def generate_sample(self, initial_pos, num_samples, stepsize=None):
"""
Returns a generator type object whose each iteration yields a sample
Parameters
----------
initial_pos: A 1d array like object
Vector representing values of parameter position, the starting
state in markov chain.
num_samples: int
Number of samples to be generated
stepsize: float , defaults to None
The stepsize for proposing new values of position and momentum in simulate_dynamics
If None, then will be chosen suitably
Returns
-------
generator: yielding a numpy.array type object for a sample
Examples
---------
>>> from ProbabilityModel.sampling import NoUTurnSampler as NUTS, GradLogPDFGaussian
>>> from ProbabilityModel.factors.continuous import GaussianDistribution as JGD
>>> import numpy as np
>>> mean = np.array([11, -6])
>>> covariance = np.array([[0.7, 0.2], [0.2, 14]])
>>> model = JGD(['x', 'y'], mean, covariance)
>>> sampler = NUTS(model=model, grad_log_pdf=GradLogPDFGaussian)
>>> samples = sampler.generate_sample(initial_pos=np.array([1, 1]), num_samples=10, stepsize=0.4)
>>> samples = np.array([sample for sample in samples])
>>> samples
array([[ 10.26357538, 0.10062725],
[ 12.70600336, 0.63392499],
[ 10.95523217, -0.62079273],
[ 10.66263031, -4.08135962],
[ 10.59255762, -8.48085076],
[ 9.99860242, -9.47096032],
[ 10.5733564 , -9.83504745],
[ 11.51302059, -9.49919523],
[ 11.31892143, -8.5873259 ],
[ 11.29008667, -0.43809674]])
"""
initial_pos = _check_1d_array_object(initial_pos, "initial_pos")
_check_length_equal(initial_pos, self.model.variables, "initial_pos",
"model.variables")
if stepsize is None:
stepsize = self._find_reasonable_stepsize(initial_pos)
position_m = initial_pos
for _ in range(0, num_samples):
position_m = self._sample(position_m, stepsize)
yield position_m
def __init__(self, variable_assignments, model):
self.variable_assignments = _check_1d_array_object(
variable_assignments, "variable_assignments")
_check_length_equal(
variable_assignments,
model.variables,
"variable_assignments",
"model.variables",
)
self.model = model
# The gradient log of probability distribution at position
self.grad_log = None
# The gradient log of probability distribution at position
self.log_pdf = None
def __init__(self,
model,
position,
momentum,
stepsize,
grad_log_pdf,
grad_log_position=None):
position = _check_1d_array_object(position, "position")
momentum = _check_1d_array_object(momentum, "momentum")
if not issubclass(grad_log_pdf, BaseGradLogPDF):
raise TypeError(
"grad_log_pdf must be an instance" +
" of ProbabilityModel.inference.continuous.base.BaseGradLogPDF"
)
_check_length_equal(position, momentum, "position", "momentum")
_check_length_equal(position, model.variables, "position",
"model.variables")
if grad_log_position is None:
grad_log_position, _ = grad_log_pdf(position,
model).get_gradient_log_pdf()
else:
grad_log_positon = _check_1d_array_object(grad_log_position,
"grad_log_position")
_check_length_equal(grad_log_position, position,
"grad_log_position", "position")
self.position = position
self.momentum = momentum
self.stepsize = stepsize
self.model = model
self.grad_log_pdf = grad_log_pdf
self.grad_log_position = grad_log_position
# new_position is the new proposed position, new_momentum is the new proposed momentum, new_grad_lop
# is the value of grad log at new_position
self.new_position = self.new_momentum = self.new_grad_logp = None
def generate_sample(self,
initial_pos,
num_adapt,
num_samples,
stepsize=None):
"""
Returns a generator type object whose each iteration yields a sample
Parameters
----------
initial_pos: A 1d array like object
Vector representing values of parameter position, the starting
state in markov chain.
