def gen(alpha, beta, name):
"""Generate fixture data and write to file.
# Arguments
* `alpha`: first shape parameter
* `alpha`: second shape parameter
* `name::str`: output filename
# Examples
``` python
python> alpha = random_sample( 100 ) * 10
python> beta = random_sample( 100 ) * 10
python> gen(alpha, beta, './data.json')
```
"""
dist = betaprime(alpha, beta)
kurtosis = dist.stats(moments="k")
# Store data to be written to file as a dictionary:
data = {
"alpha": alpha.tolist(),
"beta": beta.tolist(),
"expected": kurtosis.tolist()
}
# Based on the script directory, create an output filepath:
filepath = os.path.join(DIR, name)
# Write the data to the output filepath as JSON:
with open(filepath, "w") as outfile:
json.dump(data, outfile)
def get_limits(sigma, M, N=1):
"""
Return the limits on the spectral kurtosis value to exclude the specified confidence
interval in sigma using a Pearson Type VI distribution (betaprime in scipy.stats world).
The return value is a two-element tuple of lower limit, upper limit.
.. note::
This corresponds to Section 3.1 in Nita & Gary (2010, MNRAS 406, L60)
"""
# Adjust the NumPy error levels so that we know when ppf() may be suspect
errLevels = numpy.geterr()
numpy.seterr(all='raise')
# Convert the sigma to a fraction for the high and low clip levels
percentClip = (1.0 - erf(sigma / numpy.sqrt(2))) / 2.0
# Build the Pearson type VI distribution function - parameters then instance
a = _alpha(M, N)
b = _beta(M, N)
d = _delta(M, N)
rv = betaprime(a, b, loc=d)
# Try to get a realistic lower limit, giving up if we hit an overflow error
try:
lower = rv.ppf(percentClip)
except FloatingPointError:
lower = mean(M, N) - sigma * std(M, N)
# Try to get a realistic upper limit, giving up if we hit an overflow error
try:
upper = rv.ppf(1.0 - percentClip)
except FloatingPointError:
upper = mean(M, N) + sigma * std(M, N)
# Restore the NumPy error levels
numpy.seterr(**errLevels)
return lower, upper
mean, var, skew, kurt = betaprime.stats(a, b, moments='mvsk')
# Display the probability density function (``pdf``):
x = np.linspace(betaprime.ppf(0.01, a, b),
betaprime.ppf(0.99, a, b), 100)
ax.plot(x, betaprime.pdf(x, a, b),
'r-', lw=5, alpha=0.6, label='betaprime pdf')
# Alternatively, the distribution object can be called (as a function)
# to fix the shape, location and scale parameters. This returns a "frozen"
# RV object holding the given parameters fixed.
# Freeze the distribution and display the frozen ``pdf``:
rv = betaprime(a, b)
ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
# Check accuracy of ``cdf`` and ``ppf``:
vals = betaprime.ppf([0.001, 0.5, 0.999], a, b)
np.allclose([0.001, 0.5, 0.999], betaprime.cdf(vals, a, b))
# True
# Generate random numbers:
r = betaprime.rvs(a, b, size=1000)
# And compare the histogram:
ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
def test_logpdf(self):
alpha, beta = 267, 1472
x = np.array([0.2, 0.5, 0.6])
b = stats.betaprime(alpha, beta)
assert_(np.isfinite(b.logpdf(x)).all())
assert_allclose(b.pdf(x), np.exp(b.logpdf(x)))
def geweke_test():
"""
Create a discrete time Hawkes model and generate from it.
