class EuclideanTests(unittest.TestCase):
def setUp(self):
self.stat_calc = Identity(degree=1, cross=0)
self.distancefunc = Euclidean(self.stat_calc)
def test_distance(self):
# test simple distance computation
a = [[0, 0, 0], [0, 0, 0]]
b = [[0, 0, 0], [0, 0, 0]]
c = [[1, 1, 1], [1, 1, 1]]
#Checks whether wrong input type produces error message
self.assertRaises(TypeError, self.distancefunc.distance, 3.4, b)
self.assertRaises(TypeError, self.distancefunc.distance, a, 3.4)
# test input has different dimensionality
self.assertRaises(BaseException, self.distancefunc.distance, a,
np.array([[0, 0], [1, 2]]))
self.assertRaises(BaseException, self.distancefunc.distance, a,
np.array([[0, 0, 0], [1, 2, 3], [4, 5, 6]]))
# test whether they compute correct values
self.assertTrue(self.distancefunc.distance(a, b) == np.array([0]))
self.assertTrue(
self.distancefunc.distance(a, c) == np.array([1.7320508075688772]))
def test_dist_max(self):
self.assertTrue(self.distancefunc.dist_max() == np.inf)
def setUp(self):
self.stat_calc1 = Identity(degree=1, cross=0)
self.stat_calc2 = Identity(degree=1, cross=0)
self.distancefunc1 = Euclidean(self.stat_calc1)
self.distancefunc2 = Euclidean(self.stat_calc2)
## Define Models
# define a uniform prior distribution
mu = Uniform([[-5.0], [5.0]], name='mu')
sigma = Uniform([[0.0], [10.0]], name='sigma')
# define a Gaussian model
self.model1 = Normal([mu, sigma])
self.model2 = Normal([mu, sigma])
#Check whether wrong sized distnacefuncs gives an error
self.assertRaises(ValueError, LinearCombination,
[self.model1, self.model2], [self.distancefunc1],
[1.0, 1.0])
#Check whether wrong sized weights gives an error
self.assertRaises(ValueError, LinearCombination,
[self.model1, self.model2],
[self.distancefunc1, self.distancefunc2],
[1.0, 1.0, 1.0])
self.jointdistancefunc = LinearCombination(
[self.model1, self.model2],
[self.distancefunc1, self.distancefunc2], [1.0, 1.0])
def test_sample(self):
# setup backend
dummy = BackendDummy()
# define a uniform prior distribution
mu = Uniform([[-5.0], [5.0]], name='mu')
sigma = Uniform([[0.0], [10.0]], name='sigma')
# define a Gaussian model
self.model = Normal([mu, sigma])
# define sufficient statistics for the model
stat_calc = Identity(degree=2, cross=0)
# define a distance function
dist_calc = Euclidean(stat_calc)
# create fake observed data
y_obs = [np.array(9.8)]
# use the rejection sampling scheme
sampler = RejectionABC([self.model], [dist_calc], dummy, seed=1)
journal = sampler.sample([y_obs], 10, 1, 10)
mu_sample = np.array(journal.get_parameters()['mu'])
sigma_sample = np.array(journal.get_parameters()['sigma'])
# test shape of samples
self.assertEqual(np.shape(mu_sample), (10, 1))
self.assertEqual(np.shape(sigma_sample), (10, 1))
# Compute posterior mean
#self.assertAlmostEqual(np.average(np.asarray(samples[:,0])),1.22301,10e-2)
self.assertLess(np.average(mu_sample) - 1.22301, 1e-2)
self.assertLess(np.average(sigma_sample) - 6.992218, 10e-2)
self.assertFalse(journal.number_of_simulations == 0)
def infer_parameters_smcabc():
# define observation for true parameters mean=170, 65
rng = np.random.RandomState()
y_obs = [np.array(rng.multivariate_normal([170, 65], np.eye(2), 1).reshape(2,))]
# define prior
from abcpy.continuousmodels import Uniform
mu0 = Uniform([[150], [200]], )
mu1 = Uniform([[25], [100]], )
# define the model
height_weight_model = NestedBivariateGaussian([mu0, mu1])
# define statistics
from abcpy.statistics import Identity
statistics_calculator = Identity(degree = 2, cross = False)
# define distance
from abcpy.distances import Euclidean
distance_calculator = Euclidean(statistics_calculator)
# define sampling scheme
from abcpy.inferences import SMCABC
sampler = SMCABC([height_weight_model], [distance_calculator], backend, seed=1)
steps, n_samples, n_samples_per_param, epsilon = 2, 10, 1, 2000
journal = sampler.sample([y_obs], steps, n_samples, n_samples_per_param, epsilon, full_output=1)
return journal
def infer_parameters_abcsubsim():
# define observation for true parameters mean=170, 65
rng = np.random.RandomState(seed=1)
y_obs = [np.array(rng.multivariate_normal([170, 65], np.eye(2), 1).reshape(2, ))]
# define prior
from abcpy.continuousmodels import Uniform
mu0 = Uniform([[150], [200]], name="mu0")
mu1 = Uniform([[25], [100]], name="mu1")
# define the model
height_weight_model = NestedBivariateGaussian([mu0, mu1])
# define statistics
from abcpy.statistics import Identity
statistics_calculator = Identity(degree=2, cross=False)
# define distance
from abcpy.distances import Euclidean
distance_calculator = Euclidean(statistics_calculator)
# define sampling scheme
from abcpy.inferences import ABCsubsim
sampler = ABCsubsim([height_weight_model], [distance_calculator], backend, seed=1)
steps, n_samples, n_samples_per_param, chain_length = 2, 10, 1, 2
print('ABCsubsim Inferring')
journal = sampler.sample([y_obs], steps, n_samples, n_samples_per_param, chain_length)
return journal
def infer_parameters_sabc():
# define observation for true parameters mean=170, 65
rng = np.random.RandomState(seed=1)
y_obs = [np.array(rng.multivariate_normal([170, 65], np.eye(2), 1).reshape(2, ))]
# define prior
from abcpy.continuousmodels import Uniform
mu0 = Uniform([[150], [200]], name="mu0")
mu1 = Uniform([[25], [100]], name="mu1")
# define the model
height_weight_model = NestedBivariateGaussian([mu0, mu1])
# define statistics
from abcpy.statistics import Identity
