def mutational_effects(n, s, beta):
"""
Generate n mutations from a gamma distribution with mean effect s and shape parameter beta.
Negative (positive) values of s indicate deleterious (beneficial) mutations.
Arguments:
n -- number of mutations
s -- mean effect of a mutation
beta -- shape parameter of the gamma distribution (inf indicates equal effects)
"""
if np.sign(s) == 1:
beneficial = True
elif np.sign(s) == -1:
beneficial = False
else:
return "Invalid s: must be nonzero."
if beta > 0:
if beta == inf:
mutations = np.repeat(s, n)
else:
alpha = beta / abs(s)
if beneficial:
mutations = gamma(shape=beta, scale=1/alpha, size=n)
else:
mutations = - gamma(shape=beta, scale=1/alpha, size=n)
return mutations
else:
return "Invalid beta: must be 0 < beta < inf."
def firstStateGenerator(parameters, size):
first_state = zeros((size, 5))
first_state[:, 2] = random.gamma(size = size, \
shape = parameters[6] * (parameters[2]**2) / parameters[3], \
scale = (parameters[3] / parameters[2]))
first_state[:, 4] = random.gamma(size = size, \
shape = (1 - parameters[6]) * (parameters[2]**2) / parameters[3], \
scale = (parameters[3] / parameters[2]))
return first_state
def initializationAttributes(self):
self.Attribute['IOP'] = random.normal(28,3) # need to do truncation later
while self.Attribute['IOP'] < 22:
self.Attribute['IOP'] = random.normal(28,3)
self.Attribute['MD'] = -random.gamma(2,2.5) # need to do truncation later
while self.Attribute['MD'] > -3:
self.Attribute['MD'] = -random.gamma(2,2.5)
self.Attribute['MDR'] = random.gamma(2,0.014)
self.Attribute['Age'] = random.normal(68,5)
def _create_prices(t):
last_average = 100 if t==0 else source.data['average'][-1]
returns = asarray(lognormal(mean.value, stddev.value, 1))
average = last_average * cumprod(returns)
high = average * exp(abs(gamma(1, 0.03, size=1)))
low = average / exp(abs(gamma(1, 0.03, size=1)))
delta = high - low
open = low + delta * uniform(0.05, 0.95, size=1)
close = low + delta * uniform(0.05, 0.95, size=1)
return open[0], high[0], low[0], close[0], average[0]
def sample_eta_west(eta, nact, n0, a=1, b=0):
"""Samples the concentration parameter eta"""
## compute x, r and p
x = rn.beta(eta + 1, n0)
lx = np.log(x)
r = (a + nact - 1) / (n0 * (b - lx))
p = r / (r + 1)
## return
return rn.gamma(a + nact, 1 / (b - lx)) if rn.rand() < p else rn.gamma(a + nact - 1, 1 / (b - lx))
def _init_component(self, m, dim):
assert self.mode_dims[m] == dim
K = self.n_components
s = self.smoothness
gamma_DK = s * rn.gamma(s, 1. / s, size=(dim, K))
delta_DK = s * rn.gamma(s, 1. / s, size=(dim, K))
self.gamma_DK_M[m] = gamma_DK
self.delta_DK_M[m] = delta_DK
self.E_DK_M[m] = gamma_DK / delta_DK
self.sumE_MK[m, :] = self.E_DK_M[m].sum(axis=0)
self.G_DK_M[m] = np.exp(sp.psi(gamma_DK) - np.log(delta_DK))
self.beta_M[m] = 1. / self.E_DK_M[m].mean()
def sample(self, n=None):
"""Return a multivariate t sample."""
if n is None:
snsamps = random.standard_normal(self.ndim)
gamsamp = random.gamma(self.hnu)
return _mvnt.mvtsamp(self.mu, self.L, self.nu, snsamps, gamsamp)
samps = zeros((n, self.ndim), float)
for i in range(n):
snsamps = random.standard_normal(self.ndim)
gamsamp = random.gamma(self.hnu)
samps[i] = _mvnt.mvtsamp(self.mu, self.L, self.nu, snsamps, gamsamp)
return samps
def sample_noise(self):
if self.noise_type == "truncnorm":
return nr.uniform(0, self.upper)
elif self.noise_type == "noiseless":
return 0
elif self.noise_type == "gamma":
return nr.gamma(3, scale=3) # equivalent to gamma(3,3) in wiki
elif self.noise_type == "beta":
return nr.gamma(3, scale=3)
else:
print("Unknown noise type for generating noise")
sys.exit("sample_noise: Unknown noise type for generating noise")
def __calculate_alpha(self, graph, alpha_prev):
'''Picks alpha from a mixture of 2 gamma distributions'''
num_communities = graph.number_of_communities
num_players = graph.number_of_nodes
beta_z = npr.beta(alpha_prev + 1, num_players)
#generate a uniform random number to pick which gamma from the mixture
rnd_unif = npr.uniform()
inv_mixture_scale = self.__gamma_b - math.log(beta_z)
mixture_scale = 1.0 / inv_mixture_scale
if rnd_unif / (1 - rnd_unif) < ((self.__gamma_a + num_communities)/
(num_players * inv_mixture_scale)):
return npr.gamma(self.__gamma_a + num_communities, mixture_scale)
return npr.gamma(self.__gamma_a + num_communities - 1, mixture_scale)
def levy(self):
# landa = float(landa)
s = []
for i in range(self.lchrom):
up = gamma(1+self.beta) * (pi*self.beta/2.)
down = gamma((1+self.beta)/2.) * 2**((self.beta-1)/2.)
sigma = (up / down) ** (1/self.beta)
U = normal(0, sigma)
V = normal(0, 1)
s.append(U / abs(V)**(1/self.beta))
return np.array(s)
def sample_q(self):
"""Return a multivariate t sample and the value of its
associated quadratic form."""
if n is None:
snsamps = random.standard_normal(self.ndim)
gamsamp = random.gamma(self.hnu)
return _mvnt.mvtsampq(self.mu, self.L, self.nu, snsamps, gamsamp)
samps = zeros((n, self.ndim), float)
qvals = zeros(n, float)
for i in range(n):
snsamps = random.standard_normal(self.ndim)
gamsamp = random.gamma(self.hnu)
samps[i], qvals[i] = _mvnt.mvtsampq(self.mu, self.L, self.nu, snsamps, gamsamp)
return samps
def levy(self):
s = []
for i in range(self.lchrom):
up = gamma(1+self.beta) * (pi*self.beta/2.)
down = gamma((1+self.beta)/2.) * 2**((self.beta-1)/2.)
sigma = (up / down) ** (1/self.beta)
U = normal(0, sigma)
V = normal(0, 1)
s.append(U / abs(V)**(1/self.beta))
# s = self.map.logistic_map(self.lchrom, rand()/10., rand()*4)
return np.array(s)
def new_cluster(number_of_stars = 1000):
masses = new_salpeter_mass_distribution(
number_of_stars,
mass_min = 0.1 | units.MSun,
mass_max = 125.0 | units.MSun,
alpha = -2.35
)
particles = Particles(number_of_stars)
particles.mass = masses
particles.x = units.parsec(random.gamma(2.0, 1.0, number_of_stars))
particles.y = units.parsec(random.gamma(1.0, 1.0, number_of_stars))
particles.z = units.parsec(random.random(number_of_stars))
return particles
def sample_eta_ishwaran(lw, eta, a=0, b=0):
"""Samples the concentration parameter eta given a vector of mixture log-weights"""
eta = rn.gamma(lw.size + a - 1, 1 / (b - lw[-1])) if np.isfinite(lw[-1]) else eta
##
return eta
def __init__(self, bias_stdev=0.2, eval_stdev=0.2, mode='pareto', frac=0.1,
pareto_shape=1.4, gamma_shape=3):
"""Initializes the precision and bias of a user. Useful only for simulation."""
