def _posterior(self, X, Y, alpha0, w0):
'''
Iteratively refitted least squares method using l_bfgs_b or newton_cg.
Finds MAP estimates for weights and Hessian at convergence point
'''
n_samples,n_features = X.shape
if self.solver == 'lbfgs_b':
f = lambda w: _logistic_loss_and_grad(w,X[:,:-1],Y,alpha0)
w = fmin_l_bfgs_b(f, x0 = w0, pgtol = self.tol_solver,
maxiter = self.n_iter_solver)[0]
elif self.solver == 'newton_cg':
f = _logistic_loss
grad = lambda w,*args: _logistic_loss_and_grad(w,*args)[1]
hess = _logistic_grad_hess
args = (X[:,:-1],Y,alpha0)
w = newton_cg(hess, f, grad, w0, args=args,
maxiter=self.n_iter, tol=self.tol)[0]
else:
raise NotImplementedError('Liblinear solver is not yet implemented')
# calculate negative of Hessian at w
xw = np.dot(X,w)
s = expit(xw)
R = s * (1 - s)
Hess = np.dot(X.T*R,X)
Alpha = np.ones(n_features)*alpha0
if self.fit_intercept:
Alpha[-1] = np.finfo(np.float16).eps
np.fill_diagonal(Hess, np.diag(Hess) + Alpha)
e = eigvalsh(Hess)
return w,1./e
def _posterior(self, X, Y, alpha0, w0):
'''
Iteratively refitted least squares method using l_bfgs_b or newton_cg.
Finds MAP estimates for weights and Hessian at convergence point
'''
n_samples, n_features = X.shape
if self.solver == 'lbfgs_b':
f = lambda w: _logistic_loss_and_grad(w, X[:, :-1], Y, alpha0)
w = fmin_l_bfgs_b(f, x0=w0, pgtol=self.tol_solver,
maxiter=self.n_iter_solver)[0]
elif self.solver == 'newton_cg':
f = _logistic_loss
grad = lambda w, *args: _logistic_loss_and_grad(w, *args)[1]
hess = _logistic_grad_hess
args = (X[:, :-1], Y, alpha0)
w = newton_cg(hess, f, grad, w0, args=args,
maxiter=self.n_iter, tol=self.tol)[0]
else:
raise NotImplementedError('Liblinear solver is not yet implemented')
# calculate negative of Hessian at w
xw = np.dot(X, w)
s = sigmoid(xw)
R = s * (1 - s)
Hess = np.dot(X.T * R, X)
Alpha = np.ones(n_features) * alpha0
if self.fit_intercept:
Alpha[-1] = np.finfo(np.float16).eps
np.fill_diagonal(Hess, np.diag(Hess) + Alpha)
e = eigvalsh(Hess)
return w, 1. / e
def test_newton_cg():
rng = np.random.RandomState(0)
A = rng.normal(size=(10, 10))
x0 = np.ones(10)
def func(x):
Ax = A.dot(x)
return .5 * (Ax).dot(Ax)
def grad(x):
return A.T.dot(A.dot(x))
def grad_hess(x):
return grad(x), lambda x: A.T.dot(A.dot(x))
with pytest.warns(FutureWarning, match="removed in version 0.24"):
newton_cg(grad_hess, func, grad, x0)
def _posterior(self, X, Y, alpha0, w0, full_covar=False):
'''
Iteratively refitted least squares method using l_bfgs_b.
Finds MAP estimates for weights and Hessian at convergence point
'''
if self.solver == 'lbfgs_b':
f = lambda w: _logistic_loss_and_grad(w, X, Y, alpha0)
w = fmin_l_bfgs_b(f,
x0=w0,
pgtol=self.tol_solver,
maxiter=self.n_iter_solver)[0]
elif self.solver == 'newton_cg':
f = _logistic_loss
grad = lambda w, *args: _logistic_loss_and_grad(w, *args)[1]
hess = _logistic_grad_hess
args = (X, Y, alpha0)
w = newton_cg(hess,
f,
grad,
w0,
args=args,
maxiter=self.n_iter,
tol=self.tol)[0]
else:
raise NotImplementedError(
'Liblinear solver is not yet implemented')
# calculate negative of Hessian at w
if self.fit_intercept:
XW = np.dot(X, w[:-1]) + w[-1]
else:
XW = np.dot(X, w)
s = expit(XW)
R = s * (1 - s)
negHessian = np.dot(X.T * R, X)
# do not regularise constant
alpha_vec = np.zeros(negHessian.shape[0])
alpha_vec = alpha0
np.fill_diagonal(negHessian, np.diag(negHessian) + alpha_vec)
if full_covar is False:
eigs = 1. / eigvalsh(negHessian)
return [w, eigs]
else:
inv = pinvh(negHessian)
return [w, inv]
def test_newton_cg():
# Test that newton_cg gives same result as scipy's fmin_ncg
rng = np.random.RandomState(0)
A = rng.normal(size=(10, 10))
x0 = np.ones(10)
def func(x):
Ax = A.dot(x)
return .5 * (Ax).dot(Ax)
def grad(x):
return A.T.dot(A.dot(x))
def hess(x, p):
return p.dot(A.T.dot(A.dot(x.all())))
def func_grad_hess(x):
return func(x), grad(x), lambda x: A.T.dot(A.dot(x))
assert_array_almost_equal(newton_cg(func_grad_hess, func, grad, x0, tol=1e-10),
fmin_ncg(f=func, x0=x0, fprime=grad, fhess_p=hess))
def _posterior(self, X, Y, alpha0, w0, full_covar = False):
'''
Iteratively refitted least squares method using l_bfgs_b.
