def data_generating_process(N,
sigma_0,
p_domain,
gamma,
V,
theta,
coef,
beta=None,
random_state=None):
"""
"""
## Set Random State
if random_state is not None:
np.random.seed(random_state)
## Update Beta
if beta is None:
beta = 1 / V
## Convert Data Types
theta = np.array(theta)
coef = np.array(coef)
## Normalization of Parameters
theta = theta / theta.sum(axis=1, keepdims=True)
## Update Document Topic Concentration
theta = theta * sigma_0
## Generate Topic-Word Distributions
phi = stats.dirichlet([beta] * V).rvs(theta.shape[1])
## Data Storage
X_latent = np.zeros((N, coef.shape[1]), dtype=float)
X = np.zeros((N, phi.shape[1]), dtype=int)
D = np.zeros(N, dtype=int)
## Sample Procedure
for n in tqdm(range(N), "Sampling"):
## Sample Domain
D[n] = int(np.random.rand() < p_domain)
## Sample Document Topic Mixture (Conditioned on Domain)
X_latent[n] = stats.dirichlet(theta[D[n]]).rvs()
## Sample Number of Words
n_d = stats.poisson(gamma).rvs()
## Create Document
for _ in range(n_d):
## Sample Topic
z = np.where(stats.multinomial(1, X_latent[n]).rvs()[0] > 0)[0][0]
## Sample Word
w = np.random.choice(phi.shape[1], p=phi[z])
## Cache
X[n, w] += 1
## Standardize
X_latent_normed = standardize(X_latent, D)
## Compute P(y)
py = np.zeros(N)
py[D == 0] = (1 /
(1 + np.exp(-coef[[0]].dot(X_latent_normed[D == 0].T))))[0]
py[D == 1] = (1 /
(1 + np.exp(-coef[[1]].dot(X_latent_normed[D == 1].T))))[0]
## Sample Y
y = np.zeros(N)
y[D == 0] = (np.random.rand((D == 0).sum()) < py[D == 0]).astype(int)
y[D == 1] = (np.random.rand((D == 1).sum()) < py[D == 1]).astype(int)
return X_latent, X, y, D, theta, phi
def generate(
self,
alpha,
beta,
n,
k,
):
dirichlet()
pass
def jitter(self, concentration=100):
pi = self.params[0]
new_pi = npr.dirichlet(concentration * pi) + 1e-8
new_pi /= new_pi.sum()
fwd_lp = dirichlet(concentration * pi).logpdf(new_pi)
rev_lp = dirichlet(concentration * new_pi).logpdf(pi)
new_cluster = copy.deepcopy(self)
new_cluster._params = (new_pi,)
return new_cluster, fwd_lp, rev_lp
def batch_dirichlet(alpha):
"""Batched `np.ndarray` of Dirichlet frozen distributions.
To get each frozen distribution, index the returned `np.ndarray` followed by
`item(0)`.
