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pygam.py
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pygam.py
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# -*- coding: utf-8 -*-
from collections import defaultdict
from collections import OrderedDict
from copy import deepcopy
from progressbar import ProgressBar
import warnings
import numpy as np
import scipy as sp
from scipy import stats # noqa: F401
from pygam.core import Core
from pygam.penalties import derivative # noqa: F401
from pygam.penalties import l2 # noqa: F401
from pygam.penalties import monotonic_inc # noqa: F401
from pygam.penalties import monotonic_dec # noqa: F401
from pygam.penalties import convex # noqa: F401
from pygam.penalties import concave # noqa: F401
from pygam.penalties import none # noqa: F401
from pygam.penalties import wrap_penalty # noqa: F401
from pygam.penalties import PENALTIES, CONSTRAINTS # noqa: F401
from pygam.distributions import Distribution # noqa: F401
from pygam.distributions import NormalDist # noqa: F401
from pygam.distributions import BinomialDist # noqa: F401
from pygam.distributions import PoissonDist # noqa: F401
from pygam.distributions import GammaDist # noqa: F401
from pygam.distributions import InvGaussDist # noqa: F401
from pygam.distributions import DISTRIBUTIONS # noqa: F401
from pygam.links import Link # noqa: F401
from pygam.links import IdentityLink # noqa: F401
from pygam.links import LogitLink # noqa: F401
from pygam.links import LogLink # noqa: F401
from pygam.links import InverseLink # noqa: F401
from pygam.links import InvSquaredLink # noqa: F401
from pygam.links import LINKS # noqa: F401
from pygam.callbacks import CallBack # noqa: F401
from pygam.callbacks import Deviance # noqa: F401
from pygam.callbacks import Diffs # noqa: F401
from pygam.callbacks import Accuracy # noqa: F401
from pygam.callbacks import Coef # noqa: F401
from pygam.callbacks import validate_callback # noqa: F401
from pygam.callbacks import CALLBACKS # noqa: F401
from pygam.utils import check_y
from pygam.utils import check_X
from pygam.utils import check_X_y
from pygam.utils import make_2d
from pygam.utils import flatten
from pygam.utils import check_array
from pygam.utils import check_lengths
from pygam.utils import load_diagonal
from pygam.utils import TablePrinter
from pygam.utils import space_row
from pygam.utils import sig_code
from pygam.utils import b_spline_basis # noqa: F401
from pygam.utils import combine
from pygam.utils import cholesky
from pygam.utils import check_param
from pygam.utils import isiterable
from pygam.utils import NotPositiveDefiniteError
from pygam.utils import OptimizationError
from pygam.terms import Term # noqa: F401
from pygam.terms import Intercept, intercept # noqa: F401
from pygam.terms import LinearTerm, l # noqa: F401
from pygam.terms import SplineTerm, s # noqa: F401
from pygam.terms import FactorTerm, f # noqa: F401
from pygam.terms import TensorTerm, te # noqa: F401
from pygam.terms import TermList # noqa: F401
from pygam.terms import MetaTermMixin # noqa: F401
EPS = np.finfo(np.float64).eps # machine epsilon
class GAM(Core, MetaTermMixin):
"""Generalized Additive Model
Parameters
----------
terms : expression specifying terms to model, optional.
By default a univariate spline term will be allocated for each feature.
For example:
>>> GAM(s(0) + l(1) + f(2) + te(3, 4))
will fit a spline term on feature 0, a linear term on feature 1,
a factor term on feature 2, and a tensor term on features 3 and 4.
callbacks : list of str or list of CallBack objects, optional
Names of callback objects to call during the optimization loop.
distribution : str or Distribution object, optional
Distribution to use in the model.
link : str or Link object, optional
Link function to use in the model.
fit_intercept : bool, optional
Specifies if a constant (a.k.a. bias or intercept) should be
added to the decision function.
Note: the intercept receives no smoothing penalty.
max_iter : int, optional
Maximum number of iterations allowed for the solver to converge.
tol : float, optional
Tolerance for stopping criteria.
verbose : bool, optional
whether to show pyGAM warnings.
Attributes
----------
coef_ : array, shape (n_classes, m_features)
Coefficient of the features in the decision function.
If fit_intercept is True, then self.coef_[0] will contain the bias.
statistics_ : dict
Dictionary containing model statistics like GCV/UBRE scores, AIC/c,
parameter covariances, estimated degrees of freedom, etc.
logs_ : dict
Dictionary containing the outputs of any callbacks at each
optimization loop.