Finds MAP estimates for weights and Hessian at convergence point
'''
if self.solver == 'lbfgs_b':
f = lambda w: _logistic_loss_and_grad(w,X,Y,alpha0)
w = fmin_l_bfgs_b(f, x0 = w0, pgtol = self.tol_solver,
maxiter = self.n_iter_solver)[0]
elif self.solver == 'newton_cg':
f = _logistic_loss
grad = lambda w,*args: _logistic_loss_and_grad(w,*args)[1]
hess = _logistic_grad_hess
args = (X,Y,alpha0)
w = newton_cg(hess, f, grad, w0, args=args,
maxiter=self.n_iter, tol=self.tol)[0]
else:
raise NotImplementedError('Liblinear solver is not yet implemented')
# calculate negative of Hessian at w
if self.fit_intercept:
XW = np.dot(X,w[:-1]) + w[-1]
else:
XW = np.dot(X,w)
s = expit(XW)
R = s * (1 - s)
negHessian = np.dot(X.T*R,X)
# do not regularise constant
alpha_vec = np.zeros(negHessian.shape[0])
alpha_vec = alpha0
np.fill_diagonal(negHessian,np.diag(negHessian) + alpha_vec)
if full_covar is False:
eigs = 1./eigvalsh(negHessian)
return [w,eigs]
else:
inv = pinvh(negHessian)
return [w, inv]
def test_newton_cg():
# Test that newton_cg gives same result as scipy's fmin_ncg
rng = np.random.RandomState(0)
A = rng.normal(size=(10, 10))
x0 = np.ones(10)
def func(x):
Ax = A.dot(x)
return .5 * (Ax).dot(Ax)
def grad(x):
return A.T.dot(A.dot(x))
def hess(x, p):
return p.dot(A.T.dot(A.dot(x.all())))
def func_grad_hess(x):
return func(x), grad(x), lambda x: A.T.dot(A.dot(x))
assert_array_almost_equal(
newton_cg(func_grad_hess, func, grad, x0, tol=1e-10),
fmin_ncg(f=func, x0=x0, fprime=grad, fhess_p=hess))
def _logistic_regression_path(X,
y,
pos_class=None,
Cs=10,
fit_intercept=True,
max_iter=100,
tol=1e-4,
verbose=0,
solver='lbfgs',
coef=None,
class_weight=None,
dual=False,
penalty='l2',
intercept_scaling=1.,
multi_class='warn',
random_state=None,
check_input=True,
max_squared_sum=None,
sample_weight=None,
l1_ratio=None):
"""Compute a Logistic Regression model for a list of regularization
parameters.
This is an implementation that uses the result of the previous model
to speed up computations along the set of solutions, making it faster
than sequentially calling LogisticRegression for the different parameters.
Note that there will be no speedup with liblinear solver, since it does
not handle warm-starting.
Read more in the :ref:`User Guide <logistic_regression>`.
Parameters
----------
X : array-like or sparse matrix, shape (n_samples, n_features)
Input data.
y : array-like, shape (n_samples,) or (n_samples, n_targets)
Input data, target values.
pos_class : int, None
The class with respect to which we perform a one-vs-all fit.
If None, then it is assumed that the given problem is binary.
Cs : int | array-like, shape (n_cs,)
List of values for the regularization parameter or integer specifying
the number of regularization parameters that should be used. In this
case, the parameters will be chosen in a logarithmic scale between
1e-4 and 1e4.
fit_intercept : bool
Whether to fit an intercept for the model. In this case the shape of
the returned array is (n_cs, n_features + 1).
max_iter : int
Maximum number of iterations for the solver.
tol : float
Stopping criterion. For the newton-cg and lbfgs solvers, the iteration
will stop when ``max{|g_i | i = 1, ..., n} <= tol``
where ``g_i`` is the i-th component of the gradient.
verbose : int
For the liblinear and lbfgs solvers set verbose to any positive
number for verbosity.
solver : {'lbfgs', 'newton-cg', 'liblinear', 'sag', 'saga'}
Numerical solver to use.
coef : array-like, shape (n_features,), default None
Initialization value for coefficients of logistic regression.
Useless for liblinear solver.
class_weight : dict or 'balanced', optional
Weights associated with classes in the form ``{class_label: weight}``.
If not given, all classes are supposed to have weight one.
The "balanced" mode uses the values of y to automatically adjust
weights inversely proportional to class frequencies in the input data
as ``n_samples / (n_classes * np.bincount(y))``.
Note that these weights will be multiplied with sample_weight (passed
through the fit method) if sample_weight is specified.
dual : bool
Dual or primal formulation. Dual formulation is only implemented for
l2 penalty with liblinear solver. Prefer dual=False when
n_samples > n_features.
penalty : str, 'l1', 'l2', or 'elasticnet'
Used to specify the norm used in the penalization. The 'newton-cg',
'sag' and 'lbfgs' solvers support only l2 penalties. 'elasticnet' is
only supported by the 'saga' solver.
intercept_scaling : float, default 1.
Useful only when the solver 'liblinear' is used
and self.fit_intercept is set to True. In this case, x becomes
[x, self.intercept_scaling],
i.e. a "synthetic" feature with constant value equal to
intercept_scaling is appended to the instance vector.
The intercept becomes ``intercept_scaling * synthetic_feature_weight``.
Note! the synthetic feature weight is subject to l1/l2 regularization
as all other features.
To lessen the effect of regularization on synthetic feature weight
(and therefore on the intercept) intercept_scaling has to be increased.
multi_class : str, {'ovr', 'multinomial', 'auto'}, default: 'ovr'
If the option chosen is 'ovr', then a binary problem is fit for each
label. For 'multinomial' the loss minimised is the multinomial loss fit
across the entire probability distribution, *even when the data is
binary*. 'multinomial' is unavailable when solver='liblinear'.
'auto' selects 'ovr' if the data is binary, or if solver='liblinear',
and otherwise selects 'multinomial'.
.. versionadded:: 0.18
Stochastic Average Gradient descent solver for 'multinomial' case.