"""
if alpha.ndim == 1:
return stats.dirichlet(alpha)
return np.array([
stats.dirichlet(vec) for vec in alpha.reshape([-1, alpha.shape[-1]])
]).reshape(alpha.shape[:-1])
def sample_pi(self):
"""
sample pi from posterior
"""
param = np.ones(self.nClass) * self.alpha / self.nClass
param += self.counts
self.pi = stats.dirichlet(param).rvs(size=1).flatten()
def test_multiple_entry_calls():
# Test that calls with multiple x vectors as matrix work
np.random.seed(2846)
n = np.random.randint(1, 32)
alpha = np.random.uniform(10e-10, 100, n)
d = dirichlet(alpha)
num_tests = 10
num_multiple = 5
xm = None
for i in range(num_tests):
for m in range(num_multiple):
x = np.random.uniform(10e-10, 100, n)
x /= np.sum(x)
if xm is not None:
xm = np.vstack((xm, x))
else:
xm = x
rm = d.pdf(xm.T)
rs = None
for xs in xm:
r = d.pdf(xs)
if rs is not None:
rs = np.append(rs, r)
else:
rs = r
assert_array_almost_equal(rm, rs)
def log_prior(self):
"""
Compute the log likelihood of a set of SBM parameters
:param x: (m,p,v) tuple
:return:
"""
from scipy.stats import dirichlet
from graphistician.internals.utils import normal_inverse_wishart_log_prob
lp = 0
# Get the log probability of the block probabilities
lp += dirichlet(self.pi).logpdf(self.m)
# Get the prior probability of the Gaussian parameters under NIW prior
for c1 in xrange(self.C):
for c2 in xrange(self.C):
lp += normal_inverse_wishart_log_prob(self._gaussians[c1][c2])
if self.special_case_self_conns:
lp += normal_inverse_wishart_log_prob(self._self_gaussian)
# Get the probability of the block assignments
lp += (np.log(self.m)[self.c]).sum()
return lp
def log_prior(self):
lp = super(MixtureOfLatentSpaceModels, self).log_prior()
# p({h} | nu)
lp += np.dot(np.bincount(self.hs, minlength=self.H), np.log(1e-16 + self.nu))
# p(nu)
lp += dirichlet(self.alpha / self.H * np.ones(self.H)).logpdf(1e-16 + self.nu)
return lp
def sample_proposal(a, m, N):
"""
Sample from the proposal distribution
Parameters
----------
a, m : (k+1,) np.ndarray, dtype=float; float in [0, 1]
the parameters for the proposal distribution (Dirichlet(α) x
Bernoulli(m))
N : int
size of the sample
Returns
-------
ss : (N, k+1) np.ndarray, dtype=float
the switch positions for each sample
thetas : (N,) np.ndarray, dtype=int
the initial state for each sample
See also
--------
fit_proposal
"""
ss = stats.dirichlet(a).rvs(N)
thetas = (np.random.rand(N) < m).astype(int)
return ss, thetas
def proposal(a, m, ss, thetas):
"""
Evaluate the proposal distribution at a given point
Parameters
----------
a, m : (k+1,) np.ndarray, dtype=float; float in [0, 1]
the parameters for the proposal distribution (Dirichlet(α) x
Bernoulli(m))
ss : (n, k+1) np.ndarray, dtype=float
thetas : (n,) np.ndarray, dtype=int
Returns
-------
float
See also
--------
sample_proposal
"""
# try: # this was supposed to catch instances where dirichlet.pdf raises a
# ValueError due to the sample points not lying strictly within the
# simplex, i.e 0 < s < 1. But this should not happen in production
# anyways, so it seems appropriate to raise this error.
with np.errstate(under='ignore'): # pdf(.) == exp(_logpdf(.)) and exp may underflow
return (
stats.dirichlet(a).pdf(ss.T)
* ( m*thetas + (1-m)*(1-thetas) )
)
def random_state(d):
num_basis_vectors = 2**d
shape = [2] * d
real_part = np.sqrt(dirichlet(alpha=[1]*num_basis_vectors).rvs()[0, :])
imag_part = np.exp(1j * np.random.uniform(0, 2*np.pi, size=num_basis_vectors))
amplitudes = (real_part * imag_part).reshape(shape)
return qc.state.State(amplitudes)
def make_Dirichland(N,K, concentration_params, scalar=2):