# Chooses the bias of the user
self.true_bias = 0
if bias_stdev > 0:
self.true_bias = npr.normal(scale=bias_stdev)
# Chooses the variance of the user.
if mode == 'bimodal':
# 10% of the students are responsible for 90% of the trouble,
# where 10% is the fraction.
# This code keeps the standard deviation as specified, but explains
# it via a bimodal distribution, with values s and s / frac.
s = eval_stdev * eval_stdev * frac / (1.0 + frac - frac * frac)
if npr.uniform() < frac:
self.prec = (s / (frac * frac)) ** 0.5
else:
self.prec = s ** 0.5
elif mode == 'pareto':
# The mean of a pareto distribution of shape a is 1 / (a - 1)
# Here, we use the pareto distribution to sample the variance.
prec_sq = npr.pareto(pareto_shape) * eval_stdev * eval_stdev * (pareto_shape - 1.0)
self.prec = prec_sq ** 0.5
else:
# Gamma.
prec_sq = npr.gamma(gamma_shape, scale=eval_stdev)
self.prec = prec_sq * prec_sq
# List of items it judged.
self.items = []
# Dictionary mapping each item, to the grade assigned by the user.
self.grade = {}
def generate(self):
'''Generate some random formants.'''
bw = 10.
f1 = rng.uniform(300, 700)
f2 = rng.uniform(800, 2000)
f3 = rng.uniform(2000, 2500)
f4 = rng.uniform(2500, 3500)
def near(x, t, s):
return 1. / (1. + numpy.exp((t - x) / s))
while True:
if rng.random() < 0.1:
bw = rng.gamma(5, 5)
r = near(f1, 500, 100)
f1 += rng.uniform(-30 * r, 30 * (1 - r))
r = near(f2, 1500, 300)
f2 += rng.uniform(-50 * r, 50 * (1 - r))
r = near(f3, 2200, 500)
f3 += rng.uniform(-70 * r, 70 * (1 - r))
r = near(f4, 3000, 700)
f4 += rng.uniform(-90 * r, 90 * (1 - r))
yield (bw, ((1., f1, 200),
(0.9, f2, 100),
(0.8, f3, 100),
(0.7, f4, 100)))
def genData():
data = [[],[]]
for i in range(0,150):
data[0].append(random.gamma(2,0.5))
for i in range(0,100):
data[1].append(random.normal(1,0.25))
return data
def rand(self):
m, n = self.__m, self.__n
s = linalg.cholesky(self.__prod).transpose()
w = self.__weight
# Compute the parameters of the posterior distribution.
mu = linalg.solve(s[:m, :m], s[:m, m:])
omega = np.dot(s[:m, :m].transpose(), s[:m, :m])
sigma = np.dot(s[m:, m:].transpose(), s[m:, m:]) / w
eta = w
# Simulate the marginal Wishart distribution.
f = linalg.solve(np.diag(np.sqrt(2.0*random.gamma(
(eta - np.arange(n))/2.0))) + np.tril(random.randn(n, n), -1),
np.sqrt(eta)*linalg.cholesky(sigma).transpose())
b = np.dot(f.transpose(), f)
# Simulate the conditional Gauss distribution.
a = mu + linalg.solve(linalg.cholesky(omega).transpose(),
np.dot(random.randn(m, n),
linalg.cholesky(b).transpose()))
return a, b
def rand(self):
dim=self.__dim__
mu=self.__param__.mu
omega=self.__param__.omega
sigma=self.__param__.sigma
eta=self.__param__.eta
if numpy.isfinite(eta):
# Simulate the marginal Gamma distribution.
disp=sigma/(random.gamma(eta/2.0,size=dim)/(eta/2.0))
else:
# Account for the special case where the
# marginal distribution is singular.
disp=numpy.copy(sigma)
if numpy.isfinite(omega):
# Simulate the conditional Gauss distribution.
loc=mu+(numpy.sqrt(disp)*random.randn(dim))/math.sqrt(omega)
else:
# Account for the special case where the
# conditional distribution is singular.
loc=numpy.copy(mu)
return loc,disp
def rand(self):
dim=self.__dim__
mu=self.__param__.mu
omega=self.__param__.omega
sigma=self.__param__.sigma
eta=self.__param__.eta
if numpy.isfinite(eta):
# Simulate the marginal Wishart distribution.
diag=2.0*random.gamma((eta-numpy.arange(dim))/2.0)
fact=numpy.diag(numpy.sqrt(diag))+numpy.tril(random.randn(dim,dim),-1)
fact=linalg.solve(fact,math.sqrt(eta)*linalg.cholesky(sigma).transpose())
disp=numpy.dot(fact.transpose(),fact)
else:
# Account for the special case where the
# marginal distribution is singular.
disp=numpy.copy(sigma)
if numpy.isfinite(omega):
# Simulate the conditional Gauss distribution.
loc=mu+numpy.dot(linalg.cholesky(disp),random.randn(dim))/math.sqrt(omega)
else:
# Account for the special case where the
# conditional distribution is singular.
loc=numpy.copy(mu)
return loc,disp
def gen_inv_gaussian(a, b, p, burnin=10):
"""
Sampler based on Gibbs sampling.
Assumes scalar p.
"""
from numpy.random import gamma
from numpy import sqrt
s = a * 0. + 1.
if p < 0:
a, b = b, a
for i in range(burnin):
l = b + 2 * s
m = sqrt(l / a)
x = inv_gaussian(m, l, shape=m.shape)
s = gamma(abs(p) + 0.5, x)
if p >= 0:
return x
else:
return 1 / x
def truncated_gamma(shape=None, alpha=1., beta=1., x_min=None, x_max=None):
"""
Generate random variates from a lower-and upper-bounded gamma distribution.
@param shape: shape of the random sample
@param alpha: shape parameter (alpha > 0.)
@param beta: scale parameter (beta >= 0.)