.. versionchanged:: 0.20
Default will change from 'ovr' to 'auto' in 0.22.
random_state : int, RandomState instance or None, optional, default None
The seed of the pseudo random number generator to use when shuffling
the data. If int, random_state is the seed used by the random number
generator; If RandomState instance, random_state is the random number
generator; If None, the random number generator is the RandomState
instance used by `np.random`. Used when ``solver`` == 'sag' or
'liblinear'.
check_input : bool, default True
If False, the input arrays X and y will not be checked.
max_squared_sum : float, default None
Maximum squared sum of X over samples. Used only in SAG solver.
If None, it will be computed, going through all the samples.
The value should be precomputed to speed up cross validation.
sample_weight : array-like, shape(n_samples,) optional
Array of weights that are assigned to individual samples.
If not provided, then each sample is given unit weight.
l1_ratio : float or None, optional (default=None)
The Elastic-Net mixing parameter, with ``0 <= l1_ratio <= 1``. Only
used if ``penalty='elasticnet'``. Setting ``l1_ratio=0`` is equivalent
to using ``penalty='l2'``, while setting ``l1_ratio=1`` is equivalent
to using ``penalty='l1'``. For ``0 < l1_ratio <1``, the penalty is a
combination of L1 and L2.
Returns
-------
coefs : ndarray, shape (n_cs, n_features) or (n_cs, n_features + 1)
List of coefficients for the Logistic Regression model. If
fit_intercept is set to True then the second dimension will be
n_features + 1, where the last item represents the intercept. For
``multiclass='multinomial'``, the shape is (n_classes, n_cs,
n_features) or (n_classes, n_cs, n_features + 1).
Cs : ndarray
Grid of Cs used for cross-validation.
n_iter : array, shape (n_cs,)
Actual number of iteration for each Cs.
Notes
-----
You might get slightly different results with the solver liblinear than
with the others since this uses LIBLINEAR which penalizes the intercept.
.. versionchanged:: 0.19
The "copy" parameter was removed.
"""
if isinstance(Cs, numbers.Integral):
Cs = np.logspace(-4, 4, Cs)
solver = _check_solver(solver, penalty, dual)
# Preprocessing.
if check_input:
X = check_array(X,
accept_sparse='csr',
dtype=np.float64,
accept_large_sparse=solver != 'liblinear')
y = check_array(y, ensure_2d=False, dtype=None)
check_consistent_length(X, y)
_, n_features = X.shape
classes = np.unique(y)
random_state = check_random_state(random_state)
multi_class = _check_multi_class(multi_class, solver, len(classes))
if pos_class is None and multi_class != 'multinomial':
if (classes.size > 2):
raise ValueError('To fit OvR, use the pos_class argument')
# np.unique(y) gives labels in sorted order.
pos_class = classes[1]
# If sample weights exist, convert them to array (support for lists)
# and check length
# Otherwise set them to 1 for all examples
if sample_weight is not None:
sample_weight = np.array(sample_weight, dtype=X.dtype, order='C')
check_consistent_length(y, sample_weight)
default_weights = False
else:
sample_weight = np.ones(X.shape[0], dtype=X.dtype)
default_weights = (class_weight is None)
daal_ready = use_daal and solver in ['lbfgs', 'newton-cg'
] and not sparse.issparse(X)
# If class_weights is a dict (provided by the user), the weights
# are assigned to the original labels. If it is "balanced", then
# the class_weights are assigned after masking the labels with a OvR.
le = LabelEncoder()
if isinstance(class_weight, dict) or multi_class == 'multinomial':
class_weight_ = compute_class_weight(class_weight, classes, y)
sample_weight *= class_weight_[le.fit_transform(y)]
# For doing a ovr, we need to mask the labels first. for the
# multinomial case this is not necessary.
if multi_class == 'ovr':
w0 = np.zeros(n_features + int(fit_intercept), dtype=X.dtype)
mask_classes = np.array([-1, 1])
mask = (y == pos_class)
y_bin = np.ones(y.shape, dtype=X.dtype)
y_bin[~mask] = -1.
# for compute_class_weight
if class_weight == "balanced":
class_weight_ = compute_class_weight(class_weight, mask_classes,
y_bin)
sample_weight *= class_weight_[le.fit_transform(y_bin)]
daal_ready = daal_ready and (default_weights or np.allclose(
sample_weight, np.ones_like(sample_weight)))
if daal_ready:
w0 = np.zeros(n_features + 1, dtype=X.dtype)
y_bin[~mask] = 0.
else:
w0 = np.zeros(n_features + int(fit_intercept), dtype=X.dtype)
else:
daal_ready = daal_ready and (default_weights or np.allclose(
sample_weight, np.ones_like(sample_weight)))
if solver not in ['sag', 'saga']:
if daal_ready:
Y_multi = le.fit_transform(y).astype(X.dtype, copy=False)
else:
lbin = LabelBinarizer()
Y_multi = lbin.fit_transform(y)
if Y_multi.shape[1] == 1:
Y_multi = np.hstack([1 - Y_multi, Y_multi])
else:
# SAG multinomial solver needs LabelEncoder, not LabelBinarizer
le = LabelEncoder()
Y_multi = le.fit_transform(y).astype(X.dtype, copy=False)
if daal_ready:
w0 = np.zeros((classes.size, n_features + 1),
order='C',
dtype=X.dtype)
else:
w0 = np.zeros((classes.size, n_features + int(fit_intercept)),
order='F',
dtype=X.dtype)
if coef is not None:
# it must work both giving the bias term and not
if multi_class == 'ovr':
if coef.size not in (n_features, w0.size):
raise ValueError(
'Initialization coef is of shape %d, expected shape '
'%d or %d' % (coef.size, n_features, w0.size))
if daal_ready:
w0[-coef.size:] = np.roll(
coef, 1, -1) if coef.size != n_features else coef
else:
w0[:coef.size] = coef
else:
