def sample_vp(vparams, draws=1000, model=None, random_seed=20090425):
"""Draw samples from variational posterior.
Parameters
----------
vparams : dict or pymc3.variational.ADVIFit
Estimated variational parameters of the model.
draws : int
Number of random samples.
model : pymc3.Model
Probabilistic model.
random_seed : int
Seed of random number generator.
Returns
-------
trace : pymc3.backends.base.MultiTrace
Samples drawn from the variational posterior.
"""
model = modelcontext(model)
if isinstance(vparams, ADVIFit):
vparams = {
'means': vparams.means,
'stds': vparams.stds
}
# Make dict for replacements of random variables
r = MRG_RandomStreams(seed=random_seed)
updates = {}
for var in model.free_RVs:
u = theano.shared(vparams['means'][str(var)]).ravel()
w = theano.shared(vparams['stds'][str(var)]).ravel()
n = r.normal(size=u.tag.test_value.shape)
updates.update({var: (n * w + u).reshape(var.tag.test_value.shape)})
vars = model.free_RVs
# Replace some nodes of the graph with variational distributions
samples = theano.clone(vars, updates)
f = theano.function([], samples)
varnames = [str(var) for var in model.unobserved_RVs]
trace = NDArray(model=model, vars=model.unobserved_RVs)
trace.setup(draws=draws, chain=0)
for i in range(draws):
# 'point' is like {'var1': np.array(0.1), 'var2': np.array(0.2), ...}
point = {varname: value for varname, value in zip(varnames, f())}
trace.record(point)
return MultiTrace([trace])
def subtrace(trace, chains, reset_chains=True):
"""Get Multitrace with subset of chains from a super Multitrace"""
if type(chains) is int:
chains = [chains]
elif type(chains) is not list:
raise TypeError('chains is of type {}. Expected int or list of int')
straces = []
for chain in chains:
if chain not in trace.chains:
raise ValueError('Invalid chain {} not in {}'.format(
chain, trace.chains))
straces.append(trace._straces[chain])
if reset_chains:
for new_chain_i, strace in enumerate(straces):
strace.chain = new_chain_i
return MultiTrace(straces)
def point_list_to_multitrace(point_list: List[Dict[str, np.ndarray]],
model: Optional[Model] = None) -> MultiTrace:
"""transform point list into MultiTrace"""
_model = modelcontext(model)
varnames = list(point_list[0].keys())
with _model:
chain = NDArray(model=_model, vars=[_model[vn] for vn in varnames])
chain.setup(draws=len(point_list), chain=0)
# since we are simply loading a trace by hand, we need only a vacuous function for
# chain.record() to use. This crushes the default.
def point_fun(point):
return [point[vn] for vn in varnames]
chain.fn = point_fun
for point in point_list:
chain.record(point)
return MultiTrace([chain])
def posterior_to_trace(self):
"""
Save results into a PyMC3 trace
"""
lenght_pos = len(self.posterior)
varnames = [v.name for v in self.variables]
with self.model:
strace = NDArray(self.model)
strace.setup(lenght_pos, 0)
for i in range(lenght_pos):
value = []
size = 0
for var in varnames:
shape, new_size = self.var_info[var]
value.append(self.posterior[i][size: size + new_size].reshape(shape))
size += new_size
strace.record({k: v for k, v in zip(varnames, value)})
return MultiTrace([strace])
def sample_vp(
vparams, draws=1000, model=None, local_RVs=None, random_seed=None,
hide_transformed=True, progressbar=True):
"""Draw samples from variational posterior.
Parameters
----------
vparams : dict or pymc3.variational.ADVIFit
Estimated variational parameters of the model.
draws : int
Number of random samples.
model : pymc3.Model
Probabilistic model.
random_seed : int or None
Seed of random number generator. None to use current seed.
hide_transformed : bool
If False, transformed variables are also sampled. Default is True.
Returns
-------
trace : pymc3.backends.base.MultiTrace
Samples drawn from the variational posterior.
