def uncollapsed_likelihood(self, X, parameters):
"""
Calculates the score of the data X under this component model with mean
mu and precision kappa.
Inputs:
X: A column of data (numpy)
parameters: a dict with the following keys
mu: the Von Mises mean
kappa: the precision of the Von Mises
"""
check_data_type_column_data(X)
check_model_params_dict(parameters)
mu = parameters['mu']
kappa = parameters['kappa']
N = float(len(X))
hypers = self.get_hypers()
a = hypers['a']
b = hypers['b']
kappa = hypers['kappa']
sum_err = numpy.sum((mu-X)**2.0)
log_likelihood = self.log_likelihood(X, {'mu':mu, 'kappa':rho})
log_prior_mu = vonmises.logpdf(b, a)
log_p = log_likelihood + log_prior_mu + log_prior_rho
return log_p
def uncollapsed_likelihood(self, X, parameters):
"""
Calculates the score of the data X under this component model with mean
mu and precision kappa.
Inputs:
X: A column of data (numpy)
parameters: a dict with the following keys
mu: the Von Mises mean
kappa: the precision of the Von Mises
"""
check_data_type_column_data(X)
check_model_params_dict(parameters)
mu = parameters['mu']
kappa = parameters['kappa']
N = float(len(X))
hypers = self.get_hypers()
a = hypers['a']
b = hypers['b']
kappa = hypers['kappa']
sum_err = numpy.sum((mu - X)**2.0)
log_likelihood = self.log_likelihood(X, {'mu': mu, 'kappa': rho})
log_prior_mu = vonmises.logpdf(b, a)
log_p = log_likelihood + log_prior_mu + log_prior_rho
return log_p
def neg_log_likelihood(self, coeff, obsTime, shiftStart, shiftEnd):
location, kappa = np.abs(coeff)
return (
-np.sum(vonmises.logpdf(obsTime, kappa, location, 12 / np.pi)) +
np.sum(
np.log(
self.interval_probability(shiftStart, shiftEnd, location,
kappa))))
def test_vonmises_logpdf(T=100, K=4, D=10):
# Test single datapoint log pdf
x = npr.vonmises(0, 1, size=(T, D))
mus = npr.randn(K, D)
kappas = np.exp(npr.randn(K, D))
ll1 = vonmises_logpdf(x[:, None, :], mus, kappas)
ll2 = np.sum(vonmises.logpdf(x[:, None, :],
kappas[None, :, :],
loc=mus[None, :, :]),
axis=-1)
assert np.allclose(ll1, ll2)
def log_pdf(X, parameters):
"""
Calculates the pdf for each point in the data X given mean mu and
precision kappa.
Inputs:
X: a column of data (numpy)
parameters: a dict with the following keys
mu: the Von Mises mean
kappa: the precision of the Von Mises
"""
check_data_type_column_data(X)
check_model_params_dict(parameters)
return vonmises.logpdf(X--math.pi, parameters['kappa'],loc=parameters['mu']-math.pi)
def test_vonmises_logpdf(T=100, K=4, D=10):
"""
NOTE: Skipping this test until the scipy special functions
make it into the release version of autograd.
"""
# Test single datapoint log pdf
x = npr.vonmises(0, 1, size=(T, D))
mus = npr.randn(K, D)
kappas = np.exp(npr.randn(K, D))
ll1 = vonmises_logpdf(x[:, None, :], mus, kappas)
ll2 = np.sum(vonmises.logpdf(x[:, None, :],
kappas[None, :, :],
loc=mus[None, :, :]),
axis=-1)
assert np.allclose(ll1, ll2)
def log_likelihood(X, parameters):
"""
Calculates the log likelihood of the data X given mean mu and precision
kappa.
Inputs:
X: a column of data (numpy)
parameters: a dict with the following keys
mu: the Von Mises mean
kappa: the precision of the Von Mises
"""
check_data_type_column_data(X)
check_model_params_dict(parameters)
log_likelihood = numpy.sum(vonmises.logpdf(X-math.pi, parameters['mu']-math.pi, parameters['kappa']))
return log_likelihood
def log_pdf(X, parameters):
"""
Calculates the pdf for each point in the data X given mean mu and
precision kappa.
Inputs:
X: a column of data (numpy)
parameters: a dict with the following keys
mu: the Von Mises mean
kappa: the precision of the Von Mises
"""
check_data_type_column_data(X)
check_model_params_dict(parameters)
return vonmises.logpdf(X - -math.pi,
parameters['kappa'],
loc=parameters['mu'] - math.pi)
def log_likelihood(X, parameters):
"""
Calculates the log likelihood of the data X given mean mu and precision
kappa.
Inputs:
X: a column of data (numpy)
parameters: a dict with the following keys
mu: the Von Mises mean
kappa: the precision of the Von Mises
"""
check_data_type_column_data(X)
check_model_params_dict(parameters)
log_likelihood = numpy.sum(
vonmises.logpdf(X - math.pi, parameters['mu'] - math.pi,
parameters['kappa']))
return log_likelihood
print(
timeit("lp(a, kappa, loc, scale)",
number=1000,
globals={
**globals(),
**locals()
}))
print(
timeit("vonmises_logpdf(a, kappa, loc, scale)",
number=1000,
globals={
**globals(),
**locals()
}))
b1 = vonmises.logpdf(a, kappa, loc, scale)
b2 = vonmises_logpdf(a, kappa, loc, scale)
print(a)
print(b1)
print(b2)
print(np.abs(b1 - b2))
sys.exit()
np.random.seed()
x = np.arange(1, 10 + 1)
d = np.random.choice(x, 25, replace=True)
y = np.cumsum(np.ones(x.size) / x.size)
x = np.arange(16)