statistics_calculator = Identity(degree=2, cross=False)
# define distance
from abcpy.distances import Euclidean
distance_calculator = Euclidean(statistics_calculator)
# define sampling scheme
from abcpy.inferences import SABC
sampler = SABC([height_weight_model], [distance_calculator], backend, seed=1)
steps, epsilon, n_samples, n_samples_per_param, beta, delta, v = 2, 40000, 10, 1, 2, 0.2, 0.3
ar_cutoff, resample, n_update, full_output = 0.1, None, None, 1
print('SABC Inferring')
journal = sampler.sample([y_obs], steps, epsilon, n_samples, n_samples_per_param, beta, delta, v, ar_cutoff,
resample, n_update, full_output)
return journal
def test_sample(self):
# setup backend
dummy = BackendDummy()
# define a uniform prior distribution
lb = np.array([-5, 0])
ub = np.array([5, 10])
prior = Uniform(lb, ub, seed=1)
# define a Gaussian model
model = Gaussian(prior, mu=2.1, sigma=5.0, seed=1)
# define sufficient statistics for the model
stat_calc = Identity(degree=2, cross=0)
# define a distance function
dist_calc = Euclidean(stat_calc)
# create fake observed data
y_obs = model.simulate(1)
# use the rejection sampling scheme
sampler = RejectionABC(model, dist_calc, dummy, seed=1)
journal = sampler.sample(y_obs, 10, 1, 0.1)
samples = journal.get_parameters()
# test shape of samples
samples_shape = np.shape(samples)
self.assertEqual(samples_shape, (10, 2))
# Compute posterior mean
self.assertEqual((np.average(np.asarray(
samples[:, 0])), np.average(np.asarray(samples[:, 1]))),
(1.6818856447333246, 8.4384177826766518))
class DefaultJointDistance(Distance):
"""
This class implements a default distance to be used when multiple root
models exist. It uses LogReg as the distance calculator for each root model, and
adds all individual distances.
Parameters
----------
statistics: abcpy.statistics object
The statistics calculator to be used
number_of_models: integer
The number of root models on which the distance will act.
"""
def __init__(self, statistics):
self.statistics_calc = statistics
self.distance_calc = Euclidean(self.statistics_calc)
def distance(self, d1, d2):
total_distance = 0
for observed_data, simulated_data in zip(d1, d2):
total_distance += self.distance_calc.distance([observed_data],
[simulated_data])
total_distance /= len(d2)
return total_distance
def dist_max(self):
return np.inf
def infer_parameters_apmcabc():
# define observation for true parameters mean=170, 65
rng = np.random.RandomState(seed=1)
y_obs = [np.array(rng.multivariate_normal([170, 65], np.eye(2), 1).reshape(2, ))]
# define prior
from abcpy.continuousmodels import Uniform
mu0 = Uniform([[150], [200]], name="mu0")
mu1 = Uniform([[25], [100]], name="mu1")
# define the model
height_weight_model = NestedBivariateGaussian([mu0, mu1])
# define statistics
from abcpy.statistics import Identity
statistics_calculator = Identity(degree=2, cross=False)
# define distance
from abcpy.distances import Euclidean
distance_calculator = Euclidean(statistics_calculator)
# define sampling scheme
from abcpy.inferences import APMCABC
sampler = APMCABC([height_weight_model], [distance_calculator], backend, seed=1)
steps, n_samples, n_samples_per_param, alpha, acceptance_cutoff, covFactor, full_output, journal_file = 2, 100, 1, 0.2, 0.03, 2.0, 1, None
print('APMCABC Inferring')
journal = sampler.sample([y_obs], steps, n_samples, n_samples_per_param, alpha, acceptance_cutoff, covFactor,
full_output, journal_file)
return journal
def infer_parameters_pmcabc():
# define observation for true parameters mean=170, 65
rng = np.random.RandomState(seed=1)
y_obs = [np.array(rng.multivariate_normal([170, 65], np.eye(2), 1).reshape(2, ))]
# define prior
from abcpy.continuousmodels import Uniform
mu0 = Uniform([[150], [200]], name="mu0")
mu1 = Uniform([[25], [100]], name="mu1")
# define the model
height_weight_model = NestedBivariateGaussian([mu0, mu1])
# define statistics
from abcpy.statistics import Identity
statistics_calculator = Identity(degree=2, cross=False)
# define distance
from abcpy.distances import Euclidean
distance_calculator = Euclidean(statistics_calculator)
# define sampling scheme
from abcpy.inferences import PMCABC
sampler = PMCABC([height_weight_model], [distance_calculator], backend, seed=1)
# sample from scheme
T, n_sample, n_samples_per_param = 2, 10, 1
eps_arr = np.array([10000])
epsilon_percentile = 95
print('PMCABC Inferring')
journal = sampler.sample([y_obs], T, eps_arr, n_sample, n_samples_per_param, epsilon_percentile)
return journal
def setUp(self):
# find spark and initialize it
self.backend = BackendDummy()
# define a uniform prior distribution
mu = Uniform([[-5.0], [5.0]], name='mu')
sigma = Uniform([[0.0], [10.0]], name='sigma')
# define a Gaussian model
self.model = Normal([mu, sigma])
# define a distance function
stat_calc = Identity(degree=2, cross=0)
self.dist_calc = Euclidean(stat_calc)
# create fake observed data
#self.observation = self.model.forward_simulate(1, np.random.RandomState(1))[0].tolist()
self.observation = [np.array(9.8)]
def infer_parameters(model_num, synthetic, T, n_sample, ar_cutoff):
y_obs = [0]
#prior = Uniform([[0, 0, 0, 0], [5, 5, 2.5, 2.5]])
prior1 = Uniform([[0], [5]])
prior2 = Uniform([[0], [5]])
prior3 = Uniform([[0], [2.5]])
prior4 = Uniform([[0], [2.5]])
model = Airport([prior1, prior2, prior3, prior4],
name="Airport",
model_num=model_num,
synthetic=synthetic)
from abcpy.statistics import Identity
statistics_calculator = Identity(degree=1, cross=False)