# For binary problems coef.shape[0] should be 1, otherwise it
# should be classes.size.
n_classes = classes.size
if n_classes == 2:
n_classes = 1
if (coef.shape[0] != n_classes
or coef.shape[1] not in (n_features, n_features + 1)):
raise ValueError(
'Initialization coef is of shape (%d, %d), expected '
'shape (%d, %d) or (%d, %d)' %
(coef.shape[0], coef.shape[1], classes.size, n_features,
classes.size, n_features + 1))
if daal_ready:
w0[:, -coef.shape[1]:] = np.roll(
coef, 1, -1) if coef.shape[1] != n_features else coef
else:
if n_classes == 1:
w0[0, :coef.shape[1]] = -coef
w0[1, :coef.shape[1]] = coef
else:
w0[:, :coef.shape[1]] = coef
C_daal_multiplier = 1
# commented out because this is Py3 feature
#def _map_to_binary_logistic_regression():
# nonlocal C_daal_multiplier
# nonlocal w0
# C_daal_multiplier = 2
# w0 *= 2
if multi_class == 'multinomial':
# fmin_l_bfgs_b and newton-cg accepts only ravelled parameters.
if solver in ['lbfgs', 'newton-cg']:
if daal_ready and classes.size == 2:
w0_saved = w0
w0 = w0[-1:, :]
w0 = w0.ravel()
target = Y_multi
if solver == 'lbfgs':
if daal_ready:
if classes.size == 2:
# _map_to_binary_logistic_regression()
C_daal_multiplier = 2
w0 *= 2
daal_extra_args_func = _daal4py_logistic_loss_extra_args
else:
daal_extra_args_func = _daal4py_cross_entropy_loss_extra_args
func = _daal4py_loss_and_grad
else:
func = lambda x, *args: _multinomial_loss_grad(x, *args)[0:2]
elif solver == 'newton-cg':
if daal_ready:
if classes.size == 2:
# _map_to_binary_logistic_regression()
C_daal_multiplier = 2
w0 *= 2
daal_extra_args_func = _daal4py_logistic_loss_extra_args
else:
daal_extra_args_func = _daal4py_cross_entropy_loss_extra_args
func = _daal4py_loss_
grad = _daal4py_grad_
hess = _daal4py_grad_hess_
else:
func = lambda x, *args: _multinomial_loss(x, *args)[0]
grad = lambda x, *args: _multinomial_loss_grad(x, *args)[1]
hess = _multinomial_grad_hess
warm_start_sag = {'coef': w0.T}
else:
target = y_bin
if solver == 'lbfgs':
if daal_ready:
func = _daal4py_loss_and_grad
daal_extra_args_func = _daal4py_logistic_loss_extra_args
else:
func = _logistic_loss_and_grad
elif solver == 'newton-cg':
if daal_ready:
daal_extra_args_func = _daal4py_logistic_loss_extra_args
func = _daal4py_loss_
grad = _daal4py_grad_
hess = _daal4py_grad_hess_
else:
func = _logistic_loss
grad = lambda x, *args: _logistic_loss_and_grad(x, *args)[1]
hess = _logistic_grad_hess
warm_start_sag = {'coef': np.expand_dims(w0, axis=1)}
coefs = list()
n_iter = np.zeros(len(Cs), dtype=np.int32)
for i, C in enumerate(Cs):
if solver == 'lbfgs':
if daal_ready:
extra_args = daal_extra_args_func(classes.size,
w0,
X,
target,
0.,
0.5 / C / C_daal_multiplier,
fit_intercept,
value=True,
gradient=True,
hessian=False)
else:
extra_args = (X, target, 1. / C, sample_weight)
iprint = [-1, 50, 1, 100,
101][np.searchsorted(np.array([0, 1, 2, 3]), verbose)]
w0, loss, info = optimize.fmin_l_bfgs_b(func,
w0,
fprime=None,
args=extra_args,
iprint=iprint,
pgtol=tol,
maxiter=max_iter)
if daal_ready and C_daal_multiplier == 2:
w0 *= 0.5
if info["warnflag"] == 1:
warnings.warn(
"lbfgs failed to converge. Increase the number "
"of iterations.", ConvergenceWarning)
# In scipy <= 1.0.0, nit may exceed maxiter.
# See https://github.com/scipy/scipy/issues/7854.
n_iter_i = min(info['nit'], max_iter)
elif solver == 'newton-cg':
if daal_ready:
def make_ncg_funcs(f,
value=False,
gradient=False,
hessian=False):
daal_penaltyL2 = 0.5 / C / C_daal_multiplier
_obj_, X_, y_, n_samples = daal_extra_args_func(
classes.size,
w0,
X,
target,
0.,
daal_penaltyL2,
fit_intercept,
value=value,
gradient=gradient,
hessian=hessian)
_func_ = lambda x, *args: f(x, _obj_, *args)
return _func_, (X_, y_, n_samples, daal_penaltyL2)
loss_func, extra_args = make_ncg_funcs(func, value=True)
grad_func, _ = make_ncg_funcs(grad, gradient=True)
grad_hess_func, _ = make_ncg_funcs(hess, gradient=True)
w0, n_iter_i = newton_cg(grad_hess_func,
loss_func,
grad_func,
w0,
args=extra_args,
maxiter=max_iter,
tol=tol)
else:
args = (X, target, 1. / C, sample_weight)
w0, n_iter_i = newton_cg(hess,
func,
grad,
w0,
args=args,
maxiter=max_iter,
tol=tol)
elif solver == 'liblinear':
coef_, intercept_, n_iter_i, = _fit_liblinear(
X,
target,
C,
fit_intercept,
intercept_scaling,
None,
penalty,
dual,
verbose,
max_iter,
tol,
random_state,
sample_weight=sample_weight)
if fit_intercept:
w0 = np.concatenate([coef_.ravel(), intercept_])
else:
w0 = coef_.ravel()
elif solver in ['sag', 'saga']:
if multi_class == 'multinomial':
target = target.astype(X.dtype, copy=False)
loss = 'multinomial'
else:
loss = 'log'
# alpha is for L2-norm, beta is for L1-norm
if penalty == 'l1':
alpha = 0.
