/last knots.
dist_min = base_knots[1] - base_knots[0]
dist_max = base_knots[-1] - base_knots[-2]
knots = np.r_[
np.linspace(
base_knots[0] - degree * dist_min,
base_knots[0] - dist_min,
num=degree,
),
base_knots,
np.linspace(
base_knots[-1] + dist_max,
base_knots[-1] + degree * dist_max,
num=degree,
),
]
# With a diagonal coefficient matrix, we get back the spline basis
# elements, i.e. the design matrix of the spline.
# Note, BSpline appreciates C-contiguous float64 arrays as c=coef.
coef = np.eye(n_splines, dtype=np.float64)
if self.extrapolation == "periodic":
coef = np.concatenate((coef, coef[:degree, :]))
extrapolate = self.extrapolation in ["periodic", "continue"]
bsplines = [
BSpline.construct_fast(
knots[:, i], coef, self.degree, extrapolate=extrapolate
)
for i in range(n_features)
]
self.bsplines_ = bsplines
self.n_features_out_ = n_out - n_features * (1 - self.include_bias)
return self
def transform(self, X):
"""Transform each feature data to B-splines.
Parameters
----------
X : array-like of shape (n_samples, n_features)
The data to transform.
Returns
-------
XBS : {ndarray, sparse matrix} of shape (n_samples, n_features * n_splines)
The matrix of features, where n_splines is the number of bases
elements of the B-splines, n_knots + degree - 1.
"""
check_is_fitted(self)
X = self._validate_data(X, reset=False, accept_sparse=False, ensure_2d=True)
n_samples, n_features = X.shape
n_splines = self.bsplines_[0].c.shape[1]
degree = self.degree
# TODO: Remove this condition, once scipy 1.10 is the minimum version.
# Only scipy => 1.10 supports design_matrix(.., extrapolate=..).
# The default (implicit in scipy < 1.10) is extrapolate=False.
scipy_1_10 = sp_version >= parse_version("1.10.0")
# Note: self.bsplines_[0].extrapolate is True for extrapolation in
# ["periodic", "continue"]
if scipy_1_10:
use_sparse = self.sparse_output
kwargs_extrapolate = {"extrapolate": self.bsplines_[0].extrapolate}
else:
use_sparse = self.sparse_output and not self.bsplines_[0].extrapolate
kwargs_extrapolate = dict()
# Note that scipy BSpline returns float64 arrays and converts input
# x=X[:, i] to c-contiguous float64.
n_out = self.n_features_out_ + n_features * (1 - self.include_bias)
if X.dtype in FLOAT_DTYPES:
dtype = X.dtype
else:
dtype = np.float64
if use_sparse:
output_list = []
else:
XBS = np.zeros((n_samples, n_out), dtype=dtype, order=self.order)
for i in range(n_features):
spl = self.bsplines_[i]
if self.extrapolation in ("continue", "error", "periodic"):
if self.extrapolation == "periodic":
# With periodic extrapolation we map x to the segment
# [spl.t[k], spl.t[n]].
# This is equivalent to BSpline(.., extrapolate="periodic")
# for scipy>=1.0.0.
n = spl.t.size - spl.k - 1
# Assign to new array to avoid inplace operation
x = spl.t[spl.k] + (X[:, i] - spl.t[spl.k]) % (
spl.t[n] - spl.t[spl.k]
)
else:
x = X[:, i]
if use_sparse:
XBS_sparse = BSpline.design_matrix(
x, spl.t, spl.k, **kwargs_extrapolate
)
if self.extrapolation == "periodic":
# See the construction of coef in fit. We need to add the last
# degree spline basis function to the first degree ones and
# then drop the last ones.
# Note: See comment about SparseEfficiencyWarning below.
XBS_sparse = XBS_sparse.tolil()
XBS_sparse[:, :degree] += XBS_sparse[:, -degree:]
XBS_sparse = XBS_sparse[:, :-degree]
else:
XBS[:, (i * n_splines) : ((i + 1) * n_splines)] = spl(x)
else: # extrapolation in ("constant", "linear")
xmin, xmax = spl.t[degree], spl.t[-degree - 1]
# spline values at boundaries
f_min, f_max = spl(xmin), spl(xmax)
mask = (xmin <= X[:, i]) & (X[:, i] <= xmax)
if use_sparse:
mask_inv = ~mask
x = X[:, i].copy()
# Set some arbitrary values outside boundary that will be reassigned
# later.
x[mask_inv] = spl.t[self.degree]
XBS_sparse = BSpline.design_matrix(x, spl.t, spl.k)