The logs are structured as ``{callback: [...]}``
References
----------
Simon N. Wood, 2006
Generalized Additive Models: an introduction with R
Hastie, Tibshirani, Friedman
The Elements of Statistical Learning
http://statweb.stanford.edu/~tibs/ElemStatLearn/printings/ESLII_print10.pdf
Paul Eilers & Brian Marx, 2015
International Biometric Society: A Crash Course on P-splines
http://www.ibschannel2015.nl/project/userfiles/Crash_course_handout.pdf
"""
def __init__(
self,
terms='auto',
max_iter=100,
tol=1e-4,
distribution='normal',
link='identity',
callbacks=['deviance', 'diffs'],
fit_intercept=True,
verbose=False,
**kwargs,
):
self.max_iter = max_iter
self.tol = tol
self.distribution = distribution
self.link = link
self.callbacks = callbacks
self.verbose = verbose
self.terms = TermList(terms) if isinstance(terms, Term) else terms
self.fit_intercept = fit_intercept
for k, v in kwargs.items():
if k not in self._plural:
raise TypeError(
'__init__() got an unexpected keyword argument {}'.format(k)
)
setattr(self, k, v)
# internal settings
self._constraint_lam = 1e9 # regularization intensity for constraints
self._constraint_l2 = 1e-3 # diagononal loading to improve conditioning
self._constraint_l2_max = 1e-1 # maximum loading
# self._opt = 0 # use 0 for numerically stable optimizer, 1 for naive
self._term_location = 'terms' # for locating sub terms
# self._include = ['lam']
# call super and exclude any variables
super(GAM, self).__init__()
# @property
# def lam(self):
# if self._has_terms():
# return self.terms.lam
# else:
# return self._lam
#
# @lam.setter
# def lam(self, value):
# if self._has_terms():
# self.terms.lam = value
# else:
# self._lam = value
@property
def _is_fitted(self):
"""simple way to check if the GAM has been fitted
Parameters
---------
None
Returns
-------
bool : whether or not the model is fitted
"""
return hasattr(self, 'coef_')
def _validate_params(self):
"""method to sanitize model parameters
Parameters
---------
None
Returns
-------
None
"""
# fit_intercep
if not isinstance(self.fit_intercept, bool):
raise ValueError(
'fit_intercept must be type bool, but found {}'.format(
self.fit_intercept.__class__
)
)
# terms
if (self.terms != 'auto') and not (
isinstance(self.terms, (TermList, Term, type(None)))
):
raise ValueError(
'terms must be a TermList, but found ' 'terms = {}'.format(self.terms)
)
# max_iter
self.max_iter = check_param(
self.max_iter,
param_name='max_iter',
dtype='int',
constraint='>=1',
iterable=False,
)
# distribution
if not (
(self.distribution in DISTRIBUTIONS)
or isinstance(self.distribution, Distribution)
):
raise ValueError('unsupported distribution {}'.format(self.distribution))
if self.distribution in DISTRIBUTIONS:
self.distribution = DISTRIBUTIONS[self.distribution]()
# link
if not ((self.link in LINKS) or isinstance(self.link, Link)):
raise ValueError('unsupported link {}'.format(self.link))
if self.link in LINKS:
self.link = LINKS[self.link]()
# callbacks
if not isiterable(self.callbacks):
raise ValueError(
'Callbacks must be iterable, but found {}'.format(self.callbacks)
)
if not all([c in CALLBACKS or isinstance(c, CallBack) for c in self.callbacks]):
raise ValueError('unsupported callback(s) {}'.format(self.callbacks))
callbacks = list(self.callbacks)
for i, c in enumerate(self.callbacks):
if c in CALLBACKS:
callbacks[i] = CALLBACKS[c]()
self.callbacks = [validate_callback(c) for c in callbacks]
def _validate_data_dep_params(self, X):
"""method to validate and prepare data-dependent parameters
Parameters
---------
X : array-like
containing the input dataset
Returns
-------
None
"""
n_samples, m_features = X.shape
# terms
if self.terms == 'auto':
# one numerical spline per feature
self.terms = TermList(
*[SplineTerm(feat, verbose=self.verbose) for feat in range(m_features)]
)
elif self.terms is None:
# no terms
self.terms = TermList()
else:
# user-specified
self.terms = TermList(self.terms, verbose=self.verbose)
# add intercept
if self.fit_intercept:
self.terms = self.terms + Intercept()
if len(self.terms) == 0:
raise ValueError('At least 1 term must be specified')
# copy over things from plural
remove = []
for k, v in self.__dict__.items():
if k in self._plural:
setattr(self.terms, k, v)