beta = 1. / C
elif penalty == 'l2':
alpha = 1. / C
beta = 0.
else: # Elastic-Net penalty
alpha = (1. / C) * (1 - l1_ratio)
beta = (1. / C) * l1_ratio
w0, n_iter_i, warm_start_sag = sag_solver(
X,
target,
sample_weight,
loss,
alpha,
beta,
max_iter,
tol,
verbose,
random_state,
False,
max_squared_sum,
warm_start_sag,
is_saga=(solver == 'saga'))
else:
raise ValueError("solver must be one of {'liblinear', 'lbfgs', "
"'newton-cg', 'sag'}, got '%s' instead" % solver)
if multi_class == 'multinomial':
if daal_ready:
if classes.size == 2:
multi_w0 = w0[np.newaxis, :]
else:
multi_w0 = np.reshape(w0, (classes.size, -1))
else:
n_classes = max(2, classes.size)
multi_w0 = np.reshape(w0, (n_classes, -1))
if n_classes == 2:
multi_w0 = multi_w0[1][np.newaxis, :]
coefs.append(np.require(multi_w0, requirements='O'))
else:
coefs.append(np.require(w0, requirements='O'))
n_iter[i] = n_iter_i
if daal_ready:
if fit_intercept:
for i, ci in enumerate(coefs):
coefs[i] = np.roll(ci, -1, -1)
else:
for i, ci in enumerate(coefs):
coefs[i] = np.delete(ci, 0, axis=-1)
return np.array(coefs), np.array(Cs), n_iter
def logistic_regression(X,
y,
fit_intercept=True,
C=1e4,
max_iter=100,
tol=1e-4,
verbose=0,
solver='lbfgs',
coef=None,
class_weight=None,
dual=False,
penalty='l2',
intercept_scaling=1.,
random_state=None,
check_input=True,
max_squared_sum=None,
sample_weight=None):
"""Compute a Logistic Regression for possibly soft class labels y
Based on logistic_regression_path, but assumes multinomial and removes multiple Cs logic
Parameters
----------
X : array-like or sparse matrix, shape (n_samples, n_features)
Input data.
y : array-like, shape (n_samples,) or (n_samples, n_targets)
Input data, target values.
C : float
regularization parameter that should be used. Default is 1e4.
fit_intercept : bool
Whether to fit an intercept for the model. In this case the shape of
the returned array is (n_cs, n_features + 1).
max_iter : int
Maximum number of iterations for the solver.
tol : float
Stopping criterion. For the newton-cg and lbfgs solvers, the iteration
will stop when ``max{|g_i | i = 1, ..., n} <= tol``
where ``g_i`` is the i-th component of the gradient.
verbose : int
For the liblinear and lbfgs solvers set verbose to any positive
number for verbosity.
solver : {'lbfgs', 'newton-cg', 'liblinear', 'sag', 'saga'}
Numerical solver to use.
coef : array-like, shape (n_features,), default None
Initialization value for coefficients of logistic regression.
Useless for liblinear solver.
class_weight : dict or 'balanced', optional
Weights associated with classes in the form ``{class_label: weight}``.
If not given, all classes are supposed to have weight one.
The "balanced" mode uses the values of y to automatically adjust
weights inversely proportional to class frequencies in the input data
as ``n_samples / (n_classes * np.bincount(y))``.
Note that these weights will be multiplied with sample_weight (passed
through the fit method) if sample_weight is specified.
dual : bool
Dual or primal formulation. Dual formulation is only implemented for
l2 penalty with liblinear solver. Prefer dual=False when
n_samples > n_features.
penalty : str, 'l1' or 'l2'
Used to specify the norm used in the penalization. The 'newton-cg',
'sag' and 'lbfgs' solvers support only l2 penalties.
intercept_scaling : float, default 1.
Useful only when the solver 'liblinear' is used
and self.fit_intercept is set to True. In this case, x becomes
[x, self.intercept_scaling],
i.e. a "synthetic" feature with constant value equal to
intercept_scaling is appended to the instance vector.
The intercept becomes ``intercept_scaling * synthetic_feature_weight``.
Note! the synthetic feature weight is subject to l1/l2 regularization
as all other features.
To lessen the effect of regularization on synthetic feature weight
(and therefore on the intercept) intercept_scaling has to be increased.
random_state : int, RandomState instance or None, optional, default None
The seed of the pseudo random number generator to use when shuffling
the data. If int, random_state is the seed used by the random number
generator; If RandomState instance, random_state is the random number
generator; If None, the random number generator is the RandomState
instance used by `np.random`. Used when ``solver`` == 'sag' or
'liblinear'.
check_input : bool, default True
If False, the input arrays X and y will not be checked.
max_squared_sum : float, default None
Maximum squared sum of X over samples. Used only in SAG solver.
If None, it will be computed, going through all the samples.
The value should be precomputed to speed up cross validation.
sample_weight : array-like, shape(n_samples,) optional
Array of weights that are assigned to individual samples.
If not provided, then each sample is given unit weight.
Returns
-------
coef : ndarray, shape (n_classes, n_features) or (n_classes, n_features + 1,)
List of coefficients for the Logistic Regression model. If
fit_intercept is set to True then the second dimension will be
n_features + 1, where the last item represents the intercept.
Notes
-----
You might get slightly different results with the solver liblinear than
with the others since this uses LIBLINEAR which penalizes the intercept.