:return:
"""
T = 50
dt = 1.0
dt_max = 3.0
network_hypers = {
'C': 1,
'p': 0.5,
'kappa': 3.0,
'alpha': 3.0,
'beta': 1.0 / 20.0
}
model = DiscreteTimeNetworkHawkesModelSpikeAndSlab(
K=1, dt=dt, dt_max=dt_max, network_hypers=network_hypers)
model.generate(T=T)
# Gibbs sample and then generate new data
N_samples = 10000
samples = []
lps = []
for itr in xrange(N_samples):
if itr % 10 == 0:
print "Iteration: ", itr
# Resample the model
model.resample_model()
samples.append(model.copy_sample())
lps.append(model.log_probability())
# Geweke step
model.data_list.pop()
model.generate(T=T)
# Compute sample statistics for second half of samples
A_samples = np.array([s.weight_model.A for s in samples])
W_samples = np.array([s.weight_model.W for s in samples])
g_samples = np.array([s.impulse_model.g for s in samples])
lambda0_samples = np.array([s.bias_model.lambda0 for s in samples])
c_samples = np.array([s.network.c for s in samples])
p_samples = np.array([s.network.p for s in samples])
v_samples = np.array([s.network.v for s in samples])
lps = np.array(lps)
offset = 0
A_mean = A_samples[offset:, ...].mean(axis=0)
W_mean = W_samples[offset:, ...].mean(axis=0)
g_mean = g_samples[offset:, ...].mean(axis=0)
lambda0_mean = lambda0_samples[offset:, ...].mean(axis=0)
print "A mean: ", A_mean
print "W mean: ", W_mean
print "g mean: ", g_mean
print "lambda0 mean: ", lambda0_mean
# Plot the log probability over iterations
plt.figure()
plt.plot(np.arange(N_samples), lps)
plt.xlabel("Iteration")
plt.ylabel("Log probability")
# Plot the histogram of bias samples
plt.figure()
p_lmbda0 = gamma(model.bias_model.alpha, scale=1. / model.bias_model.beta)
_, bins, _ = plt.hist(lambda0_samples[:, 0],
bins=20,
alpha=0.5,
normed=True)
bincenters = 0.5 * (bins[1:] + bins[:-1])
plt.plot(bincenters, p_lmbda0.pdf(bincenters), 'r--', linewidth=1)
plt.xlabel('lam0')
plt.ylabel('p(lam0)')
print "Expected p(A): ", model.network.P
print "Empirical p(A): ", A_samples.mean(axis=0)
# Plot the histogram of weight samples
plt.figure()
Aeq1 = A_samples[:, 0, 0] == 1
# p_W1 = gamma(model.network.kappa, scale=1./model.network.v[0,0])
# The marginal distribution of W under a gamma prior on the scale
# is a beta prime distribution
p_W1 = betaprime(model.network.kappa,
model.network.alpha,
scale=model.network.beta)
_, bins, _ = plt.hist(W_samples[Aeq1, 0, 0],
bins=20,
alpha=0.5,
normed=True)
bincenters = 0.5 * (bins[1:] + bins[:-1])
plt.plot(bincenters, p_W1.pdf(bincenters), 'r--', linewidth=1)
plt.xlabel('W')
plt.ylabel('p(W | A=1)')
# Plot the histogram of impulse samples
plt.figure()
for b in range(model.B):
plt.subplot(1, model.B, b + 1)
a = model.impulse_model.gamma[b]
b = model.impulse_model.gamma.sum() - a
p_beta11b = beta(a, b)
_, bins, _ = plt.hist(g_samples[:, 0, 0, b],
bins=20,
alpha=0.5,
normed=True)
bincenters = 0.5 * (bins[1:] + bins[:-1])
plt.plot(bincenters, p_beta11b.pdf(bincenters), 'r--', linewidth=1)
plt.xlabel('g_%d' % b)
plt.ylabel('p(g_%d)' % b)
# Plot the histogram of weight scale
plt.figure()
for c1 in range(model.C):
for c2 in range(model.C):
plt.subplot(model.C, model.C, 1 + c1 * model.C + c2)
p_v = gamma(model.network.alpha, scale=1. / model.network.beta)
_, bins, _ = plt.hist(v_samples[:, c1, c2],
bins=20,
alpha=0.5,
normed=True)
bincenters = 0.5 * (bins[1:] + bins[:-1])
plt.plot(bincenters, p_v.pdf(bincenters), 'r--', linewidth=1)
plt.xlabel('v_{%d,%d}' % (c1, c2))
plt.ylabel('p(v)')
plt.show()
def Phi_linf(self, prob):
d = self.dim
a = self.a
g = betaprime(d, a + 1 - d).cdf
ig = betaprime(d, a - d).ppf
return g(ig(2 * prob)) * (a - d) / 2
def __init__(self, dim, sigma=None, lambd=None, a=None, device='cpu'):
self.a = a
if a is None:
raise ValueError('Parameter `a` is required.')