@param x_min: lower bound of variate
@param x_max: upper bound of variate
@return: random variates of lower-bounded gamma distribution
"""
from scipy.special import gammainc, gammaincinv
from numpy.random import gamma
from numpy import inf
if x_min is None and x_max is None:
return gamma(alpha, 1 / beta, shape)
elif x_min is None:
x_min = 0.
elif x_max is None:
x_max = inf
x_min = max(0., x_min)
x_max = min(1e300, x_max)
a = gammainc(alpha, beta * x_min)
b = gammainc(alpha, beta * x_max)
return probability_transform(shape,
lambda x, alpha=alpha: gammaincinv(alpha, x),
a, b) / beta
def sample_dirichlet(a):
"""Sample from multiple Dirichlet distributions given the matrix of concentration parameter columns a"""
x = rn.gamma(a, 1)
w = x / np.sum(x, 0)
##
return w
def distLambda(m, Nmud, Vmud, Vwell):
"""Choose m values from the distribution of lambda given Nmud, Vmud, Vwell.
m is the number of values to pull
Nmud is the number of cysts counted in estimating the concentration of cysts
Vmud is the volume of mud counted over in estimating the concentrtion of cysts
Vwell is the volume of mud placed in each well in the wellplate
"""
return Vwell/Vmud*gamma(Nmud, 1.0, m)
def EvaluateConversion (self):
"""Evaluate survival probability to conversion from OHT to POAG"""
h = (1.26**((self.Attribute['Age']-55)/10))*(1.09**(self.Attribute['IOP'] - 24))*0.02*HRother
prob = 1 - math.exp(-h*self.params['CurrentTime'])
if random.uniform(0,1) < prob:
self.params['Conversion'] = True
self.Attribute['MD'] = -random.gamma(6,0.5)
self.params['TimetoConversion'] = self.params['CurrentTime']
def test_gamma_parameters2(verbose=0):
import numpy.random as nr
n = 1000
X = nr.gamma(11., 3., n)
G = Gamma()
G.estimate(X)
if verbose:
G.parameters()
assert(np.absolute(G.scale-3)<0.5)
def sample_normal_prec_jeffreys(s1, s2, ndata):
"""Samples the precision of a normal distribution"""
##
avg = s1 / ndata
dot = s2 - 2 * avg * s1 + ndata * avg**2
##
return rn.gamma(ndata * 0.5, 2 / dot)
def test_Gamma_parameters1(verbose=0):
import numpy.random as nr
n = 1000
X = nr.gamma(11., 3., n)
G = Gamma()
G.estimate(X)
if verbose:
G.parameters()
assert(np.absolute(G.shape-11)<2.)
def sample_post(hp, ss):
z = _intermediates(hp, ss)
l_star = gamma(z.alpha, 1. / z.beta)
while True:
m_star = t.rvs(2 * z.alpha, z.mu,
z.beta / (z.alpha * z.tau)) ** -1
if m_star > 0:
break
return (m_star, l_star)
def sample(self, eta, size=1):
"""
@param eta: the natural parameters
@param size: the size of the sample
A sample of sufficient statistics
"""
from numpy.random import gamma
(a, b) = self.theta(eta)
return self.T(gamma(a, scale=1. / b, size=size))
def sample_pi(self, delta):
shapes = cu.counter(
delta, self.nMix) * self.inv_temper_temp + self.priors.pi.a
unnormalized = gamma(shape=shapes)
return unnormalized / unnormalized.sum()
def generate(self):
return gamma(self.k, self.theta)
def gen_rnas_proteins(self):
""" Creates RNA and protein objects corresponding to genes on chromosome
"""
cell = self.knowledge_base.cell
options = self.options
mean_copy_number = options.get('mean_copy_number')
mean_half_life = options.get('mean_half_life')
mean_volume = cell.properties.get_one(
id='mean_volume').value
cytosol = cell.compartments.get_one(id='c')
for chromosome in cell.species_types.get(__type=wc_kb.core.DnaSpeciesType):
for i in range(len(chromosome.loci)):
locus = chromosome.loci[i]
if type(locus) == wc_kb.prokaryote.TranscriptionUnitLocus:
tu = locus
# creates RnaSpeciesType for RNA sequence corresponding to gene
rna = cell.species_types.get_or_create(
id='rna_{}'.format(tu.id), __type=wc_kb.prokaryote.RnaSpeciesType)
rna.name = 'rna {}'.format(tu.id)
# GeneLocus object for gene sequence, attribute of ProteinSpeciesType object
if tu.genes[0].type == wc_kb.core.GeneType.mRna:
rna.type = wc_kb.core.RnaType.mRna
elif tu.genes[0].type == wc_kb.core.GeneType.rRna:
rna.type = wc_kb.core.RnaType.rRna
elif tu.genes[0].type == wc_kb.core.GeneType.tRna:
rna.type = wc_kb.core.RnaType.tRna
elif tu.genes[0].type == wc_kb.core.GeneType.sRna:
rna.type = wc_kb.core.RnaType.sRna
# print(rna.type)
rna_conc = random.gamma(1, mean_copy_number) / scipy.constants.Avogadro / mean_volume
rna_species = rna.species.get_or_create(compartment=cytosol)
rna_species.concentration = wc_kb.core.Concentration(cell=cell, value=rna_conc)
rna.half_life = random.normal(
mean_half_life, numpy.sqrt(mean_half_life))
rna.transcription_units.append(tu)
# print(rna.get_seq
if rna.type == wc_kb.core.RnaType.mRna:
for gene in tu.genes:
# creates ProteinSpecipe object for corresponding protein sequence(s)
# print(gene.get_seq()[0:3])
prot = cell.species_types.get_or_create(
id='prot_{}'.format(gene.id), __type=wc_kb.prokaryote.ProteinSpeciesType)
prot.name = 'prot_{}'.format(gene.id)
prot.cell = cell
prot.cell.knowledge_base = self.knowledge_base
prot.gene = gene # associates protein with GeneLocus object for corresponding gene
prot.rna = rna
prot.half_life = 1
prot_species = prot.species.get_or_create(compartment=cytosol)
prot_species.concentration = wc_kb.core.Concentration(cell=cell, value=rna_conc)
def simulateUtilityScore(N, VehicleShare, NumericalAttributes, CategoricalAttributes):
mcost_k_M = 100 * beta(a=4.5, b=2, size=N[0])
mcost_t_M = 0.1 * beta(a=3.5, b=2, size=N[0])
mcost_utility_M = ((-2e-3 * gamma(mcost_k_M, mcost_t_M, [len(NumericalAttributes['monthly_cost']), N[0]]))
* np.array(NumericalAttributes['monthly_cost'])[:, np.newaxis])
mcost_utility_M -= mcost_utility_M.mean(axis=0)
mcost_k_X = 100 * beta(a=4., b=2, size=N[1])
mcost_t_X = 0.1 * beta(a=4.5, b=2, size=N[1])
mcost_utility_X = ((-1.6e-3 * gamma(mcost_k_X, mcost_t_X, [len(NumericalAttributes['monthly_cost']), N[1]]))