remove.append(k)
for k in remove:
delattr(self, k)
self.terms.compile(X)
def loglikelihood(self, X, y, weights=None):
"""
compute the log-likelihood of the dataset using the current model
Parameters
---------
X : array-like of shape (n_samples, m_features)
containing the input dataset
y : array-like of shape (n,)
containing target values
weights : array-like of shape (n,), optional
containing sample weights
Returns
-------
log-likelihood : np.array of shape (n,)
containing log-likelihood scores
"""
y = check_y(y, self.link, self.distribution, verbose=self.verbose)
mu = self.predict_mu(X)
if weights is not None:
weights = np.array(weights).astype('f').ravel()
weights = check_array(
weights, name='sample weights', ndim=1, verbose=self.verbose
)
check_lengths(y, weights)
else:
weights = np.ones_like(y).astype('float64')
return self._loglikelihood(y, mu, weights=weights)
def _loglikelihood(self, y, mu, weights=None):
"""
compute the log-likelihood of the dataset using the current model
Parameters
---------
y : array-like of shape (n,)
containing target values
mu : array-like of shape (n_samples,)
expected value of the targets given the model and inputs
weights : array-like of shape (n,), optional
containing sample weights
Returns
-------
log-likelihood : np.array of shape (n,)
containing log-likelihood scores
"""
return self.distribution.log_pdf(y=y, mu=mu, weights=weights).sum()
def _linear_predictor(self, X=None, modelmat=None, b=None, term=-1):
"""linear predictor
compute the linear predictor portion of the model
ie multiply the model matrix by the spline basis coefficients
Parameters
---------
at least 1 of (X, modelmat)
and
at least 1 of (b, feature)
X : array-like of shape (n_samples, m_features) or None, optional
containing the input dataset
if None, will attempt to use modelmat
modelmat : array-like or None, optional
contains the spline basis for each feature evaluated at the input
values for each feature, ie model matrix
if None, will attempt to construct the model matrix from X
b : array-like or None, optional
contains the spline coefficients
if None, will use current model coefficients
feature : int, optional
feature for which to compute the linear prediction
if -1, will compute for all features
Returns
-------
lp : np.array of shape (n_samples,)
"""
if modelmat is None:
modelmat = self._modelmat(X, term=term)
if b is None:
b = self.coef_[self.terms.get_coef_indices(term)]
return modelmat.dot(b).flatten()
def predict_mu(self, X):
"""
preduct expected value of target given model and input X
Parameters
---------
X : array-like of shape (n_samples, m_features),
containing the input dataset
Returns
-------
y : np.array of shape (n_samples,)
containing expected values under the model
"""
if not self._is_fitted:
raise AttributeError('GAM has not been fitted. Call fit first.')
X = check_X(
X,
n_feats=self.statistics_['m_features'],
edge_knots=self.edge_knots_,
dtypes=self.dtype,
features=self.feature,
verbose=self.verbose,
)
lp = self._linear_predictor(X)
return self.link.mu(lp, self.distribution)
def predict(self, X):
"""
preduct expected value of target given model and input X
often this is done via expected value of GAM given input X
Parameters
---------
X : array-like of shape (n_samples, m_features)
containing the input dataset
Returns
-------
y : np.array of shape (n_samples,)
containing predicted values under the model
"""
return self.predict_mu(X)
def _modelmat(self, X, term=-1):
"""
Builds a model matrix, B, out of the spline basis for each feature
B = [B_0, B_1, ..., B_p]
Parameters
---------
X : array-like of shape (n_samples, m_features)
containing the input dataset
term : int, optional
term index for which to compute the model matrix
if -1, will create the model matrix for all features
Returns
-------
modelmat : sparse matrix of len n_samples
containing model matrix of the spline basis for selected features
"""
X = check_X(
X,
n_feats=self.statistics_['m_features'],
edge_knots=self.edge_knots_,
dtypes=self.dtype,
features=self.feature,
verbose=self.verbose,
)
return self.terms.build_columns(X, term=term)
def _cholesky(self, A, **kwargs):
"""
method to handle potential problems with the cholesky decomposition.