super().__init__(dim, sigma, lambd, device)
self.beta_dist = betaprime(dim, a - self.dim)
41.404620910360876)
drivingdistance_model_dict['ncx2'] = st.ncx2(0.30254190304723211,
1.1286538320791935,
14.999999999999998,
8.7361471573932192)
drivingdistance_model_dict['chi'] = st.chi(0.47882729877571095,
14.999999999999996,
44.218301183844645)
drivingdistance_model_dict['recipinvgauss'] = st.recipinvgauss(
2447246.0546641815, 14.999999999994969, 31.072009722580802)
drivingdistance_model_dict['f'] = st.f(0.85798489720127036, 4.1904554804436929,
14.99998319939356, 21.366492843433996)
drivingduration_model_dict = ct.OrderedDict()
drivingduration_model_dict['betaprime'] = st.betaprime(2.576282082814398,
9.7247974165209996,
9.1193851632305201,
261.3457987967214)
drivingduration_model_dict['exponweib'] = st.exponweib(2.6443841639764942,
0.89242254172118096,
10.603640861374947,
40.28556311444698)
drivingduration_model_dict['gengamma'] = st.gengamma(4.8743515108339581,
0.61806208678747043,
9.4649293818479716,
5.431576919220225)
drivingduration_model_dict['recipinvgauss'] = st.recipinvgauss(
0.499908918842556, 0.78319699707613699, 28.725450197674746)
drivingduration_model_dict['f'] = st.f(9.8757694313677113, 12.347442183821462,
0.051160749890587665,
73.072591767722287)
def test_logpdf(self):
alpha, beta = 267, 1472
x = np.array([0.2, 0.5, 0.6])
b = stats.betaprime(alpha, beta)
assert_(np.isfinite(b.logpdf(x)).all())
assert_allclose(b.pdf(x), np.exp(b.logpdf(x)))
mlpParams = {
'hidden_layer_sizes': [(100, ), (200, 200), (500, 500)],
'activation': ['identity', 'logistic', 'tanh', 'relu'],
'solver': ['lbfgs', 'sgd', 'adam'],
'alpha': expon(scale=.0005, loc=.0001),
'learning_rate': ['constant', 'invscaling', 'adaptive'],
'power_t': beta(a=2, b=2),
'momentum': uniform(),
'early_stopping': [True],
'beta_1': beta(a=2, b=.5),
'beta_2': beta(a=2, b=.5),
'max_iter': [500]
}
passiveAggParams = {
'C': betaprime(a=5, b=5), #list(range(0.1,3,0.3)),
'n_iter': list(range(5, 10)),
'loss': ['hinge', 'squared_hinge']
}
sgdParams = {
'loss': [
'hinge', 'log', 'modified_huber', 'squared_hinge', 'perceptron',
'squared_loss', 'huber', 'epsilon_insensitive',
'squared_epsilon_insensitive'
]
}
baggingParams = {
'n_estimators': [5, 10, 20],
'base_estimator': [None], ####################
def all_dists():
# dists param were taken from scipy.stats official
# documentaion examples
# Total - 89
return {
"alpha":
stats.alpha(a=3.57, loc=0.0, scale=1.0),