num_adapt: int
The number of iterations to run the adaptation of stepsize
num_samples: int
Number of samples to be generated
stepsize: float , defaults to None
The stepsize for proposing new values of position and momentum in simulate_dynamics
If None, then will be chosen suitably
Returns
-------
genrator: yielding a numpy.array type object for a sample
Examples
--------
>>> from ProbabilityModel.sampling import NoUTurnSamplerDA as NUTSda, GradLogPDFGaussian
>>> from ProbabilityModel.factors.continuous import GaussianDistribution as JGD
>>> import numpy as np
>>> mean = np.array([1, -100])
>>> covariance = np.array([[-12, 45], [45, -10]])
>>> model = JGD(['a', 'b'], mean, covariance)
>>> sampler = NUTSda(model=model, grad_log_pdf=GradLogPDFGaussian, simulate_dynamics=LeapFrog)
>>> samples = sampler.generate_sample(initial_pos=np.array([12, -4]), num_adapt=10,
... num_samples=10, stepsize=0.1)
>>> samples
<generator object NoUTurnSamplerDA.generate_sample at 0x7f4fed46a4c0>
>>> samples_array = np.array([sample for sample in samples])
>>> samples_array
array([[ 11.89963386, -4.06572636],
[ 10.3453755 , -7.5700289 ],
[-26.56899659, -15.3920684 ],
[-29.97143077, -12.0801625 ],
[-29.97143077, -12.0801625 ],
[-33.07960829, -8.90440347],
[-55.28263496, -17.31718524],
[-55.28263496, -17.31718524],
[-56.63440044, -16.03309364],
[-63.880094 , -19.19981944]])
"""
initial_pos = _check_1d_array_object(initial_pos, "initial_pos")
_check_length_equal(initial_pos, self.model.variables, "initial_pos",
"model.variables")
if stepsize is None:
stepsize = self._find_reasonable_stepsize(initial_pos)
if num_adapt <= 1: # return sample generated using Simple HMC algorithm
for sample in NoUTurnSampler(
self.model, self.grad_log_pdf,
self.simulate_dynamics).generate_sample(
initial_pos, num_samples, stepsize):
yield sample
return
mu = np.log(10.0 * stepsize)
stepsize_bar = 1.0
h_bar = 0.0
position_m = initial_pos.copy()
num_adapt += 1
for i in range(1, num_samples + 1):
position_m, alpha, n_alpha = self._sample(position_m, stepsize)
if i <= num_adapt:
stepsize, stepsize_bar, h_bar = self._adapt_params(
stepsize, stepsize_bar, h_bar, mu, i, alpha, n_alpha)
else:
stepsize = stepsize_bar
yield position_m
def sample(
self,
initial_pos,
num_adapt,
num_samples,
stepsize=None,
return_type="dataframe",
):
"""
Returns samples using No U Turn Sampler with dual averaging
Parameters
----------
initial_pos: A 1d array like object
Vector representing values of parameter position, the starting
state in markov chain.
num_adapt: int
The number of iterations to run the adaptation of stepsize
num_samples: int
Number of samples to be generated
stepsize: float , defaults to None
The stepsize for proposing new values of position and momentum in simulate_dynamics
If None, then will be chosen suitably
return_type: string (dataframe | recarray)
Return type for samples, either of 'dataframe' or 'recarray'.