from abcpy.distances import Euclidean
distance_calculator = Euclidean(statistics_calculator)
# define sampling scheme
from abcpy.inferences import SABC
sampler = SABC([model], [distance_calculator], backend)
# define sampling scheme
#from abcpy.inferences import PMCABC
#sampler = PMCABC([model], [distance_calculator], backend, kernel, seed=1)
# sample from scheme
journal = sampler.sample([y_obs],
T,
1000,
n_sample,
1,
ar_cutoff=ar_cutoff)
return journal
def setUp(self):
# find spark and initialize it
self.backend = BackendDummy()
# define a uniform prior distribution
lb = np.array([-5, 0])
ub = np.array([5, 10])
prior = Uniform(lb, ub, seed=1)
# define a Gaussian model
self.model = Gaussian(prior, mu=2.1, sigma=5.0, seed=1)
# define a distance function
stat_calc = Identity(degree=2, cross=0)
self.dist_calc = Euclidean(stat_calc)
# create fake observed data
self.observation = self.model.simulate(1)
# define kernel
mean = np.array([-13.0, .0, 7.0])
cov = np.eye(3)
self.kernel = MultiNormal(mean, cov, seed=1)
def infer_parameters():
# define backend
# Note, the dummy backend does not parallelize the code!
from abcpy.backends import BackendDummy as Backend
backend = Backend()
# define observation for true parameters mean=170, std=15
height_obs = [
160.82499176, 167.24266737, 185.71695756, 153.7045709, 163.40568812,
140.70658699, 169.59102084, 172.81041696, 187.38782738, 179.66358934,
176.63417241, 189.16082803, 181.98288443, 170.18565017, 183.78493886,
166.58387299, 161.9521899, 155.69213073, 156.17867343, 144.51580379,
170.29847515, 197.96767899, 153.36646527, 162.22710198, 158.70012047,
178.53470703, 170.77697743, 164.31392633, 165.88595994, 177.38083686,
146.67058471763457, 179.41946565658628, 238.02751620619537,
206.22458790620766, 220.89530574344568, 221.04082532837026,
142.25301427453394, 261.37656571434275, 171.63761180867033,
210.28121820385866, 237.29130237612236, 175.75558340169619,
224.54340549862235, 197.42448680731226, 165.88273684581381,
166.55094082844519, 229.54308602661584, 222.99844054358519,
185.30223966014586, 152.69149367593846, 206.94372818527413,
256.35498655339154, 165.43140916577741, 250.19273595481803,
148.87781549665536, 223.05547559193792, 230.03418198709608,
146.13611923127021, 138.24716809523139, 179.26755740864527,
141.21704876815426, 170.89587081800852, 222.96391329259626,
188.27229523693822, 202.67075179617672, 211.75963110985992,
217.45423324370509
]
# define prior
from abcpy.continuousmodels import Uniform
mu = Uniform([[150], [200]], )
sigma = Uniform([[5], [25]], )
# define the model
from abcpy.continuousmodels import Normal
height = Normal([mu, sigma], )
# define statistics
from abcpy.statistics import Identity
statistics_calculator = Identity(degree=3, cross=True)
# Learn the optimal summary statistics using Semiautomatic summary selection
from abcpy.statisticslearning import Semiautomatic
statistics_learning = Semiautomatic([height],
statistics_calculator,
backend,
n_samples=1000,
n_samples_per_param=1,
seed=1)
# Redefine the statistics function
new_statistics_calculator = statistics_learning.get_statistics()
# Learn the optimal summary statistics using SemiautomaticNN summary selection
from abcpy.statisticslearning import SemiautomaticNN
statistics_learning = SemiautomaticNN([height],
statistics_calculator,
backend,
n_samples=1000,
n_samples_per_param=1,
seed=1)
# Redefine the statistics function
new_statistics_calculator = statistics_learning.get_statistics()
# define distance
from abcpy.distances import Euclidean
distance_calculator = Euclidean(new_statistics_calculator)
# define kernel
from abcpy.perturbationkernel import DefaultKernel
kernel = DefaultKernel([mu, sigma])
# define sampling scheme
from abcpy.inferences import PMCABC
sampler = PMCABC([height], [distance_calculator], backend, kernel, seed=1)
# sample from scheme
T, n_sample, n_samples_per_param = 3, 10, 10
eps_arr = np.array([500])
epsilon_percentile = 10
journal = sampler.sample([height_obs], T, eps_arr, n_sample,
n_samples_per_param, epsilon_percentile)
return journal
def __init__(self, statistics):
self.statistics_calc = statistics
self.distance_calc = Euclidean(self.statistics_calc)
# resultfakeobs2 = EarthWorm.forward_simulate([1, 1, 1, 1, 1, 1, 1, 11, 0.015, 0.5, 0.25, 0.177, 0.182, 0.0002], 2)
# # Define backend
from abcpy.backends import BackendMPI as Backend
backend = Backend()
#
# Define Statistics
statistics_calculator = Identity(degree=1, cross=False)
# #print('# Check whether the statistis works')
# print(statistics_calculator.statistics(resultfakeobs1))
# print(statistics_calculator.statistics(resultfakeobs2))
# Define distance
from abcpy.distances import Euclidean
distance_calculator = Euclidean(statistics_calculator)
# print('# Check whether the distance works')
# print(distance_calculator.distance(resultfakeobs1, resultfakeobs1))
# print(distance_calculator.distance(resultfakeobs1, resultfakeobs2))
#
# Define kernel
from abcpy.perturbationkernel import DefaultKernel
kernel = DefaultKernel([
B_0, activation_energy, energy_tissue, energy_food, energy_synthesis,
half_saturation_coeff, max_ingestion_rate, mass_birth, mass_cocoon,
mass_maximum, mass_sexual_maturity, growth_constant, max_reproduction_rate,
speed
])
## SABC ##
def infer_parameters(backend,
scheme='rejection',
n_samples=250,
n_samples_per_param=10,
logging_level=logging.WARN):
"""Perform inference for this example.