"anglit":
stats.anglit(loc=0.0, scale=1.0),
"arcsine":
stats.arcsine(loc=0.0, scale=1.0),
"beta":
stats.beta(a=2.31, b=0.627, loc=0.0, scale=1.0),
"betaprime":
stats.betaprime(a=5, b=6, loc=0.0, scale=1.0),
"bradford":
stats.bradford(c=0.299, loc=0.0, scale=1.0),
"burr":
stats.burr(c=10.5, d=4.3, loc=0.0, scale=1.0),
"cauchy":
stats.cauchy(loc=0.0, scale=1.0),
"chi":
stats.chi(df=78, loc=0.0, scale=1.0),
"chi2":
stats.chi2(df=55, loc=0.0, scale=1.0),
"cosine":
stats.cosine(loc=0.0, scale=1.0),
"dgamma":
stats.dgamma(a=1.1, loc=0.0, scale=1.0),
"dweibull":
stats.dweibull(c=2.07, loc=0.0, scale=1.0),
"erlang":
stats.erlang(a=2, loc=0.0, scale=1.0),
"expon":
stats.expon(loc=0.0, scale=1.0),
"exponnorm":
stats.exponnorm(K=1.5, loc=0.0, scale=1.0),
"exponweib":
stats.exponweib(a=2.89, c=1.95, loc=0.0, scale=1.0),
"exponpow":
stats.exponpow(b=2.7, loc=0.0, scale=1.0),
"f":
stats.f(dfn=29, dfd=18, loc=0.0, scale=1.0),
"fatiguelife":
stats.fatiguelife(c=29, loc=0.0, scale=1.0),
"fisk":
stats.fisk(c=3.09, loc=0.0, scale=1.0),
"foldcauchy":
stats.foldcauchy(c=4.72, loc=0.0, scale=1.0),
"foldnorm":
stats.foldnorm(c=1.95, loc=0.0, scale=1.0),
# "frechet_r": stats.frechet_r(c=1.89, loc=0.0, scale=1.0),
# "frechet_l": stats.frechet_l(c=3.63, loc=0.0, scale=1.0),
"genlogistic":
stats.genlogistic(c=0.412, loc=0.0, scale=1.0),
"genpareto":
stats.genpareto(c=0.1, loc=0.0, scale=1.0),
"gennorm":
stats.gennorm(beta=1.3, loc=0.0, scale=1.0),
"genexpon":
stats.genexpon(a=9.13, b=16.2, c=3.28, loc=0.0, scale=1.0),
"genextreme":
stats.genextreme(c=-0.1, loc=0.0, scale=1.0),
"gausshyper":
stats.gausshyper(a=13.8, b=3.12, c=2.51, z=5.18, loc=0.0, scale=1.0),
"gamma":
stats.gamma(a=1.99, loc=0.0, scale=1.0),
"gengamma":
stats.gengamma(a=4.42, c=-3.12, loc=0.0, scale=1.0),
"genhalflogistic":
stats.genhalflogistic(c=0.773, loc=0.0, scale=1.0),
"gilbrat":
stats.gilbrat(loc=0.0, scale=1.0),
"gompertz":
stats.gompertz(c=0.947, loc=0.0, scale=1.0),
"gumbel_r":
stats.gumbel_r(loc=0.0, scale=1.0),
"gumbel_l":
stats.gumbel_l(loc=0.0, scale=1.0),
"halfcauchy":
stats.halfcauchy(loc=0.0, scale=1.0),
"halflogistic":
stats.halflogistic(loc=0.0, scale=1.0),
"halfnorm":
stats.halfnorm(loc=0.0, scale=1.0),
"halfgennorm":
stats.halfgennorm(beta=0.675, loc=0.0, scale=1.0),
"hypsecant":
stats.hypsecant(loc=0.0, scale=1.0),
"invgamma":
stats.invgamma(a=4.07, loc=0.0, scale=1.0),
"invgauss":
stats.invgauss(mu=0.145, loc=0.0, scale=1.0),
"invweibull":