Defaults to 'dataframe'
Returns
-------
sampled: A pandas.DataFrame or a numpy.recarray object depending upon return_type argument
Examples
---------
>>> from ProbabilityModel.sampling import NoUTurnSamplerDA as NUTSda, GradLogPDFGaussian, LeapFrog
>>> from ProbabilityModel.factors.continuous import GaussianDistribution as JGD
>>> import numpy as np
>>> mean = np.array([10, -13])
>>> covariance = np.array([[16, -3], [-3, 13]])
>>> model = JGD(['x', 'y'], mean, covariance)
>>> sampler = NUTSda(model=model, grad_log_pdf=GradLogPDFGaussian, simulate_dynamics=LeapFrog)
>>> samples = sampler.sample(initial_pos=np.array([12, -4]), num_adapt=10, num_samples=10,
... stepsize=0.1, return_type='dataframe')
>>> samples
x y
0 12.000000 -4.000000
1 11.864821 -3.696109
2 10.546986 -4.892169
3 8.526596 -21.555793
4 8.526596 -21.555793
5 11.343194 -6.353789
6 -1.583269 -12.802931
7 12.411957 -11.704859
8 13.253336 -20.169492
9 11.295901 -7.665058
"""
initial_pos = _check_1d_array_object(initial_pos, "initial_pos")
_check_length_equal(initial_pos, self.model.variables, "initial_pos",
"model.variables")
if stepsize is None:
stepsize = self._find_reasonable_stepsize(initial_pos)
if num_adapt <= 1:
return NoUTurnSampler(self.model, self.grad_log_pdf,
self.simulate_dynamics).sample(
initial_pos, num_samples, stepsize)
mu = np.log(10.0 * stepsize)
stepsize_bar = 1.0
h_bar = 0.0
types = [(var_name, "float") for var_name in self.model.variables]
samples = np.zeros(num_samples, dtype=types).view(np.recarray)
samples[0] = tuple(initial_pos)
position_m = initial_pos
for i in tqdm(range(1, num_samples)):
position_m, alpha, n_alpha = self._sample(position_m, stepsize)
samples[i] = tuple(position_m)
if i <= num_adapt:
stepsize, stepsize_bar, h_bar = self._adapt_params(
stepsize, stepsize_bar, h_bar, mu, i, alpha, n_alpha)
else:
stepsize = stepsize_bar
return _return_samples(return_type, samples)
def sample(self,
initial_pos,
num_samples,
stepsize=None,
return_type="dataframe"):
"""
Method to return samples using No U Turn Sampler
Parameters
----------
initial_pos: A 1d array like object
Vector representing values of parameter position, the starting
state in markov chain.
num_samples: int
Number of samples to be generated
stepsize: float , defaults to None
The stepsize for proposing new values of position and momentum in simulate_dynamics
If None, then will be choosen suitably
return_type: string (dataframe | recarray)
Return type for samples, either of 'dataframe' or 'recarray'.
Defaults to 'dataframe'
Returns
-------
sampled: A pandas.DataFrame or a numpy.recarray object depending upon return_type argument
Examples
---------
>>> from ProbabilityModel.sampling import NoUTurnSampler as NUTS, GradLogPDFGaussian, LeapFrog
>>> from ProbabilityModel.factors.continuous import GaussianDistribution as JGD
>>> import numpy as np
>>> mean = np.array([0, 0, 0])
>>> covariance = np.array([[6, 0.7, 0.2], [0.7, 3, 0.9], [0.2, 0.9, 1]])
>>> model = JGD(['x', 'y', 'z'], mean, covariance)
>>> sampler = NUTS(model=model, grad_log_pdf=GradLogPDFGaussian, simulate_dynamics=LeapFrog)
>>> samples = sampler.sample(initial_pos=np.array([1, 1, 1]), num_samples=10,
... stepsize=0.4, return_type='dataframe')
>>> samples
x y z
0 1.000000 1.000000 1.000000
1 1.760756 0.271543 -0.613309
2 1.883387 0.990745 -0.611720
3 0.980812 0.340336 -0.916283
4 0.781338 0.647220 -0.948640
5 0.040308 -1.391406 0.412201
6 1.179549 -1.450552 1.105216
7 1.100320 -1.313926 1.207815
8 1.484520 -1.349247 0.768599
9 0.934942 -1.894589 0.471772
"""
initial_pos = _check_1d_array_object(initial_pos, "initial_pos")
_check_length_equal(initial_pos, self.model.variables, "initial_pos",
"model.variables")
if stepsize is None:
stepsize = self._find_reasonable_stepsize(initial_pos)
types = [(var_name, "float") for var_name in self.model.variables]
samples = np.zeros(num_samples, dtype=types).view(np.recarray)
samples[0] = tuple(initial_pos)
position_m = initial_pos
for i in tqdm(range(1, num_samples)):
# Genrating sample
position_m = self._sample(position_m, stepsize)
samples[i] = tuple(position_m)
return _return_samples(return_type, samples)
def generate_sample(self,
initial_pos,
num_adapt,
num_samples,
trajectory_length,
stepsize=None):
"""
Method returns a generator type object whose each iteration yields a sample
using Hamiltonian Monte Carlo
Parameters
----------
initial_pos: A 1d array like object
Vector representing values of parameter position, the starting
state in markov chain.
