def lbfgs(X,
y,
regularizer=None,
lamduh=1.0,
max_iter=100,
tol=1e-4,
family=Logistic,
verbose=False,
**kwargs):
"""L-BFGS solver using scipy.optimize implementation
Parameters
----------
X : array-like, shape (n_samples, n_features)
y : array-like, shape (n_samples,)
regularizer : str or Regularizer
lamduh : float
max_iter : int
maximum number of iterations to attempt before declaring
failure to converge
tol : float
Maximum allowed change from prior iteration required to
declare convergence
family : Family
verbose : bool, default False
whether to print diagnostic information during convergence
Returns
-------
beta : array-like, shape (n_features,)
"""
pointwise_loss = family.pointwise_loss
pointwise_gradient = family.pointwise_gradient
if regularizer is not None:
regularizer = Regularizer.get(regularizer)
pointwise_loss = regularizer.add_reg_f(pointwise_loss, lamduh)
pointwise_gradient = regularizer.add_reg_grad(pointwise_gradient,
lamduh)
n, p = X.shape
beta0 = np.zeros(p)
def compute_loss_grad(beta, X, y):
loss_fn = pointwise_loss(beta, X, y)
gradient_fn = pointwise_gradient(beta, X, y)
loss, gradient = compute(loss_fn, gradient_fn)
return loss, gradient.copy()
with dask.config.set(fuse_ave_width=0): # optimizations slows this down
beta, loss, info = fmin_l_bfgs_b(compute_loss_grad,
beta0,
fprime=None,
args=(X, y),
iprint=(verbose > 0) - 1,
pgtol=tol,
maxiter=max_iter)
return beta
def proximal_grad(X, y, regularizer='l1', lamduh=0.1, family=Logistic,
max_iter=100, tol=1e-8, **kwargs):
"""
Parameters
----------
X : array-like, shape (n_samples, n_features)
y : array-like, shape (n_samples,)
max_iter : int
maximum number of iterations to attempt before declaring
failure to converge
tol : float
Maximum allowed change from prior iteration required to
declare convergence
family : Family
verbose : bool, default False
whether to print diagnostic information during convergence
Returns
-------
beta : array-like, shape (n_features,)
"""
n, p = X.shape
firstBacktrackMult = 0.1
nextBacktrackMult = 0.5
armijoMult = 0.1
stepGrowth = 1.25
stepSize = 1.0
recalcRate = 10
backtrackMult = firstBacktrackMult
beta = np.zeros(p)
regularizer = Regularizer.get(regularizer)
for k in range(max_iter):
# Compute the gradient
if k % recalcRate == 0:
Xbeta = X.dot(beta)
func = family.loglike(Xbeta, y)
gradient = family.gradient(Xbeta, X, y)
Xbeta, func, gradient = persist(
Xbeta, func, gradient)
obeta = beta
# Compute the step size
lf = func
for ii in range(100):
beta = regularizer.proximal_operator(obeta - stepSize * gradient, stepSize * lamduh)
step = obeta - beta
Xbeta = X.dot(beta)
Xbeta, beta = persist(Xbeta, beta)
func = family.loglike(Xbeta, y)
func = persist(func)[0]
func = compute(func)[0]
df = lf - func
if df > 0:
break
stepSize *= backtrackMult
if stepSize == 0:
break
df /= max(func, lf)
if df < tol:
break
stepSize *= stepGrowth
backtrackMult = nextBacktrackMult
# L2-regularization returned a dask-array
try:
return beta.compute()
except AttributeError:
return beta
def admm(X, y, regularizer='l1', lamduh=0.1, rho=1, over_relax=1,
max_iter=250, abstol=1e-4, reltol=1e-2, family=Logistic, **kwargs):
"""
Alternating Direction Method of Multipliers
Parameters
----------
X : array-like, shape (n_samples, n_features)
y : array-like, shape (n_samples,)
regularizer : str or Regularizer
lambuh : float
rho : float
over_relax : FLOAT
max_iter : int
maximum number of iterations to attempt before declaring
failure to converge
abstol, reltol : float
family : Family
Returns
-------
beta : array-like, shape (n_features,)
"""
pointwise_loss = family.pointwise_loss
pointwise_gradient = family.pointwise_gradient
regularizer = Regularizer.get(regularizer)
def create_local_gradient(func):
@functools.wraps(func)
def wrapped(beta, X, y, z, u, rho):
return func(beta, X, y) + rho * (beta - z + u)
return wrapped
def create_local_f(func):
@functools.wraps(func)
def wrapped(beta, X, y, z, u, rho):
return func(beta, X, y) + (rho / 2) * np.dot(beta - z + u,
beta - z + u)
return wrapped
f = create_local_f(pointwise_loss)
fprime = create_local_gradient(pointwise_gradient)
nchunks = getattr(X, 'npartitions', 1)
# nchunks = X.npartitions
(n, p) = X.shape
# XD = X.to_delayed().flatten().tolist()
# yD = y.to_delayed().flatten().tolist()
if isinstance(X, da.Array):
XD = X.rechunk((None, X.shape[-1])).to_delayed().flatten().tolist()
else:
XD = [X]
if isinstance(y, da.Array):
yD = y.rechunk((None, y.shape[-1])).to_delayed().flatten().tolist()