* np.array(NumericalAttributes['monthly_cost'])[:, np.newaxis])
mcost_utility_X -= mcost_utility_X.mean(axis=0)
mcost_k_B = 100 * beta(a=3.5, b=2, size=N[2])
mcost_t_B = 0.1 * beta(a=5, b=2, size=N[2])
mcost_utility_B = ((-1.8e-3 * gamma(mcost_k_B, mcost_t_B, [len(NumericalAttributes['monthly_cost']), N[2]]))
* np.array(NumericalAttributes['monthly_cost'])[:, np.newaxis])
mcost_utility_B -= mcost_utility_B.mean(axis=0)
mcost_utility = np.hstack([mcost_utility_M, mcost_utility_X, mcost_utility_B]).T
upcost_k_M = 100 * beta(a=4.5, b=2, size=N[0])
upcost_t_M = 0.1 * beta(a=3.5, b=2, size=N[0])
upcost_utility_M = ((-2e-5 * gamma(upcost_k_M, upcost_t_M, [len(NumericalAttributes['upfront_cost']), N[0]]))
* np.array(NumericalAttributes['upfront_cost'])[:, np.newaxis])
upcost_utility_M -= upcost_utility_M.mean(axis=0)
upcost_k_X = 100 * beta(a=4., b=2, size=N[1])
upcost_t_X = 0.1 * beta(a=4.5, b=2, size=N[1])
upcost_utility_X = ((-1e-5 * gamma(upcost_k_X, upcost_t_X, [len(NumericalAttributes['upfront_cost']), N[1]]))
* np.array(NumericalAttributes['upfront_cost'])[:, np.newaxis])
upcost_utility_X -= upcost_utility_X.mean(axis=0)
upcost_k_B = 100 * beta(a=3.5, b=2, size=N[2])
upcost_t_B = 0.1 * beta(a=5, b=2, size=N[2])
upcost_utility_B = ((-1.5e-5 * gamma(upcost_k_B, upcost_t_B, [len(NumericalAttributes['upfront_cost']), N[2]]))
* np.array(NumericalAttributes['upfront_cost'])[:, np.newaxis])
upcost_utility_B -= upcost_utility_B.mean(axis=0)
upcost_utility = np.hstack([upcost_utility_M, upcost_utility_X, upcost_utility_B]).T
term_k_M = 100 * beta(a=4.5, b=2, size=N[0])
term_t_M = 0.1 * beta(a=3.5, b=2, size=N[0])
term_utility_M = ((-1e-2 * gamma(term_k_M, term_t_M, [len(NumericalAttributes['term']), N[0]]))
* np.array(NumericalAttributes['term'])[:, np.newaxis])
term_utility_M -= term_utility_M.mean(axis=0)
term_k_X = 100 * beta(a=4., b=2, size=N[1])
term_t_X = 0.1 * beta(a=4.5, b=2, size=N[1])
term_utility_X = ((-1.2e-2 * gamma(term_k_X, term_t_X, [len(NumericalAttributes['term']), N[1]]))
* np.array(NumericalAttributes['term'])[:, np.newaxis])
term_utility_X -= term_utility_X.mean(axis=0)
term_k_B = 100 * beta(a=3.5, b=2, size=N[2])
term_t_B = 0.1 * beta(a=5, b=2, size=N[2])
term_utility_B = ((-1.2e-2 * gamma(term_k_B, term_t_B, [len(NumericalAttributes['term']), N[2]]))
* np.array(NumericalAttributes['term'])[:, np.newaxis])
term_utility_B -= term_utility_B.mean(axis=0)
term_utility = np.hstack([term_utility_M, term_utility_X, term_utility_B]).T
worth_k_M = 1000 * beta(a=4.5, b=2, size=N[0])
worth_t_M = 0.01 * beta(a=3.5, b=2, size=N[0])
worth_utility_M = ((1.5e-5 * gamma(worth_k_M, worth_t_M, [len(NumericalAttributes['vehicle_worth']), N[0]]))
* np.array(NumericalAttributes['vehicle_worth'])[:, np.newaxis])
worth_utility_M -= worth_utility_M.mean(axis=0)
worth_k_X = 1000 * beta(a=4, b=2, size=N[1])
worth_t_X = 0.01 * beta(a=4.5, b=2, size=N[1])
worth_utility_X = ((1.5e-5 * gamma(worth_k_X, worth_t_X, [len(NumericalAttributes['vehicle_worth']), N[1]]))
* np.array(NumericalAttributes['vehicle_worth'])[:, np.newaxis])
worth_utility_X -= worth_utility_X.mean(axis=0)
worth_k_B = 1000 * beta(a=3.5, b=2, size=N[2])
worth_t_B = 0.01 * beta(a=4, b=2, size=N[2])
worth_utility_B = ((1.5e-5 * gamma(worth_k_B, worth_t_B, [len(NumericalAttributes['vehicle_worth']), N[2]]))
* np.array(NumericalAttributes['vehicle_worth'])[:, np.newaxis])
worth_utility_B -= worth_utility_B.mean(axis=0)
worth_utility = np.hstack([worth_utility_M, worth_utility_X, worth_utility_B]).T
range_k_M = 1000 * beta(a=4.5, b=2, size=N[0])
range_t_M = 0.007 * beta(a=4, b=2, size=N[0])
range_utility_M = ((2e-3 * gamma(range_k_M, range_t_M, [len(NumericalAttributes['range']), N[0]]))
* np.array(NumericalAttributes['range'])[:, np.newaxis])
range_utility_M -= range_utility_M.mean(axis=0)
range_k_X = 1000 * beta(a=4, b=2, size=N[1])
range_t_X = 0.008 * beta(a=4, b=2, size=N[1])
range_utility_X = ((2e-3 * gamma(range_k_X, range_t_X, [len(NumericalAttributes['range']), N[1]]))
* np.array(NumericalAttributes['range'])[:, np.newaxis])
range_utility_X -= range_utility_X.mean(axis=0)
range_k_B = 1000 * beta(a=3.5, b=2, size=N[2])
range_t_B = 0.008 * beta(a=4, b=2, size=N[2])
range_utility_B = ((2e-3 * gamma(range_k_B, range_t_B, [len(NumericalAttributes['range']), N[2]]))
* np.array(NumericalAttributes['range'])[:, np.newaxis])
range_utility_B -= range_utility_B.mean(axis=0)
range_utility = np.hstack([range_utility_M, range_utility_X, range_utility_B]).T
charge_k_M = 1000 * beta(a=4.5, b=2, size=N[0])
charge_t_M = 0.007 * beta(a=4, b=2, size=N[0])
charge_utility_M = ((2e-3 * gamma(charge_k_M, charge_t_M, [len(NumericalAttributes['charge']), N[0]]))
* np.array(NumericalAttributes['charge'])[:, np.newaxis])
charge_utility_M -= charge_utility_M.mean(axis=0)
charge_k_X = 1000 * beta(a=4, b=2, size=N[1])
charge_t_X = 0.008 * beta(a=4, b=2, size=N[1])
charge_utility_X = ((2e-3 * gamma(charge_k_X, charge_t_X, [len(NumericalAttributes['charge']), N[1]]))
* np.array(NumericalAttributes['charge'])[:, np.newaxis])
charge_utility_X -= charge_utility_X.mean(axis=0)
charge_k_B = 1000 * beta(a=3.5, b=2, size=N[2])
charge_t_B = 0.008 * beta(a=4, b=2, size=N[2])
charge_utility_B = ((2e-3 * gamma(charge_k_B, charge_t_B, [len(NumericalAttributes['charge']), N[2]]))
* np.array(NumericalAttributes['charge'])[:, np.newaxis])
charge_utility_B -= charge_utility_B.mean(axis=0)
charge_utility = np.hstack([charge_utility_M, charge_utility_X, charge_utility_B]).T
energy_sig_M = 0.4 * beta(a=10, b=2, size=N[0])
energy_mu_M = normal(loc=0.9, scale=0.1, size=N[0])
energy_inter = (1 * normal(energy_mu_M, energy_sig_M, [1, N[0]]))
energy_utility_M = np.vstack([-1 * energy_inter, energy_inter]).T