"""
model = pm.modelcontext(model)
if isinstance(vparams, ADVIFit):
vparams = {
'means': vparams.means,
'stds': vparams.stds
}
ds = model.deterministics
def get_transformed(v):
return v if v not in ds else v.transformed
def rvs(x):
return [get_transformed(v) for v in x] if x is not None else []
global_RVs = list(set(model.free_RVs) - set(rvs(local_RVs)))
# Make dict for replacements of random variables
if random_seed is None:
r = MRG_RandomStreams(gen_random_state())
else:
r = MRG_RandomStreams(seed=random_seed)
updates = {}
for v in global_RVs:
u = theano.shared(vparams['means'][str(v)]).ravel()
w = theano.shared(vparams['stds'][str(v)]).ravel()
n = r.normal(size=u.tag.test_value.shape)
updates.update({v: (n * w + u).reshape(v.tag.test_value.shape)})
if local_RVs is not None:
for v_, (uw, _) in local_RVs.items():
v = get_transformed(v_)
u = uw[0].ravel()
w = uw[1].ravel()
n = r.normal(size=u.tag.test_value.shape)
updates.update(
{v: (n * tt.exp(w) + u).reshape(v.tag.test_value.shape)})
# Replace some nodes of the graph with variational distributions
vars = model.free_RVs
samples = theano.clone(vars, updates)
f = theano.function([], samples)
# Random variables which will be sampled
if hide_transformed:
vars_sampled = [v_ for v_ in model.unobserved_RVs
if not str(v_).endswith('_')]
else:
vars_sampled = [v_ for v_ in model.unobserved_RVs]
varnames = [str(var) for var in model.unobserved_RVs]
trace = pm.sampling.NDArray(model=model, vars=vars_sampled)
trace.setup(draws=draws, chain=0)
range_ = trange(draws) if progressbar else range(draws)
for _ in range_:
# 'point' is like {'var1': np.array(0.1), 'var2': np.array(0.2), ...}
point = {varname: value for varname, value in zip(varnames, f())}
trace.record(point)
return MultiTrace([trace])
def opt_nfo(
#Optimization parameters
#initialization
n0=10, #int, n0 the initial number of draws
init_samples=None, #array, Whether to provide some pre-defined sequence or do pymc3 sampling
#approximation
k_trunc=np.inf, #IW clipping, not used by default
eps_z=0.01, #float, tolerance on Z for q iter convergence (eps') #currently not used since not iterating SINF unless trainable
nf_iter=1, #int, number of NF iters -should always be 1 in our implementation
#annealing
N=10, #int, N the TOTAL number of draws we want at each iteration - this is no longer used, is from when we used to run multiple fits
t_ess=0.5, #float, ESS<t_ess*n0 t threshold on ESS for ESS3 (no longer temperature)
g_AF=0, #float, size of gradient contribution to AF, not used now
#exploration
N_AF=1000, #int,number of points to use in q_w sampling for AF
expl_top_AF=1, #int,cut for the top AF at a given temp level accepted at each beta
expl_latent=0, #int,latent draw from around top IW1 or around random draw from q_w, accepted at each step
expl_top_qw=0, #int,keep top q_w at this iteration
beta_max=1, #float>0,highest exponent on tempered posterior, support >1 for exploitation
rel_beta=1, #0<float<1, β2 = rel_beta*β, where β2 is the lower temp level used for sampling q_w, what we call 'X'
frac_rel_beta_AF=1, #int, the modifier to the AF used to up/down-weight the w vs uw contribution, what we call "Y"
latent_sigma=None, #float, the value of l
use_latent_beta2=False, #whether to get the latent sample from q_w(β2) or from q_uw
use_pq_beta_IW1=False, #whether to get the latent sample from near top IW1 or randomly from q_w
bounds=None, #array, size 2xd, bounding box for samples FIXME make this more obvious, needed for prior
N_temp=25, #int, cutoff on number of allowed temp iterations before giving up -> #FIXME eventually make this throw error
#NF parameters
model=None,
frac_validate=0.0,
iteration=None,
alpha_w=(0, 0),
alpha_uw=(0, 0),
verbose=False,
n_component=None,
interp_nbin=None,
KDE=True,
bw_factor_min=1.0,
bw_factor_max=1.0,
bw_factor_num=1,
rel_bw=1,
edge_bins=None,
ndata_wT=None,
MSWD_max_iter=None,
NBfirstlayer=True,
logit=False,
Whiten=False,
trainable_qw=False, #whether to improve our q_w at each beta iteration with SGD
sgd_steps=0, #number of steps used in Adam when training trainable q_w
knots_trainable=5,
batchsize=None,
nocuda=False,
patch=False,
shape=[28, 28, 1],
#Runtime
random_seed=-1,
parallel=False,
cores=None):
r"""
Normalizing flow-based Bayesian Optimization.