# Note: Without converting to lil_matrix we would get:
# scipy.sparse._base.SparseEfficiencyWarning: Changing the sparsity
# structure of a csr_matrix is expensive. lil_matrix is more
# efficient.
if np.any(mask_inv):
XBS_sparse = XBS_sparse.tolil()
XBS_sparse[mask_inv, :] = 0
else:
XBS[mask, (i * n_splines) : ((i + 1) * n_splines)] = spl(X[mask, i])
# Note for extrapolation:
# 'continue' is already returned as is by scipy BSplines
if self.extrapolation == "error":
# BSpline with extrapolate=False does not raise an error, but
# outputs np.nan.
if (use_sparse and np.any(np.isnan(XBS_sparse.data))) or (
not use_sparse
and np.any(
np.isnan(XBS[:, (i * n_splines) : ((i + 1) * n_splines)])
)
):
raise ValueError(
"X contains values beyond the limits of the knots."
)
elif self.extrapolation == "constant":
# Set all values beyond xmin and xmax to the value of the
# spline basis functions at those two positions.
# Only the first degree and last degree number of splines
# have non-zero values at the boundaries.
mask = X[:, i] < xmin
if np.any(mask):
if use_sparse:
# Note: See comment about SparseEfficiencyWarning above.
XBS_sparse = XBS_sparse.tolil()
XBS_sparse[mask, :degree] = f_min[:degree]
else:
XBS[mask, (i * n_splines) : (i * n_splines + degree)] = f_min[
:degree
]
mask = X[:, i] > xmax
if np.any(mask):
if use_sparse:
# Note: See comment about SparseEfficiencyWarning above.
XBS_sparse = XBS_sparse.tolil()
XBS_sparse[mask, -degree:] = f_max[-degree:]
else:
XBS[
mask,
((i + 1) * n_splines - degree) : ((i + 1) * n_splines),
] = f_max[-degree:]
elif self.extrapolation == "linear":
# Continue the degree first and degree last spline bases
# linearly beyond the boundaries, with slope = derivative at
# the boundary.
# Note that all others have derivative = value = 0 at the
# boundaries.
# spline derivatives = slopes at boundaries
fp_min, fp_max = spl(xmin, nu=1), spl(xmax, nu=1)
# Compute the linear continuation.
if degree <= 1:
# For degree=1, the derivative of 2nd spline is not zero at
# boundary. For degree=0 it is the same as 'constant'.
degree += 1
for j in range(degree):
mask = X[:, i] < xmin
if np.any(mask):
linear_extr = f_min[j] + (X[mask, i] - xmin) * fp_min[j]
if use_sparse:
# Note: See comment about SparseEfficiencyWarning above.
XBS_sparse = XBS_sparse.tolil()
XBS_sparse[mask, j] = linear_extr
else:
XBS[mask, i * n_splines + j] = linear_extr
mask = X[:, i] > xmax
if np.any(mask):
k = n_splines - 1 - j
linear_extr = f_max[k] + (X[mask, i] - xmax) * fp_max[k]
if use_sparse:
# Note: See comment about SparseEfficiencyWarning above.
XBS_sparse = XBS_sparse.tolil()
XBS_sparse[mask, k : k + 1] = linear_extr[:, None]
else:
XBS[mask, i * n_splines + k] = linear_extr
if use_sparse:
XBS_sparse = XBS_sparse.tocsr()
output_list.append(XBS_sparse)
if use_sparse:
# TODO: Remove this conditional error when the minimum supported version of
# SciPy is 1.9.2
# `scipy.sparse.hstack` breaks in scipy<1.9.2
# when `n_features_out_ > max_int32`
max_int32 = np.iinfo(np.int32).max
all_int32 = True
for mat in output_list:
all_int32 &= mat.indices.dtype == np.int32
if (
sp_version < parse_version("1.9.2")
and self.n_features_out_ > max_int32
and all_int32
):
raise ValueError(
"In scipy versions `<1.9.2`, the function `scipy.sparse.hstack`"
" produces negative columns when:\n1. The output shape contains"
" `n_cols` too large to be represented by a 32bit signed"
" integer.\n. All sub-matrices to be stacked have indices of"
" dtype `np.int32`.\nTo avoid this error, either use a version"
" of scipy `>=1.9.2` or alter the `SplineTransformer`"
" transformer to produce fewer than 2^31 output features"
)
XBS = sparse.hstack(output_list, format="csr")
elif self.sparse_output:
# TODO: Remove ones scipy 1.10 is the minimum version. See comments above.
XBS = sparse.csr_matrix(XBS)
if self.include_bias:
return XBS
else:
# We throw away one spline basis per feature.
# We chose the last one.
indices = [j for j in range(XBS.shape[1]) if (j + 1) % n_splines != 0]
return XBS[:, indices]
def _more_tags(self):
return {
"_xfail_checks": {
"check_estimators_pickle": (
"Current Scipy implementation of _bsplines does not"
"support const memory views."
),
}
}