energy_sig_X = 0.4 * beta(a=10, b=2, size=N[1])
energy_mu_X = normal(loc=0.9, scale=0.1, size=N[1])
energy_inter = (1 * normal(energy_mu_X, energy_sig_X, [1, N[1]]))
energy_utility_X = np.vstack([-1 * energy_inter, energy_inter]).T
energy_sig_B = 0.4 * beta(a=10, b=2, size=N[2])
energy_mu_B = normal(loc=1.1, scale=0.1, size=N[2])
energy_inter = (1.2 * normal(energy_mu_B, energy_sig_B, [1, N[2]]))
energy_utility_B = np.vstack([-1 * energy_inter, energy_inter]).T
energy_utility = np.vstack([energy_utility_M, energy_utility_X, energy_utility_B])
type_mix_M = binomial(n=1, p=0.4, size=N[0])
type_sig_M = 2 * beta(a=10, b=2, size=N[0])
type_mu_M = normal(loc=(3 * (type_mix_M - 0.5)), scale=0.1, size=N[0])
type_inter = (0.5 * normal(type_mu_M, type_sig_M, [1, N[0]]))
type_utility_M = np.vstack([type_inter, -1 * type_inter]).T
type_mix_X = binomial(n=1, p=0.2, size=N[1])
type_sig_X = 2 * beta(a=10, b=2, size=N[1])
type_mu_X = normal(loc=(3 * (type_mix_X - 0.5)), scale=0.1, size=N[1])
type_inter = (0.5 * normal(type_mu_X, type_sig_X, [1, N[1]]))
type_utility_X = np.vstack([type_inter, -1 * type_inter]).T
type_mix_B = binomial(n=1, p=0.4, size=N[2])
type_sig_B = 2 * beta(a=10, b=2, size=N[2])
type_mu_B = normal(loc=(3 * (type_mix_B - 0.5)), scale=0.1, size=N[2])
type_inter = (0.5 * normal(type_mu_B, type_sig_B, [1, N[2]]))
type_utility_B = np.vstack([type_inter, -1 * type_inter]).T
type_utility = np.vstack([type_utility_M, type_utility_X, type_utility_B])
type_utility = type_utility.clip(-5, 5)
brand_scale = 10 * beta(a=10, b=2, size=sum(N))
brand_alloc = dirichlet(10*np.array([0.06, 0.07, 0.07, 0.01, 0.09, 0.44, 0.16, 0.1]), size=sum(N))
brand_utility = brand_alloc * brand_scale[:, np.newaxis]
brand_utility -= brand_utility.mean(axis=1)[:, np.newaxis]
utility = np.hstack([brand_utility, mcost_utility, upcost_utility, term_utility, worth_utility, range_utility,
charge_utility, energy_utility, type_utility])
# simulate the current market share
simCust = multinomial(1, list(VehicleShare.values()), sum(N))
simProduct = [list(VehicleShare.keys())[x] for x in np.argmax(simCust, axis=1)]
aug = pd.DataFrame(np.array([list(range(1, sum(N) + 1, 1)), ['Millenial'] * N[0] + ['Gen X'] * N[1]
+ ['Baby Boomer'] * N[2], simProduct]).T, columns = ['id', 'segment', 'current brand'])
k = 3 # we start at three as first three columns reserved for id, segment and current brand
topLevel = [0, 1, 2]
topLevelLab = ['id', 'segment', 'current brand']
bottomLevelLab = ['id', 'segment', 'current brand']
dictAttributes = {**CategoricalAttributes, **NumericalAttributes}
for col in ['id', 'brand', 'model', 'monthly_cost', 'upfront_cost', 'term',
'vehicle_worth', 'range', 'charge', 'energy', 'vehicle_type']:
if col not in ['id', 'model']:
topLevel = topLevel + [k] * len(list(dictAttributes[col]))
topLevelLab = topLevelLab + [col]
bottomLevelLab = bottomLevelLab + [lvl for lvl in list(dictAttributes[col])]
k += 1
midx = pd.MultiIndex(levels=[list(topLevelLab), list(bottomLevelLab)],
codes=[topLevel, list(range(len(bottomLevelLab)))])
utilityDf = pd.DataFrame(pd.concat([aug, pd.DataFrame(utility)], axis=1).values, columns=midx)
return utilityDf
def _update_Theta_DK(self):
post_shape_DK = self.shape + self.Y_DK
post_rate_DK = self.rate + np.dot(~self.data.mask, self.Phi_KV.T)
self.Theta_DK[:] = rn.gamma(post_shape_DK, 1. / post_rate_DK)
def sample_lam_b_pri(lam_b_hyper_pri_shape, lam_b_hyper_pri_rate, lam_a_pri,
lam_mat, K):
lam_b_pri = gamma(lam_b_hyper_pri_shape + K * lam_a_pri,
1 / (lam_b_hyper_pri_rate + lam_mat.sum(axis=0)))
return lam_b_pri
def initialize_sampler(self, ns):
self.samples = Samples(ns, self.nCol) # self.nDat, self.nCol)
self.samples.zeta[0] = gamma(shape=2., scale=2., size=self.nCol)
# self.samples.rho[0] = self.sample_rho(self.samples.zeta[0])
self.curr_iter = 0
return
def sample_r(self, alpha, delta):
shapes = alpha[delta].sum(axis=1)
rates = self.data.V.sum(axis=1)
return gamma(shape=shapes, scale=1. / rates)
def sample_re(self):
enew = self.e0 + 0.5 * self.F * self.N
fnew = self.f0 + 0.5 * np.sum(self.X**2)
self.r_e = nr.gamma(enew, scale=1. / fnew)
def sample(shape: Union[float, np.ndarray],
scale: Union[float, np.ndarray],
size: int = None) -> Union[float, np.ndarray]:
return 1 / npr.gamma(shape=shape, scale=1 / scale, size=size)
import numpy as np
import numpy.random as npr
import scipy.stats as sps
import matplotlib.pyplot as plt
plt.close("all")
t = 10.
shape = 1.
scale = 4.
n = 50000
X = npr.gamma(shape, scale, size=n)
X_c = X[X > t] - t
x = np.linspace(0., max(X_c), 1000)
f_x = sps.gamma.pdf(x, a=shape, scale=scale)
plt.hist(X_c, normed=True, bins=2 * round(n**(1. / 3.))) #empirique
plt.plot(x, f_x, "r") #theorique
plt.title("Loi empirique de (X | X > t) - t pour X de loi exponentielle d'intensite " \
+ str(1./scale))
plt.show()
def sampler(self):
"""
Run blocked-Gibbs sampling
"""
#pdb.set_trace()
for key, value in self.data.items():
T = value.shape[0]
# Step 1: backwards message passing
messages = np.zeros((T, self.L))
messages[-1, :] = 1
for t in range(T - 1, 0, -1):
messages[t - 1, :] = self.PI.dot(
messages[t, :] *
np.exp(self._logphi(value[t, :], self.mu, self.sigma)))
messages[t - 1, :] /= np.max(messages[t - 1, :])
# Step 2: states by MH algorithm
for t in range(1, T):
j = choice(self.L) # proposal
k = self.state[key][t]
logprob_accept = (
np.log(messages[t, k]) - np.log(messages[t, j]) +
np.log(self.PI[self.state[key][t - 1], k]) -
np.log(self.PI[self.state[key][t - 1], j]) +
self._logphi(value[t - 1, :], self.mu[k], self.sigma[k]) -
self._logphi(value[t - 1, :], self.mu[j], self.sigma[j]))
if exponential(1) > logprob_accept:
print("state update!")