Parameters
----------
draws: int
The number of samples to draw from the posterior (i.e. last stage). And also the number of
independent chains. Defaults to 2000.
norm_tol: float
Fractional difference in the evidence estimate between two steps. If it falls below this we
stop iterating over the NF fits.
optim_iter: int
Maximum number of optimization steps to run during the initialization.
nf_iter: int
Number of NF fit iterations to go through after the optimization step.
model: Model (optional if in ``with`` context)).
frac_validate: float
Fraction of the live points at each NS iteration that we use for validation of the NF fit.
alpha: tuple of floats
Regularization parameters used for the NF fit.
verbose: boolean
Whether you want verbose output from the NF fit.
random_seed: int
random seed
parallel: bool
Distribute computations across cores if the number of cores is larger than 1.
Defaults to False.
cores : int
Number of cores available for the optimization step. Defaults to None, in which case the CPU
count is used.
"""
_log = logging.getLogger("pymc3")
_log.info("Initializing normalizing flow-based optimization...")
model = modelcontext(model)
if model.name:
raise NotImplementedError(
"The NS_NFO implementation currently does not support named models. "
"See https://github.com/pymc-devs/pymc3/pull/4365.")
if cores is None:
cores = _cpu_count()
chains = 1
_log.info(f"Sampling {chains} chain{'s' if chains > 1 else ''} "
f"Cores available for optimization: {cores}")
if random_seed == -1:
random_seed = None
if chains == 1 and isinstance(random_seed, int):
random_seed = [random_seed]
if random_seed is None or isinstance(random_seed, int):
if random_seed is not None:
np.random.seed(random_seed)
random_seed = [np.random.randint(2**30) for _ in range(chains)]
if not isinstance(random_seed, Iterable):
raise TypeError(
"Invalid value for `random_seed`. Must be tuple, list or int")
#we changed the name for end-user-facing readability, but internally more familiar with these names
aN, bN, cN, dN = N_AF, expl_top_AF, expl_latent, expl_top_qw
params = (
n0,
init_samples,
k_trunc,
eps_z,
nf_iter,
N,
t_ess,
g_AF,
aN,
bN,
cN,
dN,
beta_max,
rel_beta,
frac_rel_beta_AF,
latent_sigma,
use_latent_beta2,
use_pq_beta_IW1,
bounds,
N_temp,
model,
frac_validate,
iteration,
alpha_w,
alpha_uw,
cores,
verbose,
n_component,
interp_nbin,
KDE,
bw_factor_min,
bw_factor_max,
bw_factor_num,
rel_bw,
edge_bins,
ndata_wT,
MSWD_max_iter,
NBfirstlayer,
logit,
Whiten,
trainable_qw,
sgd_steps,
knots_trainable,
batchsize,
nocuda,
patch,
shape,
parallel,
)
t1 = time.time()
results = []
for i in range(chains):
results.append(opt_nfo_int(*params, random_seed[i], i, _log))
(
traces,
log_evidence,
q_samples,
importance_weights,
logp,
logq,
train_logp,
train_logq,
logZ,
q_models,
q_ess,
total_ess,
min_var_bws,
min_pq_bws,
betas,
) = zip(*results)
trace = MultiTrace(traces)
trace.report.log_evidence = log_evidence
trace.report.q_samples = q_samples
trace.report.importance_weights = importance_weights
trace.report.logp = logp
trace.report.logq = logq
trace.report.train_logp = train_logp
trace.report.train_logq = train_logq
trace.report.logZ = logZ
trace.report.q_models = q_models
trace.report.q_ess = q_ess
trace.report.total_ess = total_ess
trace.report.N = N
trace.report.min_var_bws = min_var_bws
trace.report.min_pq_bws = min_pq_bws
trace.report._t_sampling = time.time() - t1
trace.report.betas = betas
return trace
def sample_nfmc(draws=500,
init_draws=500,
resampling_draws=500,
init_ess=100,
init_method='prior',
init_samples=None,
start=None,
sample_mode='reinit',
finish_regularized=False,
cull_lowp_tol=0.05,
init_EL2O='adam',
mean_field_EL2O=False,
use_hess_EL2O=False,
absEL2O=1e-10,
fracEL2O=1e-2,
EL2O_draws=100,
maxiter_EL2O=500,
EL2O_optim_method='L-BFGS-B',
scipy_map_method='L-BFGS-B',
adam_lr=1e-3,
adam_b1=0.9,
adam_b2=0.999,
adam_eps=1.0e-8,
adam_steps=1000,
simulator=None,
model_data=None,
sim_data_cov=None,
sim_size=None,
sim_params=None,
sim_start=None,
sim_optim_method='lbfgs',
sim_tol=0.01,
local_thresh=3,
local_step_size=0.1,
local_grad=True,
init_local=True,
full_local=False,
nf_local_iter=3,
max_line_search=100,
k_trunc=0.25,
norm_tol=0.01,
ess_tol=0.5,
optim_iter=1000,
ftol=2.220446049250313e-9,
gtol=1.0e-5,
nf_iter=3,
model=None,
frac_validate=0.1,
iteration=None,
final_iteration=None,
alpha=(0, 0),
final_alpha=(0.75, 0.75),
verbose=False,
n_component=None,
interp_nbin=None,
KDE=True,
bw_factor_min=0.5,
bw_factor_max=2.5,
bw_factor_num=11,
edge_bins=None,
ndata_wT=None,
MSWD_max_iter=None,
NBfirstlayer=True,
logit=False,
Whiten=False,
batchsize=None,
nocuda=False,
patch=False,
shape=[28, 28, 1],
redraw=True,
random_seed=-1,
parallel=False,
chains=None,
cores=None):
r"""
Normalizing flow based nested sampling.