will try to increase L2 regularization of the penalty matrix to
do away with non-positive-definite errors
Parameters
----------
A : np.array
Returns
-------
np.array
"""
# create appropriate-size diagonal matrix
if sp.sparse.issparse(A):
diag = sp.sparse.eye(A.shape[0])
else:
diag = np.eye(A.shape[0])
constraint_l2 = self._constraint_l2
while constraint_l2 <= self._constraint_l2_max:
try:
L = cholesky(A, **kwargs)
self._constraint_l2 = constraint_l2
return L
except NotPositiveDefiniteError:
if self.verbose:
warnings.warn(
'Matrix is not positive definite. \n'
'Increasing l2 reg by factor of 10.',
stacklevel=2,
)
A -= constraint_l2 * diag
constraint_l2 *= 10
A += constraint_l2 * diag
raise NotPositiveDefiniteError('Matrix is not positive \n' 'definite.')
def _P(self):
"""
builds the GAM block-diagonal penalty matrix in quadratic form
out of penalty matrices specified for each feature.
each feature penalty matrix is multiplied by a lambda for that feature.
the first feature is the intercept.
so for m features:
P = block_diag[lam0 * P0, lam1 * P1, lam2 * P2, ... , lamm * Pm]
Parameters
---------
None
Returns
-------
P : sparse CSC matrix containing the model penalties in quadratic form
"""
return self.terms.build_penalties()
def _C(self):
"""
builds the GAM block-diagonal constraint matrix in quadratic form
out of constraint matrices specified for each feature.
behaves like a penalty, but with a very large lambda value, ie 1e6.
Parameters
---------
None
Returns
-------
C : sparse CSC matrix containing the model constraints in quadratic form
"""
return self.terms.build_constraints(
self.coef_, self._constraint_lam, self._constraint_l2
)
def _pseudo_data(self, y, lp, mu):
"""
compute the pseudo data for a PIRLS iterations
Parameters
---------
y : array-like of shape (n,)
containing target data
lp : array-like of shape (n,)
containing linear predictions by the model
mu : array-like of shape (n_samples,)
expected value of the targets given the model and inputs
Returns
-------
pseudo_data : np.array of shape (n,)
"""
return lp + (y - mu) * self.link.gradient(mu, self.distribution)
def _W(self, mu, weights, y=None):
"""
compute the PIRLS weights for model predictions.
TODO lets verify the formula for this.
if we use the square root of the mu with the stable opt,
we get the same results as when we use non-sqrt mu with naive opt.
this makes me think that they are equivalent.
also, using non-sqrt mu with stable opt gives very small edofs for even
lam=0.001 and the parameter variance is huge. this seems strange to me.
computed [V * d(link)/d(mu)] ^(-1/2) by hand and the math checks out as hoped.
ive since moved the square to the naive pirls method to make the code modular.
Parameters
---------
mu : array-like of shape (n_samples,)
expected value of the targets given the model and inputs
weights : array-like of shape (n_samples,)
containing sample weights
y = array-like of shape (n_samples,) or None, optional
does nothing. just for compatibility with ExpectileGAM
Returns
-------
weights : sp..sparse array of shape (n_samples, n_samples)
"""
return sp.sparse.diags(
(
self.link.gradient(mu, self.distribution) ** 2
* self.distribution.V(mu=mu)
* weights**-1
)
** -0.5
)
def _mask(self, weights):
"""
identifies the mask at which the weights are
greater than sqrt(machine epsilon)
and
not NaN
and
not Inf
Parameters
---------
weights : array-like of shape (n,)
containing weights in [0,1]
Returns
-------
mask : boolean np.array of shape (n,) of good weight values
"""
mask = (np.abs(weights) >= np.sqrt(EPS)) * np.isfinite(weights)
if mask.sum() == 0:
raise OptimizationError(
'PIRLS optimization has diverged.\n'
+ 'Try increasing regularization, or specifying an initial value for self.coef_' # noqa: E501
)
return mask
def _initial_estimate(self, y, modelmat):
"""
Makes an inital estimate for the model coefficients.
For a LinearGAM we simply initialize to small coefficients.
For other GAMs we transform the problem to the linear space
and solve an unpenalized version.