Parameters
----------
backend
The parallelization backend
steps : integer, optional
Number of iterations in the sequential PMCABC algoritm ("generations"). The default value is 3
n_samples : integer, optional
Number of posterior samples to generate. The default value is 250.
n_samples_per_param : integer, optional
Number of data points in each simulated data set. The default value is 10.
Returns
-------
abcpy.output.Journal
A journal containing simulation results, metadata and optionally intermediate results.
"""
logging.basicConfig(level=logging_level)
# experimental setup
T = 50. # simulation time
dt = 0.025 # time step
I_amp = 0.32 # stimulus amplitude
r_soma = 40 # radius of soma
threshold = -55 # AP threshold
# input stimulus
stimulus_dict = constant_stimulus(I_amp=I_amp,
T=T,
dt=dt,
t_stim_on=10,
t_stim_off=40,
r_soma=r_soma)
I = stimulus_dict["I"]
#I_stim = stimulus_dict["I_stim"]
# true parameters
gbar_K_true = 36
gbar_Na_true = 120
gbar_K_std = 5
gbar_Na_std = 5
# define priors
gbar_K = Normal([[gbar_K_true], [gbar_K_std]], name='gbar_K')
gbar_Na = Normal([[gbar_Na_true], [gbar_Na_std]], name='gbar_Na')
# define the model
hh_simulator = HHSimulator([gbar_K, gbar_Na], I, T, dt)
# observed data
obs_data = hh_simulator.forward_simulate([gbar_K_true, gbar_Na_true])
# define statistics
statistics_calculator = Identity()
# Learn the optimal summary statistics using Semiautomatic summary selection
statistics_learning = Semiautomatic([hh_simulator],
statistics_calculator,
backend,
n_samples=1000,
n_samples_per_param=1,
seed=42)
new_statistics_calculator = statistics_learning.get_statistics()
# define distance
distance_calculator = Euclidean(new_statistics_calculator)
# define kernel
kernel = DefaultKernel([gbar_K, gbar_Na])
# define sampling scheme
if scheme == 'rejection':
sampler = RejectionABC([hh_simulator], [distance_calculator],
backend,
seed=42)
# sample from scheme
epsilon = 2.
journal = sampler.sample([obs_data], n_samples, n_samples_per_param,
epsilon)
elif scheme == 'smc':
sampler = SMCABC([hh_simulator], [distance_calculator],
backend,
kernel,
seed=42)
# sample from scheme
steps = 3
journal = sampler.sample([obs_data], steps, n_samples,
n_samples_per_param)
elif scheme == 'pmc':
sampler = PMCABC([hh_simulator], [distance_calculator],
backend,
kernel,
seed=42)
# sample from scheme
steps = 3
eps_arr = np.array([2.])
epsilon_percentile = 10
journal = sampler.sample([obs_data], steps, eps_arr, n_samples,
n_samples_per_param, epsilon_percentile)
return journal
def infer_parameters(steps=2, n_sample=50, n_samples_per_param=1, logging_level=logging.WARN):
"""Perform inference for this example.
Parameters
----------
steps : integer, optional
Number of iterations in the sequential PMCABC algorithm ("generations"). The default value is 3
n_samples : integer, optional
Number of posterior samples to generate. The default value is 250.
n_samples_per_param : integer, optional
Number of data points in each simulated data set. The default value is 10.
Returns
-------
abcpy.output.Journal
A journal containing simulation results, metadata and optionally intermediate results.
"""
logging.basicConfig(level=logging_level)
# define backend
# Note, the dummy backend does not parallelize the code!
from abcpy.backends import BackendDummy as Backend
backend = Backend()
# define observation for true parameters mean=170, std=15
height_obs = [160.82499176, 167.24266737, 185.71695756, 153.7045709, 163.40568812, 140.70658699, 169.59102084,
172.81041696, 187.38782738, 179.66358934, 176.63417241, 189.16082803, 181.98288443, 170.18565017,
183.78493886, 166.58387299, 161.9521899, 155.69213073, 156.17867343, 144.51580379, 170.29847515,
197.96767899, 153.36646527, 162.22710198, 158.70012047, 178.53470703, 170.77697743, 164.31392633,
165.88595994, 177.38083686, 146.67058471763457, 179.41946565658628, 238.02751620619537,
206.22458790620766, 220.89530574344568, 221.04082532837026, 142.25301427453394, 261.37656571434275,
171.63761180867033, 210.28121820385866, 237.29130237612236, 175.75558340169619, 224.54340549862235,
197.42448680731226, 165.88273684581381, 166.55094082844519, 229.54308602661584, 222.99844054358519,
185.30223966014586, 152.69149367593846, 206.94372818527413, 256.35498655339154, 165.43140916577741,
250.19273595481803, 148.87781549665536, 223.05547559193792, 230.03418198709608, 146.13611923127021,
138.24716809523139, 179.26755740864527, 141.21704876815426, 170.89587081800852, 222.96391329259626,
188.27229523693822, 202.67075179617672, 211.75963110985992, 217.45423324370509]
# define prior
from abcpy.continuousmodels import Uniform
mu = Uniform([[150], [200]], name="mu")
sigma = Uniform([[5], [25]], name="sigma")
# define the model
from abcpy.continuousmodels import Normal
height = Normal([mu, sigma], )
# 1) generate simulations from prior
from abcpy.inferences import DrawFromPrior
draw_from_prior = DrawFromPrior([height], backend=backend)
# notice the use of the `.sample_par_sim_pairs` method rather than `.sample` to obtain data suitably formatted
# for the summary statistics learning routines
parameters, simulations = draw_from_prior.sample_par_sim_pairs(100, n_samples_per_param=1)