num_adapt: int
The number of iterations to run the adaptation of stepsize
num_samples: int
Number of samples to be generated
trajectory_length: int or float
Target trajectory length, stepsize * number of steps(L),
where L is the number of steps taken to propose new values of position and momentum
per HMC iteration and stepsize is step size.
stepsize: float , defaults to None
The stepsize for proposing new values of position and momentum in simulate_dynamics
If None, then will be chosen suitably
Returns
-------
genrator: yielding a numpy.array type object for a sample
Examples
--------
>>> from ProbabilityModel.sampling import HamiltonianMCDA as HMCda, GradLogPDFGaussian as GLPG, LeapFrog
>>> from ProbabilityModel.factors.continuous import GaussianDistribution as JGD
>>> import numpy as np
>>> mean = np.array([1, 1])
>>> covariance = np.array([[1, 0.7], [0.7, 3]])
>>> model = JGD(['x', 'y'], mean, covariance)
>>> sampler = HMCda(model=model, grad_log_pdf=GLPG, simulate_dynamics=LeapFrog)
>>> gen_samples = sampler.generate_sample(np.array([1, 1]), num_adapt=10000,
... num_samples = 10000, trajectory_length=2, stepsize=None)
>>> samples_array = np.array([sample for sample in gen_samples])
>>> np.cov(samples_array.T)
array([[ 0.98432155, 0.69517394],
[ 0.69517394, 2.95449533]])
"""
self.accepted_proposals = 0
initial_pos = _check_1d_array_object(initial_pos, "initial_pos")
_check_length_equal(initial_pos, self.model.variables, "initial_pos",
"model.variables")
if stepsize is None:
stepsize = self._find_reasonable_stepsize(initial_pos)
if num_adapt <= 1: # return sample generated using Simple HMC algorithm
for sample in HamiltonianMC.generate_sample(
self, initial_pos, num_samples, trajectory_length,
stepsize):
yield sample
return
mu = np.log(10.0 * stepsize)
stepsize_bar = 1.0
h_bar = 0.0
position_m = initial_pos.copy()
num_adapt += 1
for i in range(1, num_samples + 1):
position_m, alpha = self._sample(position_m, trajectory_length,
stepsize)
if i <= num_adapt:
stepsize, stepsize_bar, h_bar = self._adapt_params(
stepsize, stepsize_bar, h_bar, mu, i, alpha)
else:
stepsize = stepsize_bar
yield position_m
self.acceptance_rate = self.accepted_proposals / num_samples
def sample(
self,
initial_pos,
num_adapt,
num_samples,
trajectory_length,
stepsize=None,
return_type="dataframe",
):
"""
Method to return samples using Hamiltonian Monte Carlo
Parameters
----------
initial_pos: A 1d array like object
Vector representing values of parameter position, the starting
state in markov chain.
num_adapt: int
The number of iterations to run the adaptation of stepsize
num_samples: int
Number of samples to be generated
trajectory_length: int or float
Target trajectory length, stepsize * number of steps(L),
where L is the number of steps taken per HMC iteration,
and stepsize is step size for splitting time method.
stepsize: float , defaults to None
The stepsize for proposing new values of position and momentum in simulate_dynamics
If None, then will be chosen suitably
return_type: string (dataframe | recarray)
Return type for samples, either of 'dataframe' or 'recarray'.