self.state[key][t] = j
self.N[self.state[key][t - 1], j] += 1
self.N[self.state[key][t - 1], k] -= 1
# Step 3: auxiliary variables
P = np.tile(self.beta, (self.L, 1)) + self.n
np.fill_diagonal(P, np.diag(P) + self.kappa)
P = 1 - self.n / P
for i in range(self.L):
for j in range(self.L):
self.M[i, j] = binomial(self.M[i, j], P[i, j])
w = np.array([
binomial(self.M[i, i], 1 / (1 + self.beta[i]))
for i in range(self.L)
])
m_bar = np.sum(self.M, axis=0) - w
# pdb.set_trace()
# input("continue...")
# Step 4: beta and parameters of clusters
#self.beta = _gem(self.gma)
self.beta = dirichlet(np.ones(self.L) * (self.gma / self.L)) #+ m_bar
# Step 5: transition matrix
self.PI = np.tile(self.alpha * self.beta, (self.L, 1)) + self.N
np.fill_diagonal(self.PI, np.diag(self.PI) + self.kappa)
# pdb.set_trace()
for i in range(self.L):
self.PI[i, :] = dirichlet(self.PI[i, :])
cluster = []
for key, value in self.data.items():
idx = np.where(self.state[key] == i)
if cluster == []:
cluster = value[idx]
else:
cluster = np.vstack([cluster, value[idx, :]])
nc = cluster.shape[0]
if nc:
xmean = np.mean(cluster)
self.mu[i] = xmean / (self.nu / nc + 1)
self.sigma[i] = (2 * self.b +
(nc - 1) * np.var(cluster) + nc * xmean**2 /
(self.nu + nc)) / (2 * self.a + nc - 1)
else:
self.mu[i] = normal(0, np.sqrt(self.nu))
self.sigma[i] = 1 / gamma(self.a, self.b)
# check log likelihood
total_loglikelihood = 0
for key, value in self.data.items():
T = value.shape[0]
emis = 0
trans = 0
for t in range(T):
emis += self._logphi(value[t, :], self.mu[self.state[key][t]],
self.sigma[self.state[key][t]])
if t > 0:
trans += np.log(self.PI[self.state[key][t - 1],
self.state[key][t]])
total_loglikelihood = emis + trans
print("total log likelihood of all sequence: ", total_loglikelihood)
def _next_disconnect(self):
time_until = gamma(self.time_until_shape, self.time_until_scale)
duration = gamma(self.duration_shape, self.duration_scale)
return time_until, duration
def _update_Phi_KV(self):
post_shape_KV = self.shape + self.Y_KV
post_rate_KV = self.rate + np.dot(self.Theta_DK.T, ~self.data.mask)
self.Phi_KV[:] = rn.gamma(post_shape_KV, 1. / post_rate_KV)
def sample_r(self, alphas, betas, delta):
alpha = alphas[delta]
beta = betas[delta]
As = alpha.sum(axis=1)
Bs = (self.data.Yl * beta).sum(axis=1)
return gamma(shape=As, scale=1 / Bs)
def sample_lam_mat(lam_a_pri, lam_b_pri, ysum,
ycnt): #lam_mat is a K by # neurons mat
lam_mat = gamma(lam_a_pri + ysum, 1 / (lam_b_pri + ycnt))
return lam_mat
def _update_alpha(self, V):
a = self.ncomp + self.e - 1
b = self.f - np.log(1 - V).sum()
return npr.gamma(a, scale=1 / b)
def unsupervised_wiener(image,
psf,
reg=None,
user_params=None,
is_real=True,
clip=True):
"""Unsupervised Wiener-Hunt deconvolution.
Return the deconvolution with a Wiener-Hunt approach, where the
hyperparameters are automatically estimated. The algorithm is a
stochastic iterative process (Gibbs sampler) described in the
reference below. See also ``wiener`` function.
Parameters
----------
image : (M, N) ndarray
The input degraded image.
psf : ndarray
The impulse response (input image's space) or the transfer
function (Fourier space). Both are accepted. The transfer
function is automatically recognized as being complex
(``np.iscomplexobj(psf)``).
reg : ndarray, optional
The regularisation operator. The Laplacian by default. It can
be an impulse response or a transfer function, as for the psf.
user_params : dict, optional
Dictionary of parameters for the Gibbs sampler. See below.
clip : boolean, optional
True by default. If true, pixel values of the result above 1 or
under -1 are thresholded for skimage pipeline compatibility.
Returns
-------
x_postmean : (M, N) ndarray
The deconvolved image (the posterior mean).
chains : dict
The keys ``noise`` and ``prior`` contain the chain list of
noise and prior precision respectively.
Other parameters
----------------
The keys of ``user_params`` are:
threshold : float
The stopping criterion: the norm of the difference between to
successive approximated solution (empirical mean of object
samples, see Notes section). 1e-4 by default.
burnin : int
The number of sample to ignore to start computation of the
mean. 15 by default.
min_iter : int
The minimum number of iterations. 30 by default.
max_iter : int
The maximum number of iterations if ``threshold`` is not
satisfied. 200 by default.
callback : callable (None by default)
A user provided callable to which is passed, if the function
exists, the current image sample for whatever purpose. The user
can store the sample, or compute other moments than the
mean. It has no influence on the algorithm execution and is
only for inspection.
Examples
--------
>>> from skimage import color, data, restoration
>>> img = color.rgb2gray(data.astronaut())
>>> from scipy.signal import convolve2d
>>> psf = np.ones((5, 5)) / 25
>>> img = convolve2d(img, psf, 'same')
>>> img += 0.1 * img.std() * np.random.standard_normal(img.shape)
>>> deconvolved_img = restoration.unsupervised_wiener(img, psf)
Notes
-----
The estimated image is design as the posterior mean of a
probability law (from a Bayesian analysis). The mean is defined as
a sum over all the possible images weighted by their respective
probability. Given the size of the problem, the exact sum is not
tractable. This algorithm use of MCMC to draw image under the
posterior law. The practical idea is to only draw highly probable
images since they have the biggest contribution to the mean. At the
opposite, the less probable images are drawn less often since
their contribution is low. Finally the empirical mean of these
samples give us an estimation of the mean, and an exact
computation with an infinite sample set.