Parameters
----------
draws: int
The number of samples to draw from the posterior (i.e. last stage). And also the number of
independent chains. Defaults to 2000.
start: dict, or array of dict
Starting point in parameter space. It should be a list of dict with length `chains`.
When None (default) the starting point is sampled from the prior distribution.
init_method: str
Tells us how to initialize the NFMC fits. Default is 'prior'. If this is supplied along with init_samples
we use those instead. Current options are 'prior', 'full_rank', 'lbfgs'.
norm_tol: float
Fractional difference in the evidence estimate between two steps. If it falls below this we
stop iterating over the NF fits.
optim_iter: int
Maximum number of optimization steps to run during the initialization.
nf_iter: int
Number of NF fit iterations to go through after the optimization step.
model: Model (optional if in ``with`` context)).
frac_validate: float
Fraction of the live points at each NS iteration that we use for validation of the NF fit.
alpha: tuple of floats
Regularization parameters used for the NF fit.
verbose: boolean
Whether you want verbose output from the NF fit.
random_seed: int
random seed
parallel: bool
Distribute computations across cores if the number of cores is larger than 1.
Defaults to False.
cores : int
Number of cores available for the optimization step. Defaults to None, in which case the CPU
count is used.
chains : int
The number of chains to sample. Running independent chains is important for some
convergence statistics. Default is 2.
"""
_log = logging.getLogger("pymc3")
_log.info("Initializing normalizing flow based sampling...")
model = modelcontext(model)
if model.name:
raise NotImplementedError(
"The NS_NFMC implementation currently does not support named models. "
"See https://github.com/pymc-devs/pymc3/pull/4365.")
if cores is None:
cores = _cpu_count()
_log.info(f"Sampling {chains} chain{'s' if chains > 1 else ''} "
f"Cores available for optimization: {cores}")
if random_seed == -1:
random_seed = None
if chains == 1 and isinstance(random_seed, int):
random_seed = [random_seed]
if random_seed is None or isinstance(random_seed, int):
if random_seed is not None:
np.random.seed(random_seed)
random_seed = [np.random.randint(2**30) for _ in range(chains)]
if not isinstance(random_seed, Iterable):
raise TypeError(
"Invalid value for `random_seed`. Must be tuple, list or int")
assert (sample_mode == 'reinit' or sample_mode == 'keep_local'
or sample_mode == 'function_approx')
params = (
draws,
init_draws,
resampling_draws,
init_ess,
init_method,
init_samples,
start,
sample_mode,
finish_regularized,
cull_lowp_tol,
init_EL2O,
mean_field_EL2O,
use_hess_EL2O,
absEL2O,
fracEL2O,
EL2O_draws,
maxiter_EL2O,
EL2O_optim_method,
scipy_map_method,
adam_lr,
adam_b1,
adam_b2,
adam_eps,
adam_steps,
simulator,
model_data,
sim_data_cov,
sim_size,
sim_params,
sim_start,
sim_optim_method,
sim_tol,
local_thresh,
local_step_size,
local_grad,
init_local,
full_local,
nf_local_iter,
max_line_search,
k_trunc,
norm_tol,
ess_tol,
optim_iter,
ftol,
gtol,
nf_iter,
model,
frac_validate,
iteration,
final_iteration,
alpha,
final_alpha,
cores,
verbose,
n_component,
interp_nbin,
KDE,
bw_factor_min,
bw_factor_max,
bw_factor_num,
edge_bins,
ndata_wT,
MSWD_max_iter,
NBfirstlayer,
logit,
Whiten,
batchsize,
nocuda,
patch,
shape,
redraw,
parallel,
)
t1 = time.time()
results = []
for i in range(chains):
results.append(sample_nfmc_int(*params, random_seed[i], i, _log))
(traces, log_evidence, q_samples, importance_weights, total_samples,
total_weights, logp, logq, train_logp, train_logq, logZ, q_models, q_ess,
