def expandBoundsDDB_FB(self):
"""
Description: Expands the search space with the full Bayesian
implementation of our DDB method
"""
print('Attempting to expand search space with DDB-FB method')
alpha=self.alpha
beta=self.beta
bound_samples=100 # Number of radius sample to fit the log-logistic distribution
# Find y^+ and x^+
ymax=np.max(self.Y)
# Generate test radii
max_loc=np.argmax(self.Y)
xmax=self.X[max_loc]
test_bound=np.zeros(self.scalebounds.shape)
bound_dist=np.zeros(bound_samples)
bound_center=xmax
test_bound[:,1]=bound_center+0.5
test_bound[:,0]=bound_center-0.5
max_radius=np.max(np.array([np.max(max_bound_size-test_bound[:,1]),np.max(test_bound[:,0])]))
step=max_radius/bound_samples
packing_number=np.zeros(bound_samples)
# Generate a Thompson sample maxima to estimate internal maxima
TS=AcquisitionFunction.ThompsonSampling(self.gp)
tsb_x,tsb_y=acq_max_global(TS, self.gp, bounds=self.scalebounds)
# Generate Gumbel samples to estimate the external maxima
for i in range(0,bound_samples):
bound_length=test_bound[:,1]-test_bound[:,0]
volume=np.power(max_bound_size,self.dim)-np.prod(bound_length)
packing_number[i]=round(volume/(5*self.gp.lengthscale))
mu=stats.norm.ppf(1.0-1.0/packing_number[i])
sigma=stats.norm.ppf(1.0-(1.0/packing_number[i])*np.exp(-1.0))-stats.norm.ppf(1.0-(1.0/(packing_number[i])))
bound_dist[i]=np.exp(-np.exp(-(-tsb_y-mu)/sigma))
test_bound[:,1]=test_bound[:,1]+step
test_bound[:,0]=test_bound[:,0]-step
bound_dist[np.isnan(bound_dist)]=1
# Fit the log-logistic paramaters to the Gumbel samples
xfit=np.arange(0,max_radius,max_radius/100)
popt,pcov=optimize.curve_fit(self.sufficientBoundPDF,xfit[0:100],bound_dist,bounds=np.array([[5,1.1],[20,5]]))
print("popt={}".format(popt))
b=ymax/popt[0]
a=popt[1]
print("b={}, ymax={}".format(b,ymax))
# Sample for the optimal radius
for d in range(0,self.dim):
gamma=np.random.gamma(shape=alpha,scale=1/beta,size=100)
loglog=stats.fisk.pdf(gamma,ymax/b,scale=a)
scaled_weights=loglog/np.sum(loglog)
multi=np.random.multinomial(1,scaled_weights)
r_index=np.argmax(multi)
print("Radius of {} selected".format(gamma[r_index]))
self.scalebounds[d,1]=xmax[d]+gamma[r_index]
self.scalebounds[d,0]=xmax[d]-gamma[r_index]
print("seach space extended to {} with DDB".format(self.scalebounds))
def expandBoundsDDB_MAP(self):
"""
Description: Expands the search space with the MAP implementation of
our DDB method
"""
print('Attempting to expand search space with DDB-MAP method')
alpha=self.alpha
beta=self.beta
bound_samples=100 # Number of radius sample to fit the log-logistic distribution
# Find y^+ and x^+
ymax=np.max(self.Y)
# Generate test radii
max_loc=np.argmax(self.Y)
xmax=self.X[max_loc]
test_bound=np.zeros(self.scalebounds.shape)
bound_dist=np.zeros(bound_samples)
bound_center=xmax
test_bound[:,1]=bound_center+0.5
test_bound[:,0]=bound_center-0.5
max_radius=np.max(np.array([np.max(max_bound_size-test_bound[:,1]),np.max(test_bound[:,0])]))
step=max_radius/bound_samples
packing_number=np.zeros(bound_samples)
# Generate a Thompson sample maxima to estimate internal maxima
TS=AcquisitionFunction.ThompsonSampling(self.gp)
tsb_x,tsb_y=acq_max_global(TS, self.gp, bounds=self.scalebounds)
# Generate Gumbel samples to estimate the external maxima
for i in range(0,bound_samples):
bound_length=test_bound[:,1]-test_bound[:,0]
volume=np.power(max_bound_size,self.dim)-np.prod(bound_length)
packing_number[i]=round(volume/(5*self.gp.lengthscale))
mu=stats.norm.ppf(1.0-1.0/packing_number[i])
sigma=stats.norm.ppf(1.0-(1.0/packing_number[i])*np.exp(-1.0))-stats.norm.ppf(1.0-(1.0/(packing_number[i])))
bound_dist[i]=np.exp(-np.exp(-(-tsb_y-mu)/sigma))
test_bound[:,1]=test_bound[:,1]+step
test_bound[:,0]=test_bound[:,0]-step
bound_dist[np.isnan(bound_dist)]=1
# Fit the log-logistic paramaters to the Gumbel samples
xfit=np.arange(0,max_radius,max_radius/100)
popt,pcov=optimize.curve_fit(self.sufficientBoundPDF,xfit[0:100],bound_dist,bounds=np.array([[5,1.1],[20,5]]))
print("popt={}".format(popt))
b=ymax/popt[0]
a=popt[1]
print("b={}, ymax={}".format(b,ymax))
# Find the gamma and log-logistic modes to determine the optimisation bound
c=ymax/b
loglog_mode=a*np.power((c-1.0)/(c+1.0),(1/c))
gamma_mode=(alpha-1)/beta
opt_bound=np.ones([2])
opt_bound[0]=min(loglog_mode,gamma_mode)
opt_bound[1]=max(loglog_mode,gamma_mode)
bound_range=(opt_bound[1]-opt_bound[0])
# Find MAP Estimate of radius r
for d in range(0,self.dim):
r_max=0
p_max=0
for x0 in np.arange(opt_bound[0],opt_bound[1],bound_range/10):
res=optimize.minimize(lambda x: self.radiusPDF(x,alpha,beta,b,ymax,a),x0=x0, bounds=np.array([opt_bound]), method='L-BFGS-B')
if -res.fun>p_max:
r_max=res.x
p_max=-res.fun
if r_max>opt_bound[1]:
r_max=opt_bound[1]
xplot=np.arange(0,10,0.01)
yplot=-self.radiusPDF(xplot,alpha,beta,b,ymax,a)
max_loc=np.argmax(yplot)
print("optimal radius of {} with unscaled probability of {}".format(r_max,p_max))
self.scalebounds[d,1]=xmax[d]+r_max
self.scalebounds[d,0]=xmax[d]-r_max
print("seach space extended to {} with DDB".format(self.scalebounds))