our_dirichlet = stats.dirichlet(concentration_params) #the distribution we use
NK_land = np.random.rand(N, 2**(K+1))
fitnesses = []
permutations = []
dir_draw = our_dirichlet.rvs()[0]
all_permutations = list(itertools.product([0,1],repeat=N))
for permutation in all_permutations:
genome_fitness = 0
for currIndex in np.arange(N):
#get the fitness indices from each k based upon local gene values
localgenes = permutation[currIndex:currIndex+K+1]
#loop through to next if were are near the nth index
if currIndex+K+1 > N:
localgenes = np.append(localgenes,permutation[0:currIndex-(N-K)+1])
#get index fitness is stored at
interactIndex = ((2**(np.arange(K+1)*(localgenes)))*localgenes).sum()
#update fitness
genome_fitness += NK_land[currIndex,interactIndex] * (1-dir_draw[currIndex])
fitnesses.append(genome_fitness)
permutations.append("".join([str(i) for i in permutation]))
df = pd.DataFrame(fitnesses,index=permutations,columns=["Fitness"])
df.loc[:,'Location'] = all_permutations
return df
def sample_parameters(self, evidence_set, state_sample):
"""
This method samples parameters given the previously sampled states
"""
# Pre-processing to sample parameters faster
posteriors_theta_s = self.model.parameter_priors.theta_s_priors.copy()
posteriors_pi_lt = self.model.parameter_priors.pi_lt_priors.copy()
for t in range(1, evidence_set.time_slices):
for d in range(evidence_set.number_of_data_points):
# Incrementing the prior parameters
posteriors_theta_s[state_sample[d][t -
1]][state_sample[d][t]] += 1
posteriors_pi_lt[state_sample[d][t]][
1 - evidence_set.lt_evidence[d][t]] += 1
# Sample parameters
theta_s_sample = np.zeros(
(self.model.number_of_states, self.model.number_of_states))
pi_lt_sample = np.zeros((self.model.number_of_states, 2))
for state in range(self.model.number_of_states):
sample = dirichlet(posteriors_theta_s[state]).rvs()[0]
theta_s_sample[state] = sample
sample = beta(*posteriors_pi_lt[state]).rvs()
pi_lt_sample[state] = [1 - sample, sample]
return theta_s_sample, pi_lt_sample
def __init__(self,
a_scale=A_SCALE,
b_scale=B_SCALE,
c_d_dirichlet_alpha=C_D_DIRICHLET_ALPHA):
self.a = lognorm(s=1., scale=a_scale)
self.b = norm(scale=b_scale)
self.c_d = dirichlet(alpha=c_d_dirichlet_alpha)
def run_gam_effective_r_from_empirical(state_data,
n_splines=25,
algo=GammaGAM,
n_bootstrap=100):
# for numerical stability
epsilon = 1
R_series = (
state_data['confirmed_new'] /
state_data['confirmed_total'].shift(1)).dropna() * 1 / RECOVERY_RATE
X = np.arange(R_series.shape[0])
y = R_series.values + epsilon
# running GAM in bootstrap
bootstrap = []
for _ in range(n_bootstrap):
weights = dirichlet([1] * R_series.shape[0]).rvs(1)
gam = algo(s(0, n_splines) + l(0))
gam.fit(X, y, weights=weights[0])
bootstrap.append(gam)
preds = pd.DataFrame([m.predict(X) - epsilon for m in bootstrap]).T
estimate_rt = pd.DataFrame(index=R_series.index)
estimate_rt['ML'] = preds.mean(axis=1).values
estimate_rt['Low_90'] = preds.quantile(0.05, axis=1).values
estimate_rt['High_90'] = preds.quantile(0.95, axis=1).values
return estimate_rt.dropna()
def perturbProportion(self, irr_range, aucpn_range):
if not self.quiet:
print('Perturb Proportion')
prop = self.getMarkedParOldValue()
a = 0.25
if self.changeInfo['is_positive']:
prop_1 = dirichlet(np.ones(self.n_comps_pos)).rvs([])
else:
prop_1 = dirichlet(np.ones(self.n_comps_neg)).rvs([])
new_prop = (1 - a) * prop + a * prop_1
self.proposeChange(new_prop)
while not (self.isMetricUBSatisfied(irr_range, aucpn_range)):
a = a / 2
new_prop = (1 - a) * prop + a * prop_1
