def _Nesterov_grad(beta, A, rng=RandomUniform(-1, 1), grad_norm=grad_l2):
grad_Ab = 0
for i in xrange(len(A)):
Ai = A[i]
Ab = Ai.dot(beta)
grad_Ab += Ai.T.dot(grad_norm(Ab, rng))
return grad_Ab
def __init__(self,
l,
A,
mu=TOLERANCE,
rng=RandomUniform(-1, 1),
norm=L2.grad,
**kwargs):
super(NesterovFunction, self).__init__(l, rng=rng, norm=norm, **kwargs)
self.A = A
self.mu = mu
def grad_l1(beta, rng=RandomUniform(-1, 1)):
"""Sub-gradient of the function
f(x) = |x|_1,
where |x|_1 is the L1-norm.
"""
grad = np.zeros((beta.shape[0], 1))
grad[beta >= TOLERANCE] = 1.0
grad[beta <= -TOLERANCE] = -1.0
between = (beta > -TOLERANCE) & (beta < TOLERANCE)
grad[between] = rng(between.sum())
return grad
def grad_l2(beta, rng=RandomUniform(0, 1)):
"""Sub-gradient of the function
f(x) = |x|_2,
where |x|_2 is the L2-norm.
"""
norm_beta = norm2(beta)
if norm_beta > TOLERANCE:
return beta * (1.0 / norm_beta)
else:
D = beta.shape[0]
u = (rng(D, 1) * 2.0) - 1.0 # [-1, 1]^D
norm_u = norm2(u)
a = rng() # [0, 1]
return u * (a / norm_u)
def grad_tv(beta, A, rng=RandomUniform(0, 1)):
beta_flat = beta.ravel()
Ab = np.vstack([Ai.dot(beta_flat) for Ai in A]).T
Ab_norm2 = np.sqrt(np.sum(Ab**2.0, axis=1))
upper = Ab_norm2 > TOLERANCE
grad_Ab_norm2 = Ab
grad_Ab_norm2[upper] = (Ab[upper].T / Ab_norm2[upper]).T
lower = Ab_norm2 <= TOLERANCE
n_lower = lower.sum()
if n_lower:
D = len(A)
vec_rnd = (rng(n_lower, D) * 2.0) - 1.0
norm_vec = np.sqrt(np.sum(vec_rnd**2.0, axis=1))
a = rng(n_lower)
grad_Ab_norm2[lower] = (vec_rnd.T * (a / norm_vec)).T
grad = np.vstack([A[i].T.dot(grad_Ab_norm2[:, i]) for i in xrange(len(A))])
grad = grad.sum(axis=0)
return grad.reshape(beta.shape)
def __init__(self, l, rng=RandomUniform(-1, 1)):
super(L1, self).__init__(l, rng=rng)
def grad_gl(beta, A, rng=RandomUniform(-1, 1)):
return _Nesterov_grad(beta, A, rng, grad_l2)
def __init__(self, l, A, rng=RandomUniform(-1, 1)):
super(GroupLasso, self).__init__(l, A, rng=rng)
def __init__(self, l, A, rng=RandomUniform(0, 1)):
super(TotalVariation, self).__init__(l, A=A, rng=rng)