# if you want to use the test loss to do early stopping in the training:
parameters_val, simulations_val = draw_from_prior.sample_par_sim_pairs(100, n_samples_per_param=1)
# discard the mid dimension (n_samples_per_param, as the StatisticsLearning classes use that =1)
simulations = simulations.reshape(simulations.shape[0], simulations.shape[2])
simulations_val = simulations_val.reshape(simulations_val.shape[0], simulations_val.shape[2])
# 2) now train the NNs with the different methods with the generated data
from abcpy.statistics import Identity
identity = Identity() # to apply before computing the statistics
logging.info("semiNN")
from abcpy.statisticslearning import SemiautomaticNN, TripletDistanceLearning
semiNN = SemiautomaticNN([height], identity, backend=backend, parameters=parameters,
simulations=simulations, parameters_val=parameters_val, simulations_val=simulations_val,
early_stopping=True, # early stopping
seed=1, n_epochs=10, scale_samples=False, use_tqdm=False)
logging.info("triplet")
triplet = TripletDistanceLearning([height], identity, backend=backend, parameters=parameters,
simulations=simulations, parameters_val=parameters_val,
simulations_val=simulations_val,
early_stopping=True, # early stopping
seed=1, n_epochs=10, scale_samples=True, use_tqdm=False)
# 3) save and re-load NNs:
# get the statistics from the already fit StatisticsLearning object 'semiNN':
learned_seminn_stat = semiNN.get_statistics()
learned_triplet_stat = triplet.get_statistics()
# this has a save net method:
learned_seminn_stat.save_net("seminn_net.pth")
# if you used `scale_samples=True` in learning the NNs, need to provide a path where pickle stores the scaler too:
learned_triplet_stat.save_net("triplet_net.pth", path_to_scaler="scaler.pkl")
# to reload: need to use the Neural Embedding statistics fromFile; this needs to know which kind of NN it is using;
# need therefore to pass either the input/output size (it data size and number parameters) or the network class if
# that was specified explicitly in the StatisticsLearning class. Check the docstring for NeuralEmbedding.fromFile
# for more details.
from abcpy.statistics import NeuralEmbedding
learned_seminn_stat_loaded = NeuralEmbedding.fromFile("seminn_net.pth", input_size=1, output_size=2)
learned_triplet_stat_loaded = NeuralEmbedding.fromFile("triplet_net.pth", input_size=1, output_size=2,
path_to_scaler="scaler.pkl")
# 4) you can optionally rescale the different summary statistics be their standard deviation on a reference dataset
# of simulations. To do this, it is enough to pass at initialization the reference dataset, and the rescaling will
# be applied every time the statistics is computed on some simulation or observation.
learned_triplet_stat_loaded = NeuralEmbedding.fromFile("triplet_net.pth", input_size=1, output_size=2,
path_to_scaler="scaler.pkl",
reference_simulations=simulations_val)
# 5) perform inference
# define distance
from abcpy.distances import Euclidean
distance_calculator = Euclidean(learned_seminn_stat_loaded)
# define kernel
from abcpy.perturbationkernel import DefaultKernel
kernel = DefaultKernel([mu, sigma])
# define sampling scheme
from abcpy.inferences import PMCABC
sampler = PMCABC([height], [distance_calculator], backend, kernel, seed=1)
eps_arr = np.array([500]) # starting value of epsilon; the smaller, the slower the algorithm.
# at each iteration, take as epsilon the epsilon_percentile of the distances obtained by simulations at previous
# iteration from the observation
epsilon_percentile = 10
journal = sampler.sample([height_obs], steps, eps_arr, n_sample, n_samples_per_param, epsilon_percentile)
return journal
# 2.00000000e+01, 3.90572997e+03, 1.59328549e+01, 1.38943902e+05, 0.00000000e+00,
# 6.00000000e+01, 3.42727305e+03, 2.80052570e+01, 8.57585366e+04, 0.00000000e+00,
# 1.20000000e+02, 2.33523014e+03, 7.57715388e+01, 4.25231707e+04, 0.00000000e+00,
# 3.00000000e+02, 1.74166329e+02, 2.46413793e+03, 5.15975610e+03, 0.00000000e+00])
# obsdata = [np.array(XObserved).reshape(1, -1)]
# # Define kernel and join the defined kernels
from abcpy.perturbationkernel import DefaultKernel
kernel = DefaultKernel([pAd, pAg, pT, pF, aT, v_z_AP, v_z_NAP])
# Define Distance functions
from abcpy.distances import Euclidean
from statistic import Multiply
L = np.load('Data/L_all_3_cross.npz')['L']
stat_mult = Multiply(L=L, degree=3, cross=True)
dist_calc_mult = Euclidean(stat_mult)
# SABC - Multiply##
from abcpy.inferences import SABC
print('Inference using Classifier Loss')
sampler = SABC([PD], [dist_calc_mult], backend, kernel, seed=1)
steps, epsilon, n_samples, n_samples_per_param, ar_cutoff, full_output, journal_file = 20, 10e20, 511, 1, 0.001, 1, None
print('SABC Inferring')
fakedata = PD.forward_simulate([noAP, noNAP, SR_x, 89.0, 76.0, 2.49, 7e-3, 7.7, 6e-3, 8e-4], k=1)
print(fakedata)
journal_sabc = sampler.sample(observations=[fakedata], steps=steps, epsilon=epsilon, n_samples=n_samples,
n_samples_per_param=n_samples_per_param, beta=2, delta=0.2, v=0.3,
ar_cutoff=0.001, resample=None, n_update=None, full_output=1,
journal_file=journal_file)
perform_ABC = True
else:
perform_ABC = True
# you can perform ABC inference with both SM, FP statistics and the true ones
if technique in ["SM", "SSM"]:
if perform_ABC:
print(f"\nPerform ABC inference with {technique} statistics.")