"""
solver = _check_solver(solver, penalty, dual)
# Preprocessing.
if check_input:
X = check_array(X,
accept_sparse='csr',
dtype=np.float64,
accept_large_sparse=solver != 'liblinear')
y = check_array(y, ensure_2d=False, dtype=None)
check_consistent_length(X, y)
_, n_features = X.shape
random_state = check_random_state(random_state)
if len(y.shape) == 1:
le = LabelBinarizer()
y = le.fit_transform(y).astype(X.dtype, copy=False)
# If sample weights exist, convert them to array (support for lists)
# and check length
# Otherwise set them to 1 for all examples
if sample_weight is not None:
sample_weight = np.array(sample_weight, dtype=X.dtype, order='C')
check_consistent_length(y, sample_weight)
else:
sample_weight = np.ones(X.shape[0], dtype=X.dtype)
# If class_weights is a dict (provided by the user), the weights
# are assigned to the original labels. If it is "balanced", then
# the class_weights are assigned after masking the labels with a OvR.
class_weight_ = compute_class_weight(class_weight, y)
sample_weight *= class_weight_
Y_multi = y
nclasses = Y_multi.shape[1]
w0 = np.zeros((nclasses, n_features + int(fit_intercept)),
order='F',
dtype=X.dtype)
if coef is not None:
# it must work both giving the bias term and not
# For binary problems coef.shape[0] should be 1, otherwise it
# should be nclasses.
if nclasses == 2:
nclasses = 1
if (coef.shape[0] != nclasses
or coef.shape[1] not in (n_features, n_features + 1)):
raise ValueError(
'Initialization coef is of shape (%d, %d), expected '
'shape (%d, %d) or (%d, %d)' %
(coef.shape[0], coef.shape[1], nclasses, n_features, nclasses,
n_features + 1))
if nclasses == 1:
w0[0, :coef.shape[1]] = -coef
w0[1, :coef.shape[1]] = coef
else:
w0[:, :coef.shape[1]] = coef
# fmin_l_bfgs_b and newton-cg accepts only ravelled parameters.
if solver in ['lbfgs', 'newton-cg']:
w0 = w0.ravel()
target = Y_multi
warm_start_sag = {'coef': w0.T}
if solver == 'lbfgs':
func = lambda x, *args: _multinomial_loss_grad(x, *args)[0:2]
iprint = [-1, 50, 1, 100, 101][np.searchsorted(np.array([0, 1, 2, 3]),
verbose)]
w0, loss, info = optimize.fmin_l_bfgs_b(func,
w0,
fprime=None,
args=(X, target, 1. / C,
sample_weight),
iprint=iprint,
pgtol=tol,
maxiter=max_iter)
if info["warnflag"] == 1:
warnings.warn(
"lbfgs failed to converge. Increase the number "
"of iterations.", ConvergenceWarning)
elif solver == 'newton-cg':
func = lambda x, *args: _multinomial_loss(x, *args)[0]
grad = lambda x, *args: _multinomial_loss_grad(x, *args)[1]
hess = _multinomial_grad_hess
args = (X, target, 1. / C, sample_weight)
w0, n_iter_i = newton_cg(hess,
func,
grad,
w0,
args=args,
maxiter=max_iter,
tol=tol)
elif solver == 'liblinear':
coef_, intercept_, n_iter_i, = _fit_liblinear(
X,
target,
C,
fit_intercept,
intercept_scaling,
None,
penalty,
dual,
verbose,
max_iter,
tol,
random_state,
sample_weight=sample_weight)
if fit_intercept:
w0 = np.concatenate([coef_.ravel(), intercept_])
else:
w0 = coef_.ravel()
elif solver in ['sag', 'saga']:
target = target.astype(np.float64)
loss = 'multinomial'
if penalty == 'l1':
alpha = 0.
beta = 1. / C
else:
alpha = 1. / C
beta = 0.
w0, n_iter_i, warm_start_sag = sag_solver(X,
target,
sample_weight,
loss,
alpha,
beta,
max_iter,
tol,
verbose,
random_state,
False,
max_squared_sum,
warm_start_sag,
is_saga=(solver == 'saga'))
else:
raise ValueError("solver must be one of {'liblinear', 'lbfgs', "
"'newton-cg', 'sag'}, got '%s' instead" % solver)
nclasses = max(2, nclasses)
multi_w0 = np.reshape(w0, (nclasses, -1))
if nclasses == 2:
multi_w0 = multi_w0[1][np.newaxis, :]
coef = multi_w0.copy()
return coef
def logistic_regression_path(X, y, pos_class=None, Cs=10, fit_intercept=True,
max_iter=100, tol=1e-4, verbose=0,
solver='lbfgs', coef=None, copy=False,
class_weight=None, dual=False, penalty='l2',
intercept_scaling=1., multi_class='ovr',
random_state=None, check_input=True,
max_squared_sum=None, sample_weight=None, rho=None, q=None):
"""Compute a Logistic Regression model for a list of regularization
parameters.
This is an implementation that uses the result of the previous model
to speed up computations along the set of solutions, making it faster
than sequentially calling LogisticRegression for the different parameters.
Read more in the :ref:`User Guide <logistic_regression>`.
Parameters
----------
X : array-like or sparse matrix, shape (n_samples, n_features)
Input data.
y : array-like, shape (n_samples,)
Input data, target values.
Cs : int | array-like, shape (n_cs,)
List of values for the regularization parameter or integer specifying
the number of regularization parameters that should be used. In this
case, the parameters will be chosen in a logarithmic scale between
1e-4 and 1e4.
pos_class : int, None
The class with respect to which we perform a one-vs-all fit.
If None, then it is assumed that the given problem is binary.
fit_intercept : bool
Whether to fit an intercept for the model. In this case the shape of
the returned array is (n_cs, n_features + 1).
max_iter : int
Maximum number of iterations for the solver.
tol : float
Stopping criterion. For the newton-cg and lbfgs solvers, the iteration
will stop when ``max{|g_i | i = 1, ..., n} <= tol``
where ``g_i`` is the i-th component of the gradient.
verbose : int
For the liblinear and lbfgs solvers set verbose to any positive
number for verbosity.
solver : {'lbfgs', 'newton-cg', 'liblinear', 'sag'}
Numerical solver to use.
coef : array-like, shape (n_features,), default None
Initialization value for coefficients of logistic regression.
Useless for liblinear solver.
copy : bool, default False
Whether or not to produce a copy of the data. A copy is not required
anymore. This parameter is deprecated and will be removed in 0.19.
class_weight : dict or 'balanced', optional
Weights associated with classes in the form ``{class_label: weight}``.