# print(a)
self.proposeChange(new_prop)
def __init__(self, dim, max_comps, quiet=False):
self.dim = dim
self.max_comps = max_comps
#self.n_comps_pos = randint(1, max_comps)
#self.n_comps_neg = randint(1, max_comps)
self.n_comps_pos = max_comps
self.n_comps_neg = max_comps
self.mu_pos = list()
self.mu_neg = list()
for i in np.arange(max(self.n_comps_pos, self.n_comps_neg)):
mu = np.array([
16 / np.sqrt(self.dim) * random() - 8 / np.sqrt(self.dim)
for i in np.arange(self.dim)
])
if i < self.n_comps_pos:
self.mu_pos.append(mu)
if i < self.n_comps_neg:
self.mu_neg.append(mu)
#self.mu_pos = [np.zeros(dim) for j in np.arange(self.n_comps_pos)]
#self.mu_neg = [np.zeros(dim) for j in np.arange(self.n_comps_neg)]
self.sig_pos = [np.identity(dim) for j in np.arange(self.n_comps_pos)]
self.sig_neg = [np.identity(dim) for j in np.arange(self.n_comps_neg)]
self.p_pos = dirichlet(np.ones(self.n_comps_pos)).rvs([])
#self.p_neg = dirichlet(np.ones(self.n_comps_neg)).rvs([])
self.p_neg = self.p_pos
#self.changeInfo = {'changed': False, 'positive': True, 'mu': True, 'ix':0, 'oldvalue': self.mu_pos[0]}
self.changeInfo = {'changed': False}
self.alpha = random()
self.quiet = quiet
def log_prior(self):
"""
Compute the log likelihood of a set of SBM parameters
:param x: (m,p,v) tuple
:return:
"""
from scipy.stats import dirichlet
from graphistician.internals.utils import normal_inverse_wishart_log_prob
lp = 0
# Get the log probability of the block probabilities
lp += dirichlet(self.pi).logpdf(self.m)
# Get the prior probability of the Gaussian parameters under NIW prior
for c1 in xrange(self.C):
for c2 in xrange(self.C):
lp += normal_inverse_wishart_log_prob(self._gaussians[c1][c2])
if self.special_case_self_conns:
lp += normal_inverse_wishart_log_prob(self._self_gaussian)
# Get the probability of the block assignments
lp += (np.log(self.m)[self.c]).sum()
return lp
def test_dd_single(self):
import numpy as np
from scipy.stats import dirichlet
np.set_printoptions(precision=2)
samples = dirichlet(alpha=1000 * np.array([0.1, 0.3, 0.6])).rvs(10000)
print("element-wise mean:", samples.mean(axis=0))
print("element-wise standard deviation:", samples.std(axis=0))
print('end')
def dirichlet(G, alpha=1):
cpd = {}
for node in nx.topological_sort(G):
m = G.in_degree(node) + 1
dim = tuple([2] * m)
table = stats.dirichlet(alpha=tuple([alpha] * (2 ** m))).rvs()[0]
table = table.reshape(dim)
cpd[node] = TableCPD(table, [node], list(G.predecessors(node)))
return cpd
def __init__(self, dim, max_comps):
self.dim = dim
self.max_comps = max_comps
self.n_comps_pos = randint(1, max_comps)
self.n_comps_neg = randint(1, max_comps)
self.mu_pos = [
np.array([2 * random() - 1 for i in np.arange(dim)])
for j in np.arange(self.n_comps_pos)
]
self.mu_neg = [
np.array([2 * random() - 1 for i in np.arange(dim)])
for j in np.arange(self.n_comps_neg)
]
self.sig_pos = [spd(dim) for j in np.arange(self.n_comps_pos)]
self.sig_neg = [spd(dim) for j in np.arange(self.n_comps_neg)]
self.p_pos = dirichlet(np.ones(self.n_comps_pos)).rvs([])
self.p_neg = dirichlet(np.ones(self.n_comps_neg)).rvs([])
self.alpha = random()
def gibbs_weight(self):
"""
Get weight vector for each gibbs iteration
:return: weight vector
"""
Nk = self.components.counts[:self.components.K].tolist()
alpha = [Nk[cid] + self.alpha / self.components.K
for cid in range(self.components.K)]
return stats.dirichlet(alpha).rvs(size=1).flatten()
def test_simple_values():
alpha = np.array([1, 1])
d = dirichlet(alpha)
assert_almost_equal(d.mean(), 0.5)
assert_almost_equal(d.var(), 1. / 12.)