if weighted_euclidean_distance: # define the distance object
# keep the last 100 test samples to estimate the initial eps value if not provided
distance_calculator = WeightedEuclidean(
NeuralEmbedding(RescaleAndDiscardLastOutputNet(net_data_SM, scaler_data_SM)),
[samples_matrix_test[i].numpy() for i in
range(samples_matrix_test.shape[0] - 100 * (ABC_eps is None))])
else:
distance_calculator = Euclidean(
NeuralEmbedding(RescaleAndDiscardLastOutputNet(net_data_SM, scaler_data_SM)))
elif "FP" == technique:
if perform_ABC:
print("\nPerform ABC inference with FP statistics.")
if weighted_euclidean_distance:
distance_calculator = WeightedEuclidean(
NeuralEmbedding(RescaleAndNet(net_FP, scaler_data_FP)),
[samples_matrix_test[i].numpy() for i in
range(samples_matrix_test.shape[0] - 100 * (ABC_eps is None))])
else:
distance_calculator = Euclidean(NeuralEmbedding(RescaleAndNet(net_FP, scaler_data_FP)))
elif "true" == technique:
if perform_ABC:
print("\nPerform ABC inference with true statistics.")
def infer_parameters(steps=3,
n_sample=250,
n_samples_per_param=10,
logging_level=logging.WARN):
"""Perform inference for this example.
Parameters
----------
steps : integer, optional
Number of iterations in the sequential PMCABC algoritm ("generations"). The default value is 3
n_samples : integer, optional
Number of posterior samples to generate. The default value is 250.
n_samples_per_param : integer, optional
Number of data points in each simulated data set. The default value is 10.
Returns
-------
abcpy.output.Journal
A journal containing simulation results, metadata and optionally intermediate results.
"""
logging.basicConfig(level=logging_level)
# define backend
# Note, the dummy backend does not parallelize the code!
from abcpy.backends import BackendDummy as Backend
backend = Backend()
# define observation for true parameters mean=170, std=15
height_obs = [
160.82499176, 167.24266737, 185.71695756, 153.7045709, 163.40568812,
140.70658699, 169.59102084, 172.81041696, 187.38782738, 179.66358934,
176.63417241, 189.16082803, 181.98288443, 170.18565017, 183.78493886,
166.58387299, 161.9521899, 155.69213073, 156.17867343, 144.51580379,
170.29847515, 197.96767899, 153.36646527, 162.22710198, 158.70012047,
178.53470703, 170.77697743, 164.31392633, 165.88595994, 177.38083686,
146.67058471763457, 179.41946565658628, 238.02751620619537,
206.22458790620766, 220.89530574344568, 221.04082532837026,
142.25301427453394, 261.37656571434275, 171.63761180867033,
210.28121820385866, 237.29130237612236, 175.75558340169619,
224.54340549862235, 197.42448680731226, 165.88273684581381,
166.55094082844519, 229.54308602661584, 222.99844054358519,
185.30223966014586, 152.69149367593846, 206.94372818527413,
256.35498655339154, 165.43140916577741, 250.19273595481803,
148.87781549665536, 223.05547559193792, 230.03418198709608,
146.13611923127021, 138.24716809523139, 179.26755740864527,
141.21704876815426, 170.89587081800852, 222.96391329259626,
188.27229523693822, 202.67075179617672, 211.75963110985992,
217.45423324370509
]
# define prior
from abcpy.continuousmodels import Uniform
mu = Uniform([[150], [200]], name="mu")
sigma = Uniform([[5], [25]], name="sigma")
# define the model
from abcpy.continuousmodels import Normal
height = Normal([mu, sigma], )
# define statistics
from abcpy.statistics import Identity
statistics_calculator = Identity(degree=3, cross=True)
# Learn the optimal summary statistics using Semiautomatic summary selection
from abcpy.statisticslearning import Semiautomatic
statistics_learning = Semiautomatic([height],
statistics_calculator,
backend,
n_samples=1000,
n_samples_per_param=1,
seed=1)
# Redefine the statistics function
new_statistics_calculator = statistics_learning.get_statistics()
# Learn the optimal summary statistics using SemiautomaticNN summary selection;
# we use 200 samples as a validation set for early stopping:
from abcpy.statisticslearning import SemiautomaticNN
statistics_learning = SemiautomaticNN([height],
statistics_calculator,
backend,
n_samples=1000,
n_samples_val=200,
n_samples_per_param=1,
seed=1,
early_stopping=True)
# Redefine the statistics function
new_statistics_calculator = statistics_learning.get_statistics()
# define distance
from abcpy.distances import Euclidean
distance_calculator = Euclidean(new_statistics_calculator)
# define kernel
from abcpy.perturbationkernel import DefaultKernel
kernel = DefaultKernel([mu, sigma])
# define sampling scheme
from abcpy.inferences import PMCABC
sampler = PMCABC([height], [distance_calculator], backend, kernel, seed=1)
eps_arr = np.array([
500
]) # starting value of epsilon; the smaller, the slower the algorithm.