Defaults to 'dataframe'
Returns
-------
sampled: A pandas.DataFrame or a numpy.recarray object depending upon return_type argument
Examples
---------
>>> from ProbabilityModel.sampling import HamiltonianMCDA as HMCda, GradLogPDFGaussian as GLPG, LeapFrog
>>> from ProbabilityModel.factors.continuous import GaussianDistribution as JGD
>>> import numpy as np
>>> mean = np.array([1, 1])
>>> covariance = np.array([[1, 0.7], [0.7, 3]])
>>> model = JGD(['x', 'y'], mean, covariance)
>>> sampler = HMCda(model=model, grad_log_pdf=GLPG, simulate_dynamics=LeapFrog)
>>> samples = sampler.sample(np.array([1, 1]), num_adapt=10000, num_samples = 10000,
... trajectory_length=2, stepsize=None, return_type='recarray')
>>> samples_array = np.array([samples[var_name] for var_name in model.variables])
>>> np.cov(samples_array)
array([[ 0.98432155, 0.66517394],
[ 0.66517394, 2.95449533]])
"""
self.accepted_proposals = 1.0
initial_pos = _check_1d_array_object(initial_pos, "initial_pos")
_check_length_equal(initial_pos, self.model.variables, "initial_pos",
"model.variables")
if stepsize is None:
stepsize = self._find_reasonable_stepsize(initial_pos)
if num_adapt <= 1: # Return samples genrated using Simple HMC algorithm
return HamiltonianMC.sample(self, initial_pos, num_samples,
trajectory_length, stepsize)
# stepsize is epsilon
# freely chosen point, after each iteration xt(/position) is shrunk towards it
mu = np.log(10.0 * stepsize)
# log(10 * stepsize) large values to save computation
# stepsize_bar is epsilon_bar
stepsize_bar = 1.0
h_bar = 0.0
# See equation (6) section 3.2.1 for details
types = [(var_name, "float") for var_name in self.model.variables]
samples = np.zeros(num_samples, dtype=types).view(np.recarray)
samples[0] = tuple(initial_pos)
position_m = initial_pos
for i in tqdm(range(1, num_samples)):
# Genrating sample
position_m, alpha = self._sample(position_m, trajectory_length,
stepsize)
samples[i] = tuple(position_m)
# Adaptation of stepsize till num_adapt iterations
if i <= num_adapt:
stepsize, stepsize_bar, h_bar = self._adapt_params(
stepsize, stepsize_bar, h_bar, mu, i, alpha)
else:
stepsize = stepsize_bar
self.acceptance_rate = self.accepted_proposals / num_samples
return _return_samples(return_type, samples)
def generate_sample(self,
initial_pos,
num_samples,
trajectory_length,
stepsize=None):
"""
Method returns a generator type object whose each iteration yields a sample
using Hamiltonian Monte Carlo
Parameters
----------
initial_pos: A 1d array like object
Vector representing values of parameter position, the starting
state in markov chain.
num_samples: int
Number of samples to be generated
trajectory_length: int or float
Target trajectory length, stepsize * number of steps(L),
where L is the number of steps taken per HMC iteration,
and stepsize is step size for splitting time method.
stepsize: float , defaults to None
The stepsize for proposing new values of position and momentum in simulate_dynamics
If None, then will be chosen suitably
Returns
-------
genrator: yielding a 1d numpy.array type object for a sample
Examples
--------
>>> from ProbabilityModel.sampling import HamiltonianMC as HMC, GradLogPDFGaussian as GLPG
>>> from ProbabilityModel.factors import GaussianDistribution as JGD
>>> import numpy as np
>>> mean = np.array([4, -1])
>>> covariance = np.array([[3, 0.4], [0.4, 3]])
>>> model = JGD(['x', 'y'], mean, covariance)
>>> sampler = HMC(model=model, grad_log_pdf=GLPG)
>>> gen_samples = sampler.generate_sample(np.array([-1, 1]), num_samples = 10000,
... trajectory_length=2, stepsize=0.25)
>>> samples_array = np.array([sample for sample in gen_samples])
>>> samples_array
array([[ 0.1467264 , 0.27143857],
[ 4.0371448 , 0.15871274],
[ 3.24656208, -1.03742621],
...,
[ 6.45975905, 1.97941306],
[ 4.89007171, 0.15413156],
[ 5.9528083 , 1.92983158]])
>>> np.cov(samples_array.T)
array([[ 2.95692642, 0.4379419 ],
[ 0.4379419 , 3.00939434]])
>>> sampler.acceptance_rate
0.9969
"""
self.accepted_proposals = 0
initial_pos = _check_1d_array_object(initial_pos, "initial_pos")
_check_length_equal(initial_pos, self.model.variables, "initial_pos",
"model.variables")
if stepsize is None:
stepsize = self._find_reasonable_stepsize(initial_pos)
lsteps = int(max(1, round(trajectory_length / stepsize, 0)))
position_m = initial_pos.copy()
for i in range(0, num_samples):
position_m, _ = self._sample(position_m, trajectory_length,
stepsize, lsteps)
yield position_m
self.acceptance_rate = self.accepted_proposals / num_samples
def sample(
self,
initial_pos,
num_samples,
trajectory_length,
stepsize=None,
return_type="dataframe",
):
"""
Method to return samples using Hamiltonian Monte Carlo
Parameters
----------
initial_pos: A 1d array like object
Vector representing values of parameter position, the starting
state in markov chain.