else:
yD = [y]
z = np.zeros(p)
u = np.array([np.zeros(p) for i in range(nchunks)])
betas = np.array([np.ones(p) for i in range(nchunks)])
for k in range(max_iter):
# x-update step
new_betas = [delayed(local_update)(xx, yy, bb, z, uu, rho, f=f,
fprime=fprime) for
xx, yy, bb, uu in zip(XD, yD, betas, u)]
new_betas = np.array(da.compute(*new_betas))
beta_hat = over_relax * new_betas + (1 - over_relax) * z
# z-update step
zold = z.copy()
ztilde = np.mean(beta_hat + np.array(u), axis=0)
z = regularizer.proximal_operator(ztilde, lamduh / (rho * nchunks))
# u-update step
u += beta_hat - z
# check for convergence
primal_res = np.linalg.norm(new_betas - z)
dual_res = np.linalg.norm(rho * (z - zold))
eps_pri = np.sqrt(p * nchunks) * abstol + reltol * np.maximum(
np.linalg.norm(new_betas), np.sqrt(nchunks) * np.linalg.norm(z))
eps_dual = np.sqrt(p * nchunks) * abstol + \
reltol * np.linalg.norm(rho * u)
if primal_res < eps_pri and dual_res < eps_dual:
break
return z
def proximal_grad(X,
y,
regularizer='l1',
lamduh=0.1,
family=Logistic,
max_iter=100,
tol=1e-8,
verbose=False):
n, p = X.shape
firstBacktrackMult = 0.1
nextBacktrackMult = 0.5
armijoMult = 0.1
stepGrowth = 1.25
stepSize = 1.0
recalcRate = 10
backtrackMult = firstBacktrackMult
beta = np.zeros(p)
regularizer = Regularizer.get(regularizer)
if verbose:
print('# -f |df/f| |dx/x| step')
print('----------------------------------------------')
for k in range(max_iter):
# Compute the gradient
if k % recalcRate == 0:
Xbeta = X.dot(beta)
func = family.loglike(Xbeta, y)
gradient = family.gradient(Xbeta, X, y)
Xbeta, func, gradient = persist(Xbeta, func, gradient)
obeta = beta
# Compute the step size
lf = func
for ii in range(100):
beta = regularizer.proximal_operator(obeta - stepSize * gradient,
stepSize * lamduh)
step = obeta - beta
Xbeta = X.dot(beta)
overflow = (Xbeta < 700).all()
overflow, Xbeta, beta = persist(overflow, Xbeta, beta)
overflow = compute(overflow)[0]
# This prevents overflow
if overflow:
func = family.loglike(Xbeta, y)
func = persist(func)[0]
func = compute(func)[0]
df = lf - func
if df > 0:
break
stepSize *= backtrackMult
if stepSize == 0:
print('No more progress')
break
df /= max(func, lf)
db = 0
if verbose:
print('%2d %.6e %9.2e %.2e %.1e' %
(k + 1, func, df, db, stepSize))
if df < tol:
print('Converged')
break
stepSize *= stepGrowth
backtrackMult = nextBacktrackMult
return beta
def admm(X,
y,
regularizer='l1',
lamduh=0.1,
rho=1,
over_relax=1,
max_iter=250,
abstol=1e-4,
reltol=1e-2,
family=Logistic):
pointwise_loss = family.pointwise_loss
pointwise_gradient = family.pointwise_gradient
regularizer = Regularizer.get(regularizer)
def create_local_gradient(func):
@functools.wraps(func)
def wrapped(beta, X, y, z, u, rho):
return func(beta, X, y) + rho * (beta - z + u)
return wrapped
def create_local_f(func):
@functools.wraps(func)
def wrapped(beta, X, y, z, u, rho):
return func(beta, X,
y) + (rho / 2) * np.dot(beta - z + u, beta - z + u)
return wrapped
f = create_local_f(pointwise_loss)
fprime = create_local_gradient(pointwise_gradient)
nchunks = getattr(X, 'npartitions', 1)
# nchunks = X.npartitions
(n, p) = X.shape
# XD = X.to_delayed().flatten().tolist()
# yD = y.to_delayed().flatten().tolist()
if isinstance(X, da.Array):
XD = X.rechunk((None, X.shape[-1])).to_delayed().flatten().tolist()
else:
XD = [X]
if isinstance(y, da.Array):
yD = y.rechunk((None, y.shape[-1])).to_delayed().flatten().tolist()
else:
yD = [y]
z = np.zeros(p)
u = np.array([np.zeros(p) for i in range(nchunks)])
betas = np.array([np.ones(p) for i in range(nchunks)])
for k in range(max_iter):
# x-update step
new_betas = [
delayed(local_update)(xx, yy, bb, z, uu, rho, f=f, fprime=fprime)
for xx, yy, bb, uu in zip(XD, yD, betas, u)
]
new_betas = np.array(da.compute(*new_betas))
beta_hat = over_relax * new_betas + (1 - over_relax) * z
# z-update step
zold = z.copy()
ztilde = np.mean(beta_hat + np.array(u), axis=0)
z = regularizer.proximal_operator(ztilde, lamduh / (rho * nchunks))
# u-update step
u += beta_hat - z
# check for convergence
primal_res = np.linalg.norm(new_betas - z)
dual_res = np.linalg.norm(rho * (z - zold))
eps_pri = np.sqrt(p * nchunks) * abstol + reltol * np.maximum(
np.linalg.norm(new_betas),
np.sqrt(nchunks) * np.linalg.norm(z))
eps_dual = np.sqrt(p * nchunks) * abstol + \
reltol * np.linalg.norm(rho * u)
if primal_res < eps_pri and dual_res < eps_dual:
print("Converged!", k)
break
return z