Parameters
---------
y : array-like of shape (n,)
containing target data
modelmat : sparse matrix of shape (n, m)
containing model matrix of the spline basis
Returns
-------
coef : array of shape (m,) containing the initial estimate for the model
coefficients
Notes
-----
This method implements the suggestions in
Wood, section 2.2.2 Geometry and IRLS convergence, pg 80
"""
# do a simple initialization for LinearGAMs
if isinstance(self, LinearGAM):
n, m = modelmat.shape
return np.ones(m) * np.sqrt(EPS)
# transform the problem to the linear scale
y = deepcopy(y).astype('float64')
y[y == 0] += 0.01 # edge case for log link, inverse link, and logit link
y[y == 1] -= 0.01 # edge case for logit link
y_ = self.link.link(y, self.distribution)
y_ = make_2d(y_, verbose=False)
assert np.isfinite(
y_
).all(), "transformed response values should be well-behaved."
# solve the linear problem
return np.linalg.solve(
load_diagonal(modelmat.T.dot(modelmat).A), modelmat.T.dot(y_)
)
# not sure if this is faster...
# return np.linalg.pinv(modelmat.T.dot(modelmat)).dot(modelmat.T.dot(y_))
def _pirls(self, X, Y, weights):
"""
Performs stable PIRLS iterations to estimate GAM coefficients
Parameters
---------
X : array-like of shape (n_samples, m_features)
containing input data
Y : array-like of shape (n,)
containing target data
weights : array-like of shape (n,)
containing sample weights
Returns
-------
None
"""
modelmat = self._modelmat(X) # build a basis matrix for the GLM
n, m = modelmat.shape
# initialize GLM coefficients if model is not yet fitted
if (
not self._is_fitted
or len(self.coef_) != self.terms.n_coefs
or not np.isfinite(self.coef_).all()
):
# initialize the model
self.coef_ = self._initial_estimate(Y, modelmat)
assert np.isfinite(
self.coef_
).all(), "coefficients should be well-behaved, but found: {}".format(self.coef_)
P = self._P()
S = sp.sparse.diags(np.ones(m) * np.sqrt(EPS)) # improve condition
# S += self._H # add any user-chosen minumum penalty to the diagonal
# if we dont have any constraints, then do cholesky now
if not self.terms.hasconstraint:
E = self._cholesky(S + P, sparse=False, verbose=self.verbose)
min_n_m = np.min([m, n])
Dinv = np.zeros((min_n_m + m, m)).T
for _ in range(self.max_iter):
# recompute cholesky if needed
if self.terms.hasconstraint:
P = self._P()
C = self._C()
E = self._cholesky(S + P + C, sparse=False, verbose=self.verbose)
# forward pass
y = deepcopy(Y) # for simplicity
lp = self._linear_predictor(modelmat=modelmat)
mu = self.link.mu(lp, self.distribution)
W = self._W(mu, weights, y) # create pirls weight matrix
# check for weghts == 0, nan, and update
mask = self._mask(W.diagonal())
y = y[mask] # update
lp = lp[mask] # update
mu = mu[mask] # update
W = sp.sparse.diags(W.diagonal()[mask]) # update
# PIRLS Wood pg 183
pseudo_data = W.dot(self._pseudo_data(y, lp, mu))
# log on-loop-start stats
self._on_loop_start(vars())
WB = W.dot(modelmat[mask, :]) # common matrix product
Q, R = np.linalg.qr(WB.A)
if not np.isfinite(Q).all() or not np.isfinite(R).all():
raise ValueError(
'QR decomposition produced NaN or Inf. ' 'Check X data.'
)
# need to recompute the number of singular values
min_n_m = np.min([m, n, mask.sum()])
Dinv = np.zeros((m, min_n_m))
# SVD
U, d, Vt = np.linalg.svd(np.vstack([R, E]))
# mask out small singular values
# svd_mask = d <= (d.max() * np.sqrt(EPS))
np.fill_diagonal(Dinv, d**-1) # invert the singular values
U1 = U[:min_n_m, :min_n_m] # keep only top corner of U
# update coefficients
B = Vt.T.dot(Dinv).dot(U1.T).dot(Q.T)
coef_new = B.dot(pseudo_data).flatten()
diff = np.linalg.norm(self.coef_ - coef_new) / np.linalg.norm(coef_new)
self.coef_ = coef_new # update
# log on-loop-end stats
self._on_loop_end(vars())
# check convergence
if diff < self.tol:
break
# estimate statistics even if not converged
self._estimate_model_statistics(
Y, modelmat, inner=None, BW=WB.T, B=B, weights=weights, U1=U1
)
if diff < self.tol:
return
print('did not converge')
return
def _on_loop_start(self, variables):
"""
performs on-loop-start actions like callbacks
variables contains local namespace variables.