num_samples: int
Number of samples to be generated
trajectory_length: int or float
Target trajectory length, stepsize * number of steps(L),
where L is the number of steps taken per HMC iteration,
and stepsize is step size for splitting time method.
stepsize: float , defaults to None
The stepsize for proposing new values of position and momentum in simulate_dynamics
If None, then will be chosen suitably
return_type: string (dataframe | recarray)
Return type for samples, either of 'dataframe' or 'recarray'.
Defaults to 'dataframe'
Returns
-------
sampled: A pandas.DataFrame or a numpy.recarray object depending upon return_type argument
Examples
--------
>>> from ProbabilityModel.sampling import HamiltonianMC as HMC, GradLogPDFGaussian, ModifiedEuler
>>> from ProbabilityModel.factors.continuous import GaussianDistribution as JGD
>>> import numpy as np
>>> mean = np.array([1, -1])
>>> covariance = np.array([[1, 0.2], [0.2, 1]])
>>> model = JGD(['x', 'y'], mean, covariance)
>>> sampler = HMC(model=model, grad_log_pdf=GradLogPDFGaussian, simulate_dynamics=ModifiedEuler)
>>> samples = sampler.sample(np.array([1, 1]), num_samples = 5,
... trajectory_length=6, stepsize=0.25, return_type='dataframe')
>>> samples
x y
0 1.000000e+00 1.000000e+00
1 1.592133e+00 1.152911e+00
2 1.608700e+00 1.315349e+00
3 1.608700e+00 1.315349e+00
4 6.843856e-01 6.237043e-01
>>> mean = np.array([4, 1, -1])
>>> covariance = np.array([[1, 0.7 , 0.8], [0.7, 1, 0.2], [0.8, 0.2, 1]])
>>> model = JGD(['x', 'y', 'z'], mean, covariance)
>>> sampler = HMC(model=model, grad_log_pdf=GLPG)
>>> samples = sampler.sample(np.array([1, 1]), num_samples = 10000,
... trajectory_length=6, stepsize=0.25, return_type='dataframe')
>>> np.cov(samples.values.T)
array([[ 1.00795398, 0.71384233, 0.79802097],
[ 0.71384233, 1.00633524, 0.21313767],
[ 0.79802097, 0.21313767, 0.98519017]])
"""
self.accepted_proposals = 1.0
initial_pos = _check_1d_array_object(initial_pos, "initial_pos")
_check_length_equal(initial_pos, self.model.variables, "initial_pos",
"model.variables")
if stepsize is None:
stepsize = self._find_reasonable_stepsize(initial_pos)
types = [(var_name, "float") for var_name in self.model.variables]
samples = np.zeros(num_samples, dtype=types).view(np.recarray)
# Assigning after converting into tuple because value was being changed after assignment
# Reason for this is unknown
samples[0] = tuple(initial_pos)
position_m = initial_pos
lsteps = int(max(1, round(trajectory_length / stepsize, 0)))
for i in tqdm(range(1, num_samples)):
# Genrating sample
position_m, _ = self._sample(position_m, trajectory_length,
stepsize, lsteps)
samples[i] = tuple(position_m)
self.acceptance_rate = self.accepted_proposals / num_samples
return _return_samples(return_type, samples)