References
----------
.. [1] François Orieux, Jean-François Giovannelli, and Thomas
Rodet, "Bayesian estimation of regularization and point
spread function parameters for Wiener-Hunt deconvolution",
J. Opt. Soc. Am. A 27, 1593-1607 (2010)
https://www.osapublishing.org/josaa/abstract.cfm?URI=josaa-27-7-1593
http://research.orieux.fr/files/papers/OGR-JOSA10.pdf
"""
params = {
'threshold': 1e-4,
'max_iter': 200,
'min_iter': 30,
'burnin': 15,
'callback': None
}
params.update(user_params or {})
if reg is None:
reg, _ = uft.laplacian(image.ndim, image.shape, is_real=is_real)
if not np.iscomplexobj(reg):
reg = uft.ir2tf(reg, image.shape, is_real=is_real)
if psf.shape != reg.shape:
trans_fct = uft.ir2tf(psf, image.shape, is_real=is_real)
else:
trans_fct = psf
# The mean of the object
x_postmean = np.zeros(trans_fct.shape)
# The previous computed mean in the iterative loop
prev_x_postmean = np.zeros(trans_fct.shape)
# Difference between two successive mean
delta = np.NAN
# Initial state of the chain
gn_chain, gx_chain = [1], [1]
# The correlation of the object in Fourier space (if size is big,
# this can reduce computation time in the loop)
areg2 = np.abs(reg)**2
atf2 = np.abs(trans_fct)**2
# The Fourier transform may change the image.size attribute, so we
# store it.
if is_real:
data_spectrum = uft.urfft2(image.astype(np.float))
else:
data_spectrum = uft.ufft2(image.astype(np.float))
# Gibbs sampling
for iteration in range(params['max_iter']):
# Sample of Eq. 27 p(circX^k | gn^k-1, gx^k-1, y).
# weighting (correlation in direct space)
precision = gn_chain[-1] * atf2 + gx_chain[-1] * areg2 # Eq. 29
excursion = np.sqrt(0.5) / np.sqrt(precision) * (
np.random.standard_normal(data_spectrum.shape) +
1j * np.random.standard_normal(data_spectrum.shape))
# mean Eq. 30 (RLS for fixed gn, gamma0 and gamma1 ...)
wiener_filter = gn_chain[-1] * np.conj(trans_fct) / precision
# sample of X in Fourier space
x_sample = wiener_filter * data_spectrum + excursion
if params['callback']:
params['callback'](x_sample)
# sample of Eq. 31 p(gn | x^k, gx^k, y)
gn_chain.append(
npr.gamma(
image.size / 2,
2 / uft.image_quad_norm(data_spectrum - x_sample * trans_fct)))
# sample of Eq. 31 p(gx | x^k, gn^k-1, y)
gx_chain.append(
npr.gamma((image.size - 1) / 2,
2 / uft.image_quad_norm(x_sample * reg)))
# current empirical average
if iteration > params['burnin']:
x_postmean = prev_x_postmean + x_sample
if iteration > (params['burnin'] + 1):
current = x_postmean / (iteration - params['burnin'])
previous = prev_x_postmean / (iteration - params['burnin'] - 1)
delta = np.sum(np.abs(current - previous)) / \
np.sum(np.abs(x_postmean)) / (iteration - params['burnin'])
prev_x_postmean = x_postmean
# stop of the algorithm
if (iteration > params['min_iter']) and (delta < params['threshold']):
break
# Empirical average \approx POSTMEAN Eq. 44
x_postmean = x_postmean / (iteration - params['burnin'])
if is_real:
x_postmean = uft.uirfft2(x_postmean, shape=image.shape)
else:
x_postmean = uft.uifft2(x_postmean)
if clip:
x_postmean[x_postmean > 1] = 1
x_postmean[x_postmean < -1] = -1
return (x_postmean, {'noise': gn_chain, 'prior': gx_chain})
from numpy.random import uniform, normal, gamma
from numpy import sqrt
from sys import argv, stdout, stderr
# Process arguments
if len(argv) != 3:
stderr.write("Incorrect number of arguments\n".format(argv[0]))
exit(1)
a_diff = float(argv[1])
a_udiff = float(argv[2])
diff_sigma2 = 1.0 / gamma(3, 78)
udiff_sigma2 = 1.0 / gamma(3, 78)
t1 = uniform(low=0, high=1)
t2 = uniform(low=0, high=1)
diff_sampled = normal(loc=0.23, scale=sqrt(diff_sigma2))
udiff_sampled = normal(loc=0.64, scale=sqrt(udiff_sigma2))
if t1 > a_diff: #draw from just diffusion coefficient
diff_sampled = 0
elif t2 > a_udiff: #draw from just u*diffusion coefficient
udiff_sampled = 0
# Print sampled parameters
stdout.write("{:0.6f} {:0.6f} {:0.6f} {:0.6f}\n".format(
diff_sampled, udiff_sampled, diff_sigma2, udiff_sigma2))
stdDev = sqrt(variance)
stdDev = std(valArray) # Biased estimate - 1.0833
stdDev = valArray.std(ddof=1) # "Unbiased" estimate - 1.1362
print('Std:', stdDev)
stdErrMean = valArray.std(ddof=1)/sqrt(len(valArray))
from scipy.stats import sem
stdErrMean = sem(valArray, ddof=1) # Result is 0.3426
from scipy.stats import skew
from numpy import random
samples = random.gamma(3.0, 2.0, 100) # Example data
skewness = skew(samples)
print( 'Skew', skewness ) # Result is 1.0537
from scipy.stats import binom_test
count, nTrials, pEvent = 530, 1000, 0.5
result = binom_test(count, nTrials, pEvent)
print( 'Binomial two tail', result)
from scipy.stats import binom
from numpy import array, zeros
def binomialTailTest(counts, nTrials, pEvent, oneSided=True):
def sample(self, data, parents, T, dt_max):
start = time.time()
times, nodes = data
# sufficient statistics
M_0n = np.zeros(self.N)
M_n = np.zeros(self.N)
M_mn = np.zeros((self.N, self.N))
xbar_mn = np.zeros((self.N, self.N))
nu_mn = np.zeros((self.N, self.N))
# Direct Method
X = [[[] for n in range(self.N)] for n in range(self.N)]
for t in range(len(times)):
n = nodes[t]
# M_n
M_n[n] += 1
sn = times[t]
w = parents[
t] # (0 = background, 1, ..., M - 1 = last possible parent)
if w > 0: # if not a background event...