If not given, all classes are supposed to have weight one.
The "balanced" mode uses the values of y to automatically adjust
weights inversely proportional to class frequencies in the input data
as ``n_samples / (n_classes * np.bincount(y))``
Note that these weights will be multiplied with sample_weight (passed
through the fit method) if sample_weight is specified.
dual : bool
Dual or primal formulation. Dual formulation is only implemented for
l2 penalty with liblinear solver. Prefer dual=False when
n_samples > n_features.
penalty : str, 'l1' or 'l2'
Used to specify the norm used in the penalization. The 'newton-cg',
'sag' and 'lbfgs' solvers support only l2 penalties.
intercept_scaling : float, default 1.
This parameter is useful only when the solver 'liblinear' is used
and self.fit_intercept is set to True. In this case, x becomes
[x, self.intercept_scaling],
i.e. a "synthetic" feature with constant value equals to
intercept_scaling is appended to the instance vector.
The intercept becomes intercept_scaling * synthetic feature weight
Note! the synthetic feature weight is subject to l1/l2 regularization
as all other features.
To lessen the effect of regularization on synthetic feature weight
(and therefore on the intercept) intercept_scaling has to be increased.
multi_class : str, {'ovr', 'multinomial'}
Multiclass option can be either 'ovr' or 'multinomial'. If the option
chosen is 'ovr', then a binary problem is fit for each label. Else
the loss minimised is the multinomial loss fit across
the entire probability distribution. Works only for the 'lbfgs' and
'newton-cg' solvers.
random_state : int seed, RandomState instance, or None (default)
The seed of the pseudo random number generator to use when
shuffling the data.
check_input : bool, default True
If False, the input arrays X and y will not be checked.
max_squared_sum : float, default None
Maximum squared sum of X over samples. Used only in SAG solver.
If None, it will be computed, going through all the samples.
The value should be precomputed to speed up cross validation.
sample_weight : array-like, shape(n_samples,) optional
Array of weights that are assigned to individual samples.
If not provided, then each sample is given unit weight.
Returns
-------
coefs : ndarray, shape (n_cs, n_features) or (n_cs, n_features + 1)
List of coefficients for the Logistic Regression model. If
fit_intercept is set to True then the second dimension will be
n_features + 1, where the last item represents the intercept.
Cs : ndarray
Grid of Cs used for cross-validation.
n_iter : array, shape (n_cs,)
Actual number of iteration for each Cs.
Notes
-----
You might get slighly different results with the solver liblinear than
with the others since this uses LIBLINEAR which penalizes the intercept.
"""
if copy:
warnings.warn("A copy is not required anymore. The 'copy' parameter "
"is deprecated and will be removed in 0.19.",
DeprecationWarning)
if isinstance(Cs, numbers.Integral):
Cs = np.logspace(-4, 4, Cs)
_check_solver_option(solver, multi_class, penalty, dual)
# Preprocessing.
if check_input or copy:
X = check_array(X, accept_sparse='csr', dtype=np.float64)
y = check_array(y, ensure_2d=False, copy=copy, dtype=None)
check_consistent_length(X, y)
_, n_features = X.shape
classes = np.unique(y)
random_state = check_random_state(random_state)
if pos_class is None and multi_class != 'multinomial':
if (classes.size > 2):
raise ValueError('To fit OvR, use the pos_class argument')
# np.unique(y) gives labels in sorted order.
pos_class = classes[1]
# If sample weights exist, convert them to array (support for lists)
# and check length
# Otherwise set them to 1 for all examples
if sample_weight is not None:
sample_weight = np.array(sample_weight, dtype=np.float64, order='C')
check_consistent_length(y, sample_weight)
else:
sample_weight = np.ones(X.shape[0])
# If class_weights is a dict (provided by the user), the weights
# are assigned to the original labels. If it is "balanced", then
# the class_weights are assigned after masking the labels with a OvR.
le = LabelEncoder()
if isinstance(class_weight, dict) or multi_class == 'multinomial':
if solver == "liblinear":
if classes.size == 2:
# Reconstruct the weights with keys 1 and -1
temp = {1: class_weight[pos_class],
-1: class_weight[classes[0]]}
class_weight = temp.copy()
else:
raise ValueError("In LogisticRegressionCV the liblinear "
"solver cannot handle multiclass with "
"class_weight of type dict. Use the lbfgs, "
"newton-cg or sag solvers or set "
"class_weight='balanced'")
else:
class_weight_ = compute_class_weight(class_weight, classes, y)
sample_weight *= class_weight_[le.fit_transform(y)]
# For doing a ovr, we need to mask the labels first. for the
# multinomial case this is not necessary.
if multi_class == 'ovr':
w0 = np.zeros(n_features + int(fit_intercept))
mask_classes = np.array([-1, 1])
mask = (y == pos_class)
y_bin = np.ones(y.shape, dtype=np.float64)
y_bin[~mask] = -1.
# for compute_class_weight
# 'auto' is deprecated and will be removed in 0.19
if class_weight in ("auto", "balanced"):
class_weight_ = compute_class_weight(class_weight, mask_classes,
y_bin)
sample_weight *= class_weight_[le.fit_transform(y_bin)]
else:
lbin = LabelBinarizer()
Y_binarized = lbin.fit_transform(y)
if Y_binarized.shape[1] == 1:
Y_binarized = np.hstack([1 - Y_binarized, Y_binarized])
w0 = np.zeros((Y_binarized.shape[1], n_features + int(fit_intercept)),
order='F')
if coef is not None:
# it must work both giving the bias term and not
if multi_class == 'ovr':
if coef.size not in (n_features, w0.size):
raise ValueError(
'Initialization coef is of shape %d, expected shape '
'%d or %d' % (coef.size, n_features, w0.size))
w0[:coef.size] = coef
else:
