def onestep(D, xlb, xub, Xinit, Yinit, flogprior = None, \
nhist = 5, resolution = 0.01, \
T = 1, B = 10000, N = 10000, M = 5, \
parallel = False, processes = 4, sampler = None):
"""
An adaptive surrogate modeling-based sampling strategy for parameter
optimization and distribution estimation (ASMO-PODE)
use Metropolis/AM/DRAM sampler, Markov Chain Monte Carlo
One-step mode for offline optimization
Do NOT call the model evaluation function
Parameters for ASMO-PODE
D: dimension of input X
xlb: lower bound of input
xub: upper bound of input
Xinit: initial value of X, Ninit x D matrix
Yinit: initial value of Y, Ninit dim vector
flogprior: -2log prior distribution function,
should be very simple that do not need surrogate
use uniform distribution as default
nhist: number of histograms in each iteration
resolution: use uniform sampling if the nearest neighbour distance
is smaller than resolution
(parameter space normalized to [0,1])
Parameters for MCMC:
T: temperature, default is 1
B: length of burn-in period
N: Markov Chain length (after burn-in)
M: number of Markov Chain
parallel: evaluate MChain parallelly or not
processes: number of parallel processes
sampler: name of sampler, one of Metropolis/AM/DRAM
"""
nbin = int(np.floor(N / (nhist - 1)))
x = Xinit.copy()
y = Yinit.copy()
ntoc = 0
# construct surrogate model
#sm = gp.GPR_Matern(x, y, D, 1, x.shape[0], xlb, xub)
sm = gwgp.MOGPR('CovMatern5', x, y.reshape((-1,1)), D, 1, xlb, xub, \
mean = np.zeros(1), noise = 1e-3)
# for surrogate-based MCMC, use larger value for noise, i.e. 1e-3, to smooth the response surface
# run MCMC on surrogate model
if sampler == 'AM':
[Chain, LogPost, ACC, GRB] = \
DRAM.sampler(sm, D, xlb, xub, None, flogprior, T, B, N, M, \
parallel, processes)
elif sampler == 'DRAM':
[Chain, LogPost, ACC, GRB] = \
AM.sampler(sm, D, xlb, xub, None, flogprior, T, B, N, M, \
parallel, processes)
else:
[Chain, LogPost, ACC, GRB] = \
Metropolis.sampler(sm, D, xlb, xub, None, flogprior, T, B, N, M, None, \
parallel, processes)
# sort -2logpost with ascending order
lidx = np.argsort(LogPost)
Chain = Chain[lidx, :]
LogPost = LogPost[lidx]
# normalize the data
xu = (x - xlb) / (xub - xlb)
xp = (Chain - xlb) / (xub - xlb)
# resampling
xrf = np.zeros([nhist, D])
for ihist in range(nhist - 1):
xpt = xp[nbin * ihist:nbin * (ihist + 1), :]
xptt, pidx = np.unique(xpt.view(xpt.dtype.descr * xpt.shape[1]),\
return_index=True)
xpt = xpt[pidx, :]
[xtmp, mdist] = maxmindist(xu, xpt)
if mdist < resolution:
[xtmp, mdist] = maxmindist(xu, np.random.random([10000, D]))
ntoc += 1
xrf[ihist, :] = xtmp
xu = np.vstack((xu, xtmp))
xrf[nhist - 1, :] = xp[0, :]
xu = np.vstack((xu, xrf[nhist - 1, :]))
# return resample points
x_resample = xrf * (xub - xlb) + xlb
return x_resample, Chain, LogPost, ACC, GRB
def sampler(floglike, D, xlb, xub, \
Xinit = None, Yinit = None, flogprior = None, \
niter = 10, nhist = 5, resolution = 0.0001, \
T = 1, B = 10000, N = 10000, M = 5, \
parallel = False, processes = 4, sampler = None):
''' An adaptive surrogate modeling-based sampling strategy for parameter
optimization and distribution estimation (ASMO-PODE)
use Metropolis/AM/DRAM sampler, Markov Chain Monte Carlo
Parameters for ASMO-PODE
floglike: -2log likelihood function, floglike.evaluate(X)
D: dimension of input X
xlb: lower bound of input