b = beta(1, 1)
assert_almost_equal(d.mean(), b.mean())
assert_almost_equal(d.var(), b.var())
def variational_bayesian_inference_double_loop(self,S_outer=0,S_inner=0):
# Initialize approximation of posterior distribution
q_z = np.array([[[1/self.K for k in range(self.K)] for _ in d] for _ in self.docs])
q_theta = np.array([1/K for d in self.docs for _ in range(K)])
q_phi = np.array([1/K for k in range(K) for _ in range(self.V)])
# Derivation variational lower bound
#TODO
# F = np.sum(q_z*q_theta*q_phi*np.log(p_w*p_z)
# Initialize E[n_d_k] and E[n_k_v]
# TODO: is this correct??
E_n_k_v = q_z.sum(axis=0)
# Convergence criterion
# A. difference between variational lower bound in each iteration
# B. the number of iterations
for _o in range(S_outer):
for d,doc in enumerate(doc):
n_d = len(doc)
# Initialize E[n_d_k] = n_d/K
E_n_d_k = np.array(len(doc) / K)
# Absolute Error
# TODO
for _i in range(S_inner):
for i in range(n_d):
# Update q(z_d_i)
q_z = {np.exp(sp.psi(E_n_k_v[v]+self.beta[v])) # K-dimension
/ np.exp(sp.psi(np.sum(E_n_k_v+np.matrix(self.beta).T,axis=0))) # 1-dimension
* np.exp(sp.psi(E_n_d_k[d]+self.alpha)) # K-dimension
/ np.exp(sp.psi(np.sum(E_n_d_k+self.alpha,axis=1)))} #1-dimension
new_q_z = q_z / sum(q_z)
q_z[d][i] = new_q_z
# Update q(theta_d) by (3.90)
#TODO: is this corrct???
q_theta[d] = stats.dirichlet(E_n_d_k[d]+self.alpha)
for k in range(K):
# Update q(phi_k) by (3.96)
# TODO: is this corrct???
q_phi[k] = stats.dirichlet(E_n_k_v[k]+self.beta)
def __init__(self, α: np.ndarray, z: np.ndarray, bor: float):
"""
:param α: sufficient statistics of the posterior Dirichlet density on model/family frequencies
:param z: posterior probabilities for each subject to belong to each model/family
:param bor: Bayesian omnibus risk p(y|H0)/(p(y|H0)+p(y|H1))
"""
self.attribution = z.copy()
self.frequency_mean = dirichlet.mean(α)
self.frequency_var = dirichlet.var(α)
self.exceedance_probability = exceedance_probability(dirichlet(α))
self.protected_exceedance_probability = self.exceedance_probability * (
1 - bor) + bor / len(α) # (7)
def compute_elbo(self, phi, nu, kappa, epsilon, m, L, V, N, gamma_1, gamma_2):
"""
Function compute the evidence lower bound as defined for HRMF-DPCMM From the variational parameters.
