/
admm_dp.py
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/
admm_dp.py
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import logging
import scipy
from prox_dp import *
from numpy import *
import numpy.random
import scipy.linalg
from scipy.linalg import fblas as FB
def shrink(A, rho, regDiagonal):
shrunk = sign(A)*maximum(abs(A) - rho, 0.0)
if not regDiagonal:
fill_diagonal(shrunk, diagonal(A))
return shrunk
## Find solution using ADMM method
# For L1 methods, A is a weight matrix or scalar for the prior
# For degree prior, A is a 1d array of the degree weights
def admmDP(C, a=1.0, props={}, warmX=None, warmU=None):
n = C.shape[0]
logger = logging.getLogger("search.admm.dp")
beta = props.get('priorWeight', 0.01)
maxIter = props.get("maxParamaterOptIters", 1000)
epsilon = props.get("epsilon", 1e-6)
returnIntermediate = props.get("returnIntermediate", False)
regDiagonal = props.get("regDiagonal", False)
degreePriorADMM = props.get("degreePrior", True)
adaptiveMu = props.get("adaptiveMu", True)
props['dualDecompEpsilon'] = props.get('dualDecompEpsilon', 1e-10)
sTime = time.time()
logger.info("Starting ADMM learning. n=%d beta=%1.4f", n, beta)
mu = props.get("mu", 0.1) #10.0
muChange = props.get("muChange", 0.1)
if props.get("normalizeForADMM", True):
logger.info("-- NORMALIZING C --")
covNormalizer = sqrt(diagonal(C))
C = C / outer(covNormalizer, covNormalizer)
else:
logger.info("NOT NORMALIZING C")
# Rescale to make beta's range a better fit
maxOffDiag = numpy.max(numpy.abs(tril(C, -1)))
C = array(C / maxOffDiag)
if warmX is not None:
X = warmX
else:
X = eye(n)
if warmU is not None:
U = warmU
else:
U = eye(n)
Z = copy(X)
ll = inf
Xs = []
gs = []
ds = []
if degreePriorADMM:
adelta = -a[:n] + a[1:]
adeltaMat = outer(ones(n), adelta)
beta = beta / 2
logger.error("adelta: %s", adelta[:6])
warmV = zeros((n,n))
if a is None:
a = 1.0
for i in range(maxIter):
#####################################################################
##### Eigenvalue update to X
logger.debug("Performing eigenvalue decomposition")
for retry in range(6):
try:
A = mu*(Z - U) - C
(lamb, Q) = linalg.eigh(A)
logger.debug("Decomposition finished")
break
except numpy.linalg.linalg.LinAlgError as err:
# If A is not in the PSD cone, we reduce the step size mu
logger.error("Failed eigendecomposition with mu=%2.2e", mu)
mu *= 0.5
U /= 0.5
logger.error("Retry %d, halving mu to: %2.5f", retry, mu)
newEigs = (lamb + sqrt(lamb*lamb + 4*mu)) / (2*mu)
X = FB.dgemm(alpha=1.0, a=(Q*newEigs), b=Q, trans_b=True)
#### Soft thresholding update Z
logger.debug("Starting Proximal step")
Zpreshrink = X + U
Zlast = copy(Z)
if degreePriorADMM:
Z = proxSubDualDecomp(Zpreshrink, beta/mu, adelta, adeltaMat, props, warmV)
else:
Z = shrink(Zpreshrink, beta*a/mu, regDiagonal)
if props.get("nonpositivePrecision", False):
Z = Z * (Z < 0) + diag(diag(Z))
### Update U ( U is the sum of residuals so far )
logger.debug("Updating U")
U += X - Z
#####################################################################
dualResidual = linalg.norm(Z - Zlast)
residual = linalg.norm(X-Z)
if adaptiveMu:
# if the two residuals differ my more than this factor, adjust mu (p20)
differenceMargin = 10
if residual > dualResidual*differenceMargin:
mu *= 1.0 + muChange
U /= 1.0 + muChange
logger.debug("*** Increasing mu to %2.6f", mu)
elif dualResidual > residual*differenceMargin:
mu *= 1.0 - muChange
U /= 1.0 - muChange
logger.debug("*** Decreasing mu to %2.6f", mu)
# Ensure that the dual decomp procedure is run with enough accuracy
ddeps = props['dualDecompEpsilon']
margin = 50.0
if residual < margin*ddeps or dualResidual < margin*ddeps:
props['dualDecompEpsilon'] = min(residual, dualResidual)/margin
if returnIntermediate:
ds.append(dualResidual)
gs.append(residual)
if residual < epsilon and dualResidual < epsilon:
logger.info("Converged to %2.3e in %i iters", residual, i+1)
break
edges = (count_nonzero(Z) - n) / 2
logger.info("Iter %d, res: %2.2e, dual res: %2.2e, mu=%1.1e, %d edges free",
i+1, residual, dualResidual, mu, edges)
eTime = time.time()
timeTaken = eTime-sTime
logger.info("Time taken(s): %5.7f", timeTaken)
if residual > epsilon or dualResidual > epsilon:
logger.error("NONCONVERGENCE!!, res: %2.2e, dres: %2.2e, iters: %d",
residual, dualResidual, i)
edges = (count_nonzero(Z) - n) / 2
logger.info("regDiagonal: %s, beta: %2.4f", regDiagonal, beta)
logger.info("Edges %d out of %d | eps=%1.1e", edges, (n*n - n)/2, epsilon)
logger.info("Final residual=%2.2e, dual res=%2.2e", residual, dualResidual)
return {'X': Z, 'U': U, 'obj': ll, 'iteration': i+1, 'Xs': Xs, 'gs': gs, 'ds': ds,
'timeTaken': timeTaken, 'edges': edges, 'Zpreshrink': Zpreshrink, 'bm': beta/mu}