# at each iteration, take as epsilon the epsilon_percentile of the distances obtained by simulations at previous
# iteration from the observation
epsilon_percentile = 10
journal = sampler.sample([height_obs], steps, eps_arr, n_sample,
n_samples_per_param, epsilon_percentile)
return journal
def infer_parameters():
# The data corresponding to model_1 defined below
grades_obs = [3.872486707973337, 4.6735380808674405, 3.9703538990858376, 4.11021272048805, 4.211048655421368, 4.154817956586653, 4.0046893064392695, 4.01891381384729, 4.123804757702919, 4.014941267301294, 3.888174595940634, 4.185275142948246, 4.55148774469135, 3.8954427675259016, 4.229264035335705, 3.839949451328312, 4.039402553532825, 4.128077814241238, 4.361488645531874, 4.086279074446419, 4.370801602256129, 3.7431697332475466, 4.459454162392378, 3.8873973643008255, 4.302566721487124, 4.05556051626865, 4.128817316703757, 3.8673704442215984, 4.2174459453805015, 4.202280254493361, 4.072851400451234, 3.795173229398952, 4.310702877332585, 4.376886328810306, 4.183704734748868, 4.332192463368128, 3.9071312388426587, 4.311681374107893, 3.55187913252144, 3.318878360783221, 4.187850500877817, 4.207923106081567, 4.190462065625179, 4.2341474252986036, 4.110228694304768, 4.1589891480847765, 4.0345604687633045, 4.090635481715123, 3.1384654393449294, 4.20375641386518, 4.150452690356067, 4.015304457401275, 3.9635442007388195, 4.075915739179875, 3.5702080541929284, 4.722333310410388, 3.9087618197155227, 4.3990088006390735, 3.968501165774181, 4.047603645360087, 4.109184340976979, 4.132424805281853, 4.444358334346812, 4.097211737683927, 4.288553086265748, 3.8668863066511303, 3.8837108501541007]
# The prior information changing the class size and the teacher student ratio, depending on the yearly budget of the school
from abcpy.continuousmodels import Uniform, Normal
school_budget = Uniform([[1], [10]], name = 'school_budget')
# The average class size of a certain school
class_size = Normal([[800*school_budget], [1]], name = 'class_size')
# The number of teachers in the school
no_teacher = Normal([[20*school_budget], [1]], name = 'no_teacher')
# The grade a student would receive without any bias
grade_without_additional_effects = Normal([[4.5], [0.25]], name = 'grade_without_additional_effects')
# The grade a student of a certain school receives
final_grade = grade_without_additional_effects - .001 * class_size + .02 * no_teacher
# The data corresponding to model_2 defined below
scholarship_obs = [2.7179657436207805, 2.124647285937229, 3.07193407853297, 2.335024761813643, 2.871893855192, 3.4332002458233837, 3.649996835818173, 3.50292335102711, 2.815638168018455, 2.3581613289315992, 2.2794821846395568, 2.8725835459926503, 3.5588573782815685, 2.26053126526137, 1.8998143530749971, 2.101110815311782, 2.3482974964831573, 2.2707679029919206, 2.4624550491079225, 2.867017757972507, 3.204249152084959, 2.4489542437714213, 1.875415915801106, 2.5604889644872433, 3.891985093269989, 2.7233633223405205, 2.2861070389383533, 2.9758813233490082, 3.1183403287267755, 2.911814060853062, 2.60896794303205, 3.5717098647480316, 3.3355752461779824, 1.99172284546858, 2.339937680892163, 2.9835630207301636, 2.1684912355975774, 3.014847335983034, 2.7844122961916202, 2.752119871525148, 2.1567428931391635, 2.5803629307680644, 2.7326646074552103, 2.559237193255186, 3.13478196958166, 2.388760269933492, 3.2822443541491815, 2.0114405441787437, 3.0380056368041073, 2.4889680313769724, 2.821660164621084, 3.343985964873723, 3.1866861970287808, 4.4535037154856045, 3.0026333138006027, 2.0675706089352612, 2.3835301730913185, 2.584208398359566, 3.288077633446465, 2.6955853384148183, 2.918315169739928, 3.2464814419322985, 2.1601516779909433, 3.231003347780546, 1.0893224045062178, 0.8032302688764734, 2.868438615047827]
# A quantity that determines whether a student will receive a scholarship
scholarship_without_additional_effects = Normal([[2], [0.5]], name = 'schol_without_additional_effects')
# A quantity determining whether a student receives a scholarship, including his social teacher_student_ratio
final_scholarship = scholarship_without_additional_effects + .03 * no_teacher
# Define a summary statistics for final grade and final scholarship
from abcpy.statistics import Identity
statistics_calculator_final_grade = Identity(degree = 2, cross = False)
statistics_calculator_final_scholarship = Identity(degree = 3, cross = False)
# Define a distance measure for final grade and final scholarship
from abcpy.distances import Euclidean
distance_calculator_final_grade = Euclidean(statistics_calculator_final_grade)
distance_calculator_final_scholarship = Euclidean(statistics_calculator_final_scholarship)
# Define a backend
from abcpy.backends import BackendDummy as Backend
backend = Backend()
# Define kernels
from abcpy.perturbationkernel import MultivariateNormalKernel, MultivariateStudentTKernel
kernel_1 = MultivariateNormalKernel([school_budget,\
scholarship_without_additional_effects, grade_without_additional_effects])
kernel_2 = MultivariateStudentTKernel([class_size, no_teacher], df=3)
# Join the defined kernels
from abcpy.perturbationkernel import JointPerturbationKernel
kernel = JointPerturbationKernel([kernel_1, kernel_2])
# Define sampling parameters
T, n_sample, n_samples_per_param = 3, 250, 10
eps_arr = np.array([.75])
epsilon_percentile = 10
# Define sampler
from abcpy.inferences import PMCABC
sampler = PMCABC([final_grade, final_scholarship], [distance_calculator, distance_calculator], backend, kernel)
# Sample
journal = sampler.sample([y_obs_grades, y_obs_scholarship], T, eps_arr, n_sample, n_samples_per_param, epsilon_percentile)