# For binary problems coef.shape[0] should be 1, otherwise it
# should be classes.size.
n_vectors = classes.size
if n_vectors == 2:
n_vectors = 1
if (coef.shape[0] != n_vectors or
coef.shape[1] not in (n_features, n_features + 1)):
raise ValueError(
'Initialization coef is of shape (%d, %d), expected '
'shape (%d, %d) or (%d, %d)' % (
coef.shape[0], coef.shape[1], classes.size,
n_features, classes.size, n_features + 1))
w0[:, :coef.shape[1]] = coef
if multi_class == 'multinomial':
# fmin_l_bfgs_b and newton-cg accepts only ravelled parameters.
w0 = w0.ravel()
target = Y_binarized
if solver == 'lbfgs':
func = lambda x, *args: _multinomial_loss_grad(x, *args)[0:2]
elif solver == 'newton-cg':
func = lambda x, *args: _multinomial_loss(x, *args)[0]
grad = lambda x, *args: _multinomial_loss_grad(x, *args)[1]
hess = _multinomial_grad_hess
else:
target = y_bin
if solver == 'lbfgs':
func = lambda *args: _logistic_loss_and_grad(rho=rho, q=q, *args)
elif solver == 'newton-cg':
func = _logistic_loss
grad = lambda x, *args: _logistic_loss_and_grad(x, *args)[1]
hess = _logistic_grad_hess
coefs = list()
warm_start_sag = {'coef': w0}
n_iter = np.zeros(len(Cs), dtype=np.int32)
for i, C in enumerate(Cs):
if solver == 'lbfgs':
try:
w0, loss, info = optimize.fmin_l_bfgs_b(
func, w0, fprime=None,
args=(X, target, 1. / C, sample_weight),
iprint=(verbose > 0) - 1, pgtol=tol, maxiter=max_iter)
except TypeError:
# old scipy doesn't have maxiter
w0, loss, info = optimize.fmin_l_bfgs_b(
func, w0, fprime=None,
args=(X, target, 1. / C, sample_weight),
iprint=(verbose > 0) - 1, pgtol=tol)
if info["warnflag"] == 1 and verbose > 0:
warnings.warn("lbfgs failed to converge. Increase the number "
"of iterations.")
try:
n_iter_i = info['nit'] - 1
except:
n_iter_i = info['funcalls'] - 1
elif solver == 'newton-cg':
args = (X, target, 1. / C, sample_weight)
w0, n_iter_i = newton_cg(hess, func, grad, w0, args=args,
maxiter=max_iter, tol=tol)
elif solver == 'liblinear':
coef_, intercept_, n_iter_i, = _fit_liblinear(
X, target, C, fit_intercept, intercept_scaling, class_weight,
penalty, dual, verbose, max_iter, tol, random_state)
if fit_intercept:
w0 = np.concatenate([coef_.ravel(), intercept_])
else:
w0 = coef_.ravel()
elif solver == 'sag':
w0, n_iter_i, warm_start_sag = sag_solver(
X, target, sample_weight, 'log', 1. / C, max_iter, tol,
verbose, random_state, False, max_squared_sum,
warm_start_sag)
else:
raise ValueError("solver must be one of {'liblinear', 'lbfgs', "
"'newton-cg', 'sag'}, got '%s' instead" % solver)
if multi_class == 'multinomial':
multi_w0 = np.reshape(w0, (classes.size, -1))
if classes.size == 2:
multi_w0 = multi_w0[1][np.newaxis, :]
coefs.append(multi_w0)
else:
coefs.append(w0.copy())
n_iter[i] = n_iter_i
return coefs, np.array(Cs), n_iter
def fit(self, X, Y, sample_weight = None):
"""
fit the weighted model
Parameters
----------
X : design matrix
Y : response matrix
sample_weight: sample weight vector
"""
if sample_weight is None:
sample_weight = np.ones((X.shape[0],))
assert X.shape[0] == Y.shape[0]
assert X.shape[0] == sample_weight.shape[0]
if X.ndim == 1:
X = X.reshape(-1,1)
if self.fit_intercept:
X = addIntercept(X)
self.n_samples = X.shape[0]
self.n_features = X.shape[1]
self.n_targets = Y.shape[1]
if self.n_targets < 2:
raise ValueError('n_targets < 2')
w0 = np.zeros((self.n_targets*self.n_features, ))
if self.solver == 'lbfgs':
func = lambda x, *args: _multinomial_loss_grad(x, *args)[0:2]
else:
func = lambda x, *args: _multinomial_loss(x, *args)[0]
grad = lambda x, *args: _multinomial_loss_grad(x, *args)[1]
hess = _multinomial_grad_hess
if self.solver == 'lbfgs':
try:
w0, loss, info = optimize.fmin_l_bfgs_b(
func, w0, fprime=None,
args=(X, Y, self.reg, sample_weight),
iprint=0, pgtol=self.tol, maxiter=self.max_iter)
except TypeError:
# old scipy doesn't have maxiter
w0, loss, info = optimize.fmin_l_bfgs_b(
func, w0, fprime=None,
args=(X, Y, self.reg, sample_weight),
iprint=0, pgtol=self.tol)
if info["warnflag"] == 1:
warnings.warn("lbfgs failed to converge. Increase the number "
"of iterations.")
try:
n_iter_i = info['nit'] - 1
except:
n_iter_i = info['funcalls'] - 1
else:
args = (X, Y, self.reg, sample_weight)
w0, n_iter_i = newton_cg(hess, func, grad, w0, args=args,
maxiter=self.max_iter, tol=self.tol)
w1 = w0.reshape(self.n_targets, -1)
w1 = w1.T - w1.T[:,0].reshape(-1,1)
self.coef = w1
self.converged = n_iter_i < self.max_iter
self.dispersion = self.estimate_dispersion()
if self.est_sd:
self.sd = self.estimate_sd(X, sample_weight)
self.ll = self.estimate_loglikelihood(X, Y, sample_weight)