stats.invweibull(c=10.6, loc=0.0, scale=1.0),
"johnsonsb":
stats.johnsonsb(a=4.32, b=3.18, loc=0.0, scale=1.0),
"johnsonsu":
stats.johnsonsu(a=2.55, b=2.25, loc=0.0, scale=1.0),
"ksone":
stats.ksone(n=1e03, loc=0.0, scale=1.0),
"kstwobign":
stats.kstwobign(loc=0.0, scale=1.0),
"laplace":
stats.laplace(loc=0.0, scale=1.0),
"levy":
stats.levy(loc=0.0, scale=1.0),
"levy_l":
stats.levy_l(loc=0.0, scale=1.0),
"levy_stable":
stats.levy_stable(alpha=0.357, beta=-0.675, loc=0.0, scale=1.0),
"logistic":
stats.logistic(loc=0.0, scale=1.0),
"loggamma":
stats.loggamma(c=0.414, loc=0.0, scale=1.0),
"loglaplace":
stats.loglaplace(c=3.25, loc=0.0, scale=1.0),
"lognorm":
stats.lognorm(s=0.954, loc=0.0, scale=1.0),
"lomax":
stats.lomax(c=1.88, loc=0.0, scale=1.0),
"maxwell":
stats.maxwell(loc=0.0, scale=1.0),
"mielke":
stats.mielke(k=10.4, s=3.6, loc=0.0, scale=1.0),
"nakagami":
stats.nakagami(nu=4.97, loc=0.0, scale=1.0),
"ncx2":
stats.ncx2(df=21, nc=1.06, loc=0.0, scale=1.0),
"ncf":
stats.ncf(dfn=27, dfd=27, nc=0.416, loc=0.0, scale=1.0),
"nct":
stats.nct(df=14, nc=0.24, loc=0.0, scale=1.0),
"norm":
stats.norm(loc=0.0, scale=1.0),
"pareto":
stats.pareto(b=2.62, loc=0.0, scale=1.0),
"pearson3":
stats.pearson3(skew=0.1, loc=0.0, scale=1.0),
"powerlaw":
stats.powerlaw(a=1.66, loc=0.0, scale=1.0),
"powerlognorm":
stats.powerlognorm(c=2.14, s=0.446, loc=0.0, scale=1.0),
"powernorm":
stats.powernorm(c=4.45, loc=0.0, scale=1.0),
"rdist":
stats.rdist(c=0.9, loc=0.0, scale=1.0),
"reciprocal":
stats.reciprocal(a=0.00623, b=1.01, loc=0.0, scale=1.0),
"rayleigh":
stats.rayleigh(loc=0.0, scale=1.0),
"rice":
stats.rice(b=0.775, loc=0.0, scale=1.0),
"recipinvgauss":
stats.recipinvgauss(mu=0.63, loc=0.0, scale=1.0),
"semicircular":
stats.semicircular(loc=0.0, scale=1.0),
"t":
stats.t(df=2.74, loc=0.0, scale=1.0),
"triang":
stats.triang(c=0.158, loc=0.0, scale=1.0),
"truncexpon":
stats.truncexpon(b=4.69, loc=0.0, scale=1.0),
"truncnorm":
stats.truncnorm(a=0.1, b=2, loc=0.0, scale=1.0),
"tukeylambda":
stats.tukeylambda(lam=3.13, loc=0.0, scale=1.0),
"uniform":
stats.uniform(loc=0.0, scale=1.0),
"vonmises":
stats.vonmises(kappa=3.99, loc=0.0, scale=1.0),
"vonmises_line":
stats.vonmises_line(kappa=3.99, loc=0.0, scale=1.0),
"wald":
stats.wald(loc=0.0, scale=1.0),
"weibull_min":
stats.weibull_min(c=1.79, loc=0.0, scale=1.0),
"weibull_max":
stats.weibull_max(c=2.87, loc=0.0, scale=1.0),
"wrapcauchy":
stats.wrapcauchy(c=0.0311, loc=0.0, scale=1.0),
}