:param phi: of shape [N,K]
:param nu: of shape [1, K]
:param kappa: of shape [1, K]
:param epsilon: of shape [1, K]
:param m: of shape [N, d]
:param L: of shape [N, d, d]
:param V: of shape [K, K]
:param N: of shape [1, K]
:param gamma_1: of shape [1, K]
:param gamma_2: of shape [1, K]
:return:
"""
hmrf_term = 0
log_likelihood_term = 0
if self.weight_prior == "Dirichelet distribution":
val = digamma(epsilon) - digamma(np.sum(epsilon))
else:
val = digamma(gamma_1) - digamma(gamma_1 + gamma_2) + cumsum_ex(
digamma(gamma_2) - digamma(gamma_1 + gamma_2))
for n in range(self.N):
for k in range(self.K):
log_likelihood_term += - 0.5 * phi[n, k] * nu[k] * np.trace(np.matmul(L[k,:,:], np.matmul(self.X[n,:].reshape(self.d, 1) - m[k].reshape(self.d, 1),
self.X[n,:].reshape(1, self.d) - m[k].reshape(1, self.d) )) ) \
- 0.5 * self.d * N[k] / kappa[k]
if self.mask[n] == 0:
log_likelihood_term += phi[n,k] * val[k]
for k in range(self.K):
log_likelihood_term += 0.5 * (nu[k] - self.d + N[k]) * (multivar_digamma(nu[k], self.d) + np.log(self.eps + LA.det(L[k, :, :]))) - 0.5 * self.d * nu[k]
for tuple in self.tuples_ml:
hmrf_term += - self.lambda_ * np.sum(np.sum(phi[tuple[0],:].reshape(self.K, 1) * phi[tuple[1],:].reshape(1,self.K) * V))
for k in range(self.K):
log_likelihood_term += wishart(nu[k],L[k,:,:]).entropy() + 0.5*(multivar_digamma(nu[k], self.d) + np.log(self.eps + LA.det(L[k, :, :]))) + 0.5*self.d*np.log(eps + kappa[k]) \
- np.sum(phi[:,k] * np.log(phi[:,k] + eps))
if self.weight_prior != "Dirichelet distribution":
log_likelihood_term += beta(gamma_1[k], gamma_2[k]).entropy()
if self.weight_prior == "Dirichelet distribution":
log_likelihood_term += dirichlet(epsilon).entropy()
elbo = log_likelihood_term + hmrf_term
return elbo/self.N, log_likelihood_term, hmrf_term
def __init__(self, dist_params):
'''
Creates Dirichlet distribution with parameter `dist_params`.
e.x.,dist_params={
'mix_coef':[0.5,0.5],
'dir1_params':[2,3,19],
'dir2_params':[17,10,7]
}
'''
from scipy.stats import dirichlet
self.mix_coef = dist_params.pop('mix_coef')
self.K = len(self.mix_coef)
self.dir_mixtures = [dirichlet(dir_param) for dir_param in dist_params.values()]
def sample_tau(state):
# "Escobar and West's auxiliary variable method (1995)," https://lists.cs.princeton.edu/pipermail/topic-models/2011-October/001629.html
# http://bit.ly/1FelVcL
mk = get_mk(state)
state['T'] = sum(mk.values()) - state['gamma']
assert state['T'] > 0
topics, mk_vals = zip(*mk.items())
new_tau = dirichlet(mk_vals).rvs()[0]
state['tau'] = {}
for topic, tau_i in zip(topics, new_tau):
state['tau'][topic] = tau_i
assert set(state['tau'].keys()) - state['used_topics'] == set([-1])
return state
def get_dirichlet_mle(x):
"""
Get maximum likelihood estimation for dirichlet concentration parameters
:param x: Data array of size nxp where n is the number of observations and p is the dimensionality of the
dirichlet distribution to estimate
:return: Dirichlet distribution (with `alpha` parameter set to MLE inferred from given data)
"""
assert len(x.shape) == 2, 'Data array must be two dimensional'
assert np.allclose(x.sum(axis=1), 1), 'Sum of observations across rows must equal 1'
from ml.bayesian.dirichlet import dirichlet
alpha = dirichlet.mle(x)
return stats.dirichlet(alpha)
def get_dirichlet_multinomial_posterior(x, alpha):
"""
Return posterior dirichlet distribution with dirichlet prior and multinomial likelihood
Posterior for dirichlet distribution with parameters equal to (alpha1 + x1, alpha2 + x2, ..., alphap + xp)
where p is the number of categories (i.e. number of columns in x)
:param x: Integer array where index indicates category (must have length > 1)
:param alpha: Concentration parameter for dirichlet prior; can be scalar or array of size len(x)
:return: Dirichlet distribution
"""
assert len(x) > 1, 'Number of categories for dirichlet/multinomial model must be > 1'
return stats.dirichlet(x + alpha)
def set_result(self, successes, trials):
assert len(successes) == len(trials)
assert len(successes) == len(self.variants)
self.posteriors = [None] * len(successes)
for i, (conv, vis,
pri) in enumerate(zip(successes, trials, self.priors)):
obs = conv + [vis - sum(conv)]
self.posteriors[i] = dirichlet(pri + obs)
self.conversions = successes
self.visitors = trials
def test_K_and_K_minus_1_calls_equal():