xub: upper bound of input
Xinit: initial value of X, Ninit x D matrix
Yinit: initial value of Y, Ninit dim vector
flogprior: -2log prior distribution function,
should be very simple that do not need surrogate
use uniform distribution as default
niter: total number of iteration
nhist: number of histograms in each iteration
resolution: use uniform sampling if the nearest neighbour distance
is smaller than resolution
(parameter space normalized to [0,1])
Parameters for MCMC:
T: temperature, default is 1
B: length of burn-in period
N: Markov Chain length (after burn-in)
M: number of Markov Chain
parallel: evaluate MChain parallelly or not
processes: number of parallel processes
sampler: name of sampler, one of Metropolis/AM/DRAM
'''
nbin = int(np.floor(N / (nhist - 1)))
if (Xinit is None and Yinit is None):
Ninit = D * 10
Xinit = sampling.glp(Ninit, D)
for i in range(Ninit):
Xinit[i, :] = Xinit[i, :] * (xub - xlb) + xlb
Yinit = np.zeros(Ninit)
for i in range(Ninit):
Yinit[i] = floglike.evaluate(Xinit[i, :])
else:
Ninit = Xinit.shape[0]
if len(Yinit.shape) == 2:
Yinit = Yinit[:, 0]
x = Xinit.copy()
y = Yinit.copy()
ntoc = 0
if sampler is None:
sampler = 'Metropolis'
resamples = []
for i in range(niter):
print('Surrogate Opt loop: %d' % i)
# construct surrogate model
#sm = gp.GPR_Matern(x, y, D, 1, x.shape[0], xlb, xub)
sm = gwgp.MOGPR('CovMatern5', x, y.reshape((-1,1)), D, 1, xlb, xub, \
mean = np.zeros(1), noise = 1e-3)
# for surrogate-based MCMC, use larger value for noise, i.e. 1e-3, to smooth the response surface
# run MCMC on surrogate model
if sampler == 'AM':
[Chain, LogPost, ACC, GRB] = \
AM.sampler(sm, D, xlb, xub, None, flogprior, T, B, N, M, \
parallel, processes)
elif sampler == 'DRAM':
[Chain, LogPost, ACC, GRB] = \
DRAM.sampler(sm, D, xlb, xub, None, flogprior, T, B, N, M, \
parallel, processes)
elif sampler == 'Metropolis':
[Chain, LogPost, ACC, GRB] = \
Metropolis.sampler(sm, D, xlb, xub, None, flogprior, T, B, N, M, None, \
parallel, processes)
else:
[Chain, LogPost, ACC, GRB] = \
Metropolis.sampler(sm, D, xlb, xub, None, flogprior, T, B, N, M, None, \
parallel, processes)
# sort -2logpost with ascending order
lidx = np.argsort(LogPost)
Chain = Chain[lidx, :]
LogPost = LogPost[lidx]
# store result of MCMC on surrogate
resamples.append({'Chain': Chain.copy(), \
'LogPost': LogPost.copy(),'ACC': ACC, 'GRB': GRB})
# normalize the data
xu = (x - xlb) / (xub - xlb)
xp = (Chain - xlb) / (xub - xlb)
# resampling
xrf = np.zeros([nhist, D])
for ihist in range(nhist - 1):
xpt = xp[nbin * ihist:nbin * (ihist + 1), :].copy()
xptt, pidx = np.unique(xpt.view(xpt.dtype.descr * xpt.shape[1]),\
return_index=True)
xpt = xpt[pidx, :]
[xtmp, mdist] = maxmindist(xu, xpt)
if mdist < resolution:
[xtmp, mdist] = maxmindist(xu, np.random.random([10000, D]))
ntoc += 1
xrf[ihist, :] = xtmp
xu = np.vstack((xu, xtmp))
xrf[nhist - 1, :] = xp[0, :]
xu = np.vstack((xu, xrf[nhist - 1, :]))
resamples[i]['ntoc'] = ntoc
# run dynamic model
xrf = xrf * (xub - xlb) + xlb
yrf = np.zeros(nhist)
for i in range(nhist):
yrf[i] = floglike.evaluate(xrf[i, :])
x = np.concatenate((x, xrf.copy()), axis=0)
y = np.concatenate((y, yrf.copy()), axis=0)
bestidx = np.argmin(y)
bestx = x[bestidx, :]
besty = y[bestidx]
return Chain, LogPost, ACC, GRB, bestx, besty, x, y, resamples