Parameters
---------
variables : dict of available variables
Returns
-------
None
"""
for callback in self.callbacks:
if hasattr(callback, 'on_loop_start'):
self.logs_[str(callback)].append(callback.on_loop_start(**variables))
def _on_loop_end(self, variables):
"""
performs on-loop-end actions like callbacks
variables contains local namespace variables.
Parameters
---------
variables : dict of available variables
Returns
-------
None
"""
for callback in self.callbacks:
if hasattr(callback, 'on_loop_end'):
self.logs_[str(callback)].append(callback.on_loop_end(**variables))
def fit(self, X, y, weights=None):
"""Fit the generalized additive model.
Parameters
----------
X : array-like, shape (n_samples, m_features)
Training vectors.
y : array-like, shape (n_samples,)
Target values,
ie integers in classification, real numbers in
regression)
weights : array-like shape (n_samples,) or None, optional
Sample weights.
if None, defaults to array of ones
Returns
-------
self : object
Returns fitted GAM object
"""
# validate parameters
self._validate_params()
# validate data
y = check_y(y, self.link, self.distribution, verbose=self.verbose)
X = check_X(X, verbose=self.verbose)
check_X_y(X, y)
if weights is not None:
weights = np.array(weights).astype('f').ravel()
weights = check_array(
weights, name='sample weights', ndim=1, verbose=self.verbose
)
check_lengths(y, weights)
else:
weights = np.ones_like(y).astype('float64')
# validate data-dependent parameters
self._validate_data_dep_params(X)
# set up logging
if not hasattr(self, 'logs_'):
self.logs_ = defaultdict(list)
# begin capturing statistics
self.statistics_ = {}
self.statistics_['n_samples'] = len(y)
self.statistics_['m_features'] = X.shape[1]
# optimize
self._pirls(X, y, weights)
# if self._opt == 0:
# self._pirls(X, y, weights)
# if self._opt == 1:
# self._pirls_naive(X, y)
return self
def score(self, X, y, weights=None):
"""compute the explained deviance for a trained model for a given X data and
y labels
Parameters
----------
X : array-like
Input data array of shape (n_samples, m_features)
y : array-like
Output data vector of shape (n_samples,)
weights : array-like shape (n_samples,) or None, optional
Sample weights.
if None, defaults to array of ones
Returns
-------
explained deviancce score: np.array() (n_samples,)
"""
r2 = self._estimate_r2(X=X, y=y, mu=None, weights=weights)
return r2['explained_deviance']
def deviance_residuals(self, X, y, weights=None, scaled=False):
"""
method to compute the deviance residuals of the model
these are analogous to the residuals of an OLS.
Parameters
----------
X : array-like
Input data array of shape (n_samples, m_features)
y : array-like
Output data vector of shape (n_samples,)
weights : array-like shape (n_samples,) or None, optional
Sample weights.
if None, defaults to array of ones
scaled : bool, optional
whether to scale the deviance by the (estimated) distribution scale
Returns
-------
deviance_residuals : np.array
with shape (n_samples,)
"""
if not self._is_fitted:
raise AttributeError('GAM has not been fitted. Call fit first.')
y = check_y(y, self.link, self.distribution, verbose=self.verbose)
X = check_X(
X,
n_feats=self.statistics_['m_features'],
edge_knots=self.edge_knots_,
dtypes=self.dtype,
features=self.feature,
verbose=self.verbose,
)
check_X_y(X, y)
if weights is not None:
weights = np.array(weights).astype('f').ravel()
weights = check_array(
weights, name='sample weights', ndim=1, verbose=self.verbose
)
check_lengths(y, weights)
else:
weights = np.ones_like(y).astype('float64')
mu = self.predict_mu(X)
sign = np.sign(y - mu)
return (
sign
* self.distribution.deviance(y, mu, weights=weights, scaled=scaled) ** 0.5
)
def _estimate_model_statistics(
self, y, modelmat, inner=None, BW=None, B=None, weights=None, U1=None
):
"""
method to compute all of the model statistics