# Test that calls with K and K-1 entries yield the same results.
np.random.seed(2846)
n = np.random.randint(1, 32)
alpha = np.random.uniform(10e-10, 100, n)
d = dirichlet(alpha)
num_tests = 10
for i in range(num_tests):
x = np.random.uniform(10e-10, 100, n)
x /= np.sum(x)
assert_almost_equal(d.pdf(x[:-1]), d.pdf(x))
def updateMixtureWeight(Z, weightPrior):
'''
Z: length n, array like component indicator
weightPrior: length K, array like prior (for the Dirichlet prior)
'''
unique, counts = np.unique(Z, return_counts=True)
mixtureCounts = dict(zip(unique, counts))
alpha = weightPrior
for k in mixtureCounts:
alpha[k] += mixtureCounts[k]
return dirichlet(alpha).rvs()[0]
def sample_hist(dims: SomDims,
data: Optional[Array] = None,
**kwargs) -> Array:
"""Sample sum-normalized histograms.
Args:
dims: Dimensions of SOM.
data: Input data set.
Returns:
Two-dimensional array in which each row is a historgram.
"""
n_rows, n_cols, n_feats = dims
return _stats.dirichlet(np.ones(n_feats)).rvs(n_rows * n_cols)
def updateProbs(C, probPrior):
'''
C: length N, array like type indicator for all points (value in 0,1,2)
0=outside, 1=MF, 2=FM
probPrior: length 3, array like prior (for the Dirichlet prior)
'''
unique, counts = np.unique(C, return_counts=True)
typeCounts = dict(zip(unique, counts))
alpha = copy(probPrior)
for k in typeCounts:
alpha[k] += typeCounts[k]
return dirichlet(alpha).rvs()[0]
def test_2D_dirichlet_is_beta():
np.random.seed(2846)
alpha = np.random.uniform(10e-10, 100, 2)
d = dirichlet(alpha)
b = beta(alpha[0], alpha[1])
num_tests = 10
for i in range(num_tests):
x = np.random.uniform(10e-10, 100, 2)
x /= np.sum(x)
assert_almost_equal(b.pdf(x), d.pdf([x]))
assert_almost_equal(b.mean(), d.mean()[0])
assert_almost_equal(b.var(), d.var()[0])
def test_frozen_dirichlet():
np.random.seed(2846)
n = np.random.randint(1, 32)
alpha = np.random.uniform(10e-10, 100, n)
d = dirichlet(alpha)
assert_equal(d.var(), dirichlet.var(alpha))
assert_equal(d.mean(), dirichlet.mean(alpha))
assert_equal(d.entropy(), dirichlet.entropy(alpha))
num_tests = 10
for i in range(num_tests):
x = np.random.uniform(10e-10, 100, n)
x /= np.sum(x)
assert_equal(d.pdf(x[:-1]), dirichlet.pdf(x[:-1], alpha))
assert_equal(d.logpdf(x[:-1]), dirichlet.logpdf(x[:-1], alpha))
def log_prior(self):
"""
Compute the log likelihood of a set of SBM parameters
:param x: (m,p,v) tuple
:return:
"""
from scipy.stats import dirichlet, beta
lp = 0
lp += dirichlet(self.pi).logpdf(self.m)
lp += beta(self.tau1 * np.ones((self.C, self.C)),
self.tau0 * np.ones((self.C, self.C))).logpdf(self.p).sum()
if self.special_case_self_conns:
lp += beta(self.tau1, self.tau0).logpdf(self.p_self)
lp += (np.log(self.m)[self.c]).sum()
return lp
def prob_locked(experiences, joint_pos, p_same, alpha_prior, model_prior,
model_post=None):
"""
Computes the Dirichlet distribution over the possible joint state
distributions.