m = nodes[w - 1] # parent node
sm = times[w - 1] # parent time
# M_mn
M_mn[m, n] += 1
x = np.log((sn - sm) / (dt_max - (sn - sm)))
X[m][n].append(x)
else:
M_0n[n] += 1
# xbar_mn, nu_mn
for n in range(self.N): # event node
for m in range(self.N): # parent node
if len(X[m][n]) > 0:
xbar_mn[m, n] = np.mean(X[m][n])
nu_mn[m, n] = np.var(X[m][n]) * M_mn[m, n]
else:
# print("No {} -> {} events found.".format(m,n))
xbar_mn[m, n] = 0.1
nu_mn[m, n] = 0.1
assert M_mn.sum() + M_0n.sum() == len(times), "Event count error 1"
assert M_n.sum() == len(times), "Event count error 2"
# check for zeros
if FLAGS_VERBOSE:
print('M_mn={}'.format(M_mn))
print('xbar_mn={}'.format(xbar_mn))
print('nu_mn={}'.format(nu_mn))
xbar_mn[xbar_mn == 0] = 0.01
nu_mn[nu_mn == 0] = 0.01
# calculate posterior parameters
alpha_0 = self.alpha_0 + M_0n
beta_0 = self.beta_0 + T
kappa = self.kappa + M_mn
nu = self.nu + M_n.reshape((self.N, 1))
mu_mu = (self.kappa_mu * self.mu_mu +
M_mn * xbar_mn) / (self.kappa_mu + M_mn)
kappa_mu = self.kappa_mu + M_mn
alpha_tau = self.alpha_tau + (M_mn / 2)
beta_tau = (nu_mn /
2) + (M_mn * self.kappa_mu *
(xbar_mn - self.mu_mu)**2) / (2 *
(M_mn + self.kappa_mu))
# sample posteriors
lamb = gamma(alpha_0, (1 / beta_0)) # N x 1 parameters
W = self.A * gamma(kappa, (1 / nu)) # N x N parameters
mu, tau = normal_gamma(mu_mu, kappa_mu, alpha_tau,
beta_tau) # N x N parameters
stop = time.time()
if FLAGS_VERBOSE:
print('Sampled parameters in {} seconds.'.format(stop - start))
return lamb, W, mu, tau
def _numpy(self, loc=0.0, scale=1.0, size=(1, )):
return lambda: nr.gamma(
shape=self.alpha, scale=self.theta * scale, size=size) + loc
def sim_gamma(shape, scale, size):
return npr.gamma(shape, scale, size)
def run_chain(self, steps=1):
"""Run a Gibbs sampler
"""
z_chain = np.zeros((steps, self.n), dtype=int)
self.assignments = z_chain
M = float(self.params['M'])
for i in range(1, steps):
if i % 50 == 0: print("MCMC Chain: {}".format(i))
# find the number of points in each clusters
old_unique, old_counts = np.unique(self.assignments[i - 1, :],
return_counts=True)
num_pts_clusters = dict(zip(old_unique, old_counts))
# old_unique = list(old_unique)
# initialise the arrays of the chain as the array lengths differ
# as we increase the number of clusters
mu_new = np.zeros(old_unique.shape)
sigma_new = np.zeros(old_unique.shape)
weights_new = np.zeros(old_unique.shape)
mu_old = self.chain["mu"][i - 1]
sigma_old = self.chain["sigma"][i - 1]
weights_old = self.chain["weights"][i - 1]
for k in old_unique:
num_pts_cluster = num_pts_clusters[k]
data_cluster = self.data[np.where(
self.assignments[i - 1, :] == k)[0]]
if num_pts_cluster > 0:
# now sample mu[k] given mu[-k], sigma and the partition
# see lecture 15 last slide calculations N(a, b) trick
sigma_tmp = sigma_old[k]
b = np.sqrt(1 / (num_pts_cluster / sigma_tmp**2 +
1 / self.hyperparam["sigma_0"]**2))
a = b**2 * (sum(data_cluster) / sigma_tmp**2 +
self.hyperparam["mu_0"] /
self.hyperparam["sigma_0"]**2)
# update mu
mu_new[k] = normal(loc=a, scale=b)
# now sample sigma[k] given sigma[-k], mu and the partition
c = self.hyperparam["alpha_0"] + num_pts_cluster / 2
d = self.hyperparam["beta_0"] + 0.5 * sum(
(data_cluster - mu_new[k])**2)
# update sigma
sigma_new[k] = 1.0 / np.sqrt(gamma(shape=c, scale=1 / d))
self.assignments[i, :] = self.assignments[i - 1, :].copy()
# now, loop through all the datapoints to compute the new cluster probabilities
for j in range(self.n):
# TODO: this bit could definitely be taken out in the future, but i
# will just leave it for now
old_unique, old_counts = np.unique(self.assignments[i, :],
return_counts=True)
old_cluster_assigned = int(self.assignments[i, j])
old_counts[old_cluster_assigned] -= 1
K = len(old_unique)
# probability for each existing k cluster -> gives a vector of probabilities
p_old_cluster = (old_counts + 1. / M) * norm(
mu_new, sigma_new).pdf(self.data[j])
mu_update = normal(loc=self.hyperparam["mu_0"],
scale=self.hyperparam["sigma_0"])
sigma_update = 1 / np.sqrt(
gamma(
shape=self.hyperparam["alpha_0"],
scale=1 / self.hyperparam["beta_0"],
))
p_new_cluster = (M - K) / M * self.params["alpha"] * norm(
mu_update, sigma_update).pdf(self.data[j])
# logging.debug(p_old_cluster)
# logging.debug(p_new_cluster)
p_new_cluster = np.atleast_1d(p_new_cluster)
# normlise the probabilities
prob_clusters = np.concatenate((p_old_cluster, p_new_cluster))
prob_clusters = prob_clusters / sum(prob_clusters)
# select a new cluster!
# if we get K then new cluster!
# try:
cluster_pick = np.random.choice(K + 1, p=prob_clusters)
# except Exception as e:
# logging.info("Iteration {}, datapoint {}".format(i, j))
# logging.info("{}".format(sigma_new),
# "nan probabilities occurring due to values "
# "mu_new and sigma_new: \n\n"
# "mu_new: {} \n sigma_new: {}".format(
# mu_new, sigma_new),
# "\n with probabilities: {}".format(prob_clusters))
if cluster_pick == K:
self.assignments[i, j] = cluster_pick
# update the indices and shift the parameters up the list
mu_new = np.append(mu_new, mu_update)
sigma_new = np.append(sigma_new, sigma_update)
else:
self.assignments[i, j] = cluster_pick
# obtain the number of members in the cluster belonging to the ith element, with
# it removed!
# find the number of points in each clusters as it will change with each iteration
# unique, counts = np.unique(
# self.assignments[i, :], return_counts=True)
# num_pts_clusters = dict(zip(unique, counts))
# remove empty clusters and their parameters
# now, sample the cluster weights!
if (old_counts[old_cluster_assigned]
== 0) & (cluster_pick != old_cluster_assigned):
mu_new = np.delete(mu_new, old_cluster_assigned)
sigma_new = np.delete(sigma_new, old_cluster_assigned)
ind = self.assignments[i, :] > (old_cluster_assigned)
self.assignments[i, ind] = self.assignments[i, ind] - 1
# update the weights
_, counts = np.unique(self.assignments[i, :], return_counts=True)
weights_update = dirichlet(alpha=self.params["alpha"] + counts)
weights_new = weights_update.copy()
self.chain["mu"].append(mu_new)
self.chain["sigma"].append(sigma_new)
self.chain["weights"].append(weights_new)
print("Complete sampling")
return self.chain, self.assignments
def firstStateGenerator(parameters, size):
first_state = zeros((size, 2))
first_state[:, 1] = random.gamma(size=size,
shape=(parameters[2]**2) / parameters[3],
scale=(parameters[3] / parameters[2]))
return first_state
def draw_nparray(self, shape=(1, )):
""" Draw a numpy array of random samples, of a certain shape."""
return np.minimum(
np.maximum(gamma(self.shape, self.scale, size=shape), self.min),
self.max)
def ichi2(degFreedom, scale):
shape = degFreedom / 2
return ((shape * scale) / random.gamma(shape))
traj_BD = []
t_label = []
while len(traj_BD) < nb_simul:
#Initialization
x = x0
tabx = []
t = 0
while x > 0 and t < tau:
tabx.append(x)
x += numpy.random.normal(2 * dt, math.sqrt(2 * x * dt))
t += dt
gamma = random.gamma(n, 1.0 / n)
exp = -math.log(random.random()) / n
if x > 0 and gamma <= x <= (gamma + exp):
traj_BD.append(tabx)
#
#Mean trajectory over time
#
avg_BD = [float(sum(col)) / len(col) for col in zip(*traj_BD)]
with open(path, "w") as file_BD:
for i in xrange(len(avg_BD)):
file_BD.write(str(i * dt) + '\t' + str(avg_BD[i]) + '\n')
def rvs(self, size=None):
return random.gamma(self.a, scale=self.scale, size=size)
def box_rng(self) -> int:
return int(random.gamma(2, 400))