# Define backend
from abcpy.backends import BackendDummy as Backend
backend = Backend()
#
# Define Statistics
statistics_calculator = HakkarainenLorenzStatistics(degree=1, cross=False)
print('# Check whether the statistis works')
print(statistics_calculator.statistics(resultfakeobs1))
#
# Define distance
from abcpy.distances import Euclidean
distance_calculator = Euclidean(statistics_calculator)
#
print('# Check whether the distance works')
print(distance_calculator.distance(resultfakeobs1, resultfakeobs1))
print(distance_calculator.distance(resultfakeobs1, resultfakeobs2))
# Define kernel
from abcpy.perturbationkernel import MultivariateNormalKernel, JointPerturbationKernel
# Join the defined kernels
kernel1 = MultivariateNormalKernel([theta1, theta2])
kernel = JointPerturbationKernel([kernel1])
#
## APMCABC ##
from abcpy.inferences import APMCABC
# observed data
rseed = 42
rng = np.random.RandomState(rseed)
n_samples = int(T / dt) + 1
noise = rng.normal(loc=0, scale=0.05, size=(n_samples))
obs_data = hh_simulator.forward_simulate([gbar_K_true, gbar_Na_true])
# define statistics
# statistics_calculator = Identity()
t = stimulus_dict["t"]
stim_duration = stimulus_dict["duration"]
t_stim_on = stimulus_dict["t_stim_on"]
statistics_calculator = Features(t, stim_duration, t_stim_on)
# define distance
distance_calculator = Euclidean(statistics_calculator)
distance_calculator2 = Wasserstein(statistics_calculator)
distance_calculator3 = LogReg(statistics_calculator)
# checking
sim_data = hh_simulator.forward_simulate(
[gbar_K_true + 3, gbar_Na_true + 4])
#obs_data = [obs_data[0] / np.max(obs_data[0]) + noise]
#sim_data = [sim_data[0] / np.max(sim_data[0])]
s1 = statistics_calculator.statistics(obs_data)
s2 = statistics_calculator.statistics(sim_data)
dist = distance_calculator.distance(obs_data, sim_data)
dist2 = distance_calculator2.distance(obs_data, sim_data)
dist3 = distance_calculator3.distance(obs_data, sim_data)
def setUp(self):
self.stat_calc = Identity(degree=1, cross=0)
self.distancefunc = Euclidean(self.stat_calc)
true_parameters_fake_1 = [0.05, 5, 7, 5, 5, 6, 0.06, .1, .2, .3, .4, .1, .2, .3, .4, .5, 50, .4, .3, 0.3]
# print(len(true_parameters_fake_1))
observation_france_1 = model.forward_simulate(true_parameters_fake_1, 1)
true_parameters_fake_2 = [0.05, 5, 7, 5, 5, 6, 0.05, .1, .2, .3, .4, .1, .2, .3, .4, .5, 50, .4, .3, 0.3]
observation_france_2 = model.forward_simulate(true_parameters_fake_2, 1)
# we define now the statistics and distances:
rho = 1 # multiplier to decrease importance of past
distances_list = []
# this has to be used if the model returns already the correct observations (return_observation_only=True)
# now add the distance on the number of death and hospitalized people, that needs to discard the first 21 elements because there
# is no data on that before that.
for i in range(n):
distances_list.append(
Euclidean(ExtractSingleTimeseries2DArray(index=i, rho=rho, start_step=21, end_step=-1))) # deceased
distances_list.append(Euclidean(ExtractSingleTimeseries2DArray(index=5, rho=rho, start_step=17, end_step=-1)))
# define a weighted distance:
# max values of the daily counts: 1., 9., 73., 354., 462., 17933.
# we could use the inverse of them as weights; I think however the last timeseries have less noise as they are sampled
# from larger numbers, so they should be slightly less important.
weights = [1, 1, 1, 2, 2, .1]
# weights = [1.0 / 1 * 0.75, 1.0 / 9 * 0.75, 1.0 / 68 * 0.85, 1.0 / 338, 1.0 / 445, 1.0 / 4426]
# weights = [1, 0.1, 0.01, 0.005, 0.005, 0.005]
final_distance = WeightedDistance(distances_list, weights=weights)
print("dist", final_distance.distance(observation_france_1, [observation_france]))
# define backend
backend = Backend()
learned_triplet_stat.save_net("Data/Pilots/triplet_net_fake.pth")
else:
learned_seminn_stat.save_net("Data/Pilots/seminn_net_"+str(whichobs)+".pth")
learned_triplet_stat.save_net("Data/Pilots/triplet_net_"+str(whichobs)+".pth")
if sample:
if fake:
learned_seminn_stat_loaded = NeuralEmbedding.fromFile("Data/Pilots/seminn_net_fake.pth", input_size=len(InformativeIndices), output_size=7, previous_statistics=identity)
learned_triplet_stat_loaded = NeuralEmbedding.fromFile("Data/Pilots/triplet_net_fake.pth", input_size=len(InformativeIndices), output_size=7, previous_statistics=identity)
else:
learned_seminn_stat_loaded = NeuralEmbedding.fromFile("Data/Pilots/seminn_net_"+str(whichobs)+".pth", input_size=len(InformativeIndices), output_size=7, previous_statistics=identity)
learned_triplet_stat_loaded = NeuralEmbedding.fromFile("Data/Pilots/triplet_net_"+str(whichobs)+".pth", input_size=len(InformativeIndices), output_size=7, previous_statistics=identity)
# Define Distance functions
from abcpy.distances import Euclidean
dist_calc_seminn = Euclidean(learned_seminn_stat_loaded)
dist_calc_triplet = Euclidean(learned_triplet_stat_loaded)
from statistic import Multiply
L = np.load('Data/L_all_3_cross.npz')['L']
stat_mult = Multiply(L=L, degree=3, cross=True)
dist_calc_mult = Euclidean(stat_mult)
print(dist_calc_mult.distance(obsdata, obsdata))
# print('Inference starting')
# # ## SABC - SemiNN##
from abcpy.inferences import SABC
print('Inference using Semi NN')
sampler = SABC([PD], [dist_calc_seminn], backend, kernel, seed=1)
steps, epsilon, n_samples, n_samples_per_param, ar_cutoff, full_output, journal_file = 25, 10e20, 511, 1, 0.001, 1, None
print('SABC Inferring')
journal_sabc = sampler.sample(observations=[obsdata], steps=steps, epsilon=epsilon, n_samples=n_samples,