:param experiences: The experiences so far
:param joint_pos: The joint positions of all joints (array-like)
:param p_same: The probability of two joint states being in the same
segment. (I.e. no change point in between)
:param alpha_prior: The prior over the different joint locking states
:param model_prior: The prior over the different joint dependency models
:return: A Dirichlet distribution object giving the probability for the
different locking state distributions
"""
alpha = np.array(alpha_prior)
if model_post is None:
model_post = model_posterior(experiences, p_same, alpha_prior,
model_prior)
for joint_idx, pos in enumerate(joint_pos):
c = create_alpha(pos, experiences,
joint_idx,
p_same[joint_idx])
a = model_post[joint_idx] * c
if np.min(a) < 0:
print("c = {}".format(c))
print("mp = {}".format(model_post[joint_idx]))
print("a = c * mp = {}".format(a))
alpha += a
if np.min(alpha) <= 0:
print("alpha_prior = {}".format(alpha_prior))
print("alpha = {}".format(alpha))
d = dirichlet(alpha)
return d
def __init__(self, alpha):
self.alpha = alpha
self._dist = stats.dirichlet(alpha)
self.dim = len(alpha)
def stats(scale_factor, G0=[.2, .2, .6], N=10000):
samples = dirichlet(alpha = scale_factor * np.array(G0)).rvs(N) #rvs:draw random samples from this distribution.
print(" alpha:", scale_factor)
print(" element-wise mean:", samples.mean(axis=0)) #sample element junzhi
print("element-wise standard deviation:", samples.std(axis=0)) #biao zhun cha
print()
def draw_pi(alpha):
return sts.dirichlet(alpha).rvs()[0]
import matplotlib.pyplot as plt
import pickle
alpha = [1,1,2]
mu = [0.05,0.05,0.95] # constraint must add to 1
def dirichlet(mu, alpha):
mu = np.array(mu)
alpha = np.array(alpha)
product = np.product(mu ** (alpha - 1))
normaliser = gamma(alpha.sum())/np.product(gamma(alpha))
result = product * normaliser
return result
print(dirichlet(mu, alpha))
print(dirichlet(mu, alpha))
print(np.random.dirichlet([1,1,100]))
#plt.plot()
x = np.linspace(0,4,100)
y = gamma(x+2) - gamma(x)
y = np.log(x)
#plt.plot(x, y)
#plt.draw()
def create_reward(a):
e = np.random.rand()/100
p6 = np.dot(p1, m_0)
p7 = {i: p5[i]+p6 for i in xrange(k)}
return {i: np.dot(p2[i], p7[i]) for i in xrange(k)}
def draw_mu_k(mk_dict, inv_vk_dict,k):
return {i:sts.multivariate_normal(mk_dict[i], np.linalg.inv(inv_vk_dict[i])).rvs() for i in xrange(k)}
#Constants
N = 6 # dimension of the MVN
J = 200 # number of data points
K = 3 #number of MVN distributions
#Bulding test data
true_pi = sts.dirichlet([3,6,9]).rvs()
s1 = np.random.rand(6,6)*np.random.uniform(0,30)
s1 = np.dot(s1, s1.T)
s2 = np.random.rand(6,6)*np.random.uniform(0,30)
s2 = np.dot(s1, s1.T)
s3 = np.random.rand(6,6)*np.random.uniform(0,30)
s3 = np.dot(s1, s1.T)
true_g1 =sts.multivariate_normal(np.random.uniform(-100,100,6),s1)
true_g2 =sts.multivariate_normal(np.random.uniform(-100,100,6),s2)
true_g3 =sts.multivariate_normal(np.random.uniform(-100,100,6),s3)
true_z = np.random.multinomial(J, true_pi[0])
def draw_pi(pi_0, nk_dict, k):
alpha = np.array([nk_dict[i] for i in xrange(k)])
return sts.dirichlet(alpha+pi_0).rvs()