train_ess, total_ess, min_var_bws, min_pq_bws) = zip(*results)
trace = MultiTrace(traces)
trace.report.log_evidence = log_evidence
trace.report.q_samples = q_samples
trace.report.importance_weights = importance_weights
trace.report.total_samples = total_samples
trace.report.total_weights = total_weights
trace.report.logp = logp
trace.report.logq = logq
trace.report.train_logp = train_logp
trace.report.train_logq = train_logq
trace.report.logZ = logZ
trace.report.q_models = q_models
trace.report.q_ess = q_ess
trace.report.train_ess = train_ess
trace.report.total_ess = total_ess
trace.report._n_draws = draws
trace.report.min_var_bws = min_var_bws
trace.report.min_pq_bws = min_pq_bws
trace.report._t_sampling = time.time() - t1
return trace
def sample_ns_nfmc(
draws=2000,
start=None,
rho=0.01,
epsilon=0.01,
model=None,
frac_validate=0.8,
alpha=(0,0),
verbose=False,
random_seed=-1,
parallel=False,
chains=None,
cores=None,
):
r"""
Normalizing flow based nested sampling.
Parameters
----------
draws: int
The number of samples to draw from the posterior (i.e. last stage). And also the number of
independent chains. Defaults to 2000.
start: dict, or array of dict
Starting point in parameter space. It should be a list of dict with length `chains`.
When None (default) the starting point is sampled from the prior distribution.
rho: float
Sets fraction of points we want to be above the likelihood threshold at each iteration.
Used to adaptively set the likelihood threshold during sampling.
epsilon: float
Stopping factor for the algorithm. At each iteration we compare the ratio of the evidences
from the current and previous iterations. If it is less than 1-epsilon we stop.
model: Model (optional if in ``with`` context)).
frac_validate: float
Fraction of the live points at each NS iteration that we use for validation of the NF fit.
alpha: tuple of floats
Regularization parameters used for the NF fit.
verbose: boolean
Whether you want verbose output from the NF fit.
random_seed: int
random seed
parallel: bool
Distribute computations across cores if the number of cores is larger than 1.
Defaults to False.
cores : int
The number of chains to run in parallel. If ``None``, set to the number of CPUs in the
system, but at most 4.
chains : int
The number of chains to sample. Running independent chains is important for some
convergence statistics. If ``None`` (default), then set to either ``cores`` or 2, whichever
is larger.
"""
_log = logging.getLogger("pymc3")
_log.info("Initializing normalizing flow based nested sampling...")
model = modelcontext(model)
if model.name:
raise NotImplementedError(
"The NS_NFMC implementation currently does not support named models. "
"See https://github.com/pymc-devs/pymc3/pull/4365."
)
if cores is None:
cores = _cpu_count()
if chains is None:
chains = max(2, cores)
elif chains == 1:
cores = 1
_log.info(
f"Sampling {chains} chain{'s' if chains > 1 else ''} "
f"in {cores} job{'s' if cores > 1 else ''}"
)
if random_seed == -1:
random_seed = None
if chains == 1 and isinstance(random_seed, int):
random_seed = [random_seed]
if random_seed is None or isinstance(random_seed, int):
if random_seed is not None:
np.random.seed(random_seed)
random_seed = [np.random.randint(2 ** 30) for _ in range(chains)]
if not isinstance(random_seed, Iterable):
raise TypeError("Invalid value for `random_seed`. Must be tuple, list or int")
params = (
draws,
start,
rho,
epsilon,
model,
frac_validate,
alpha,
verbose,
)
t1 = time.time()
if parallel and chains > 1:
loggers = [_log] + [None] * (chains - 1)
pool = mp.Pool(cores)
results = pool.starmap(
sample_ns_nfmc_int, [(*params, random_seed[i], i, loggers[i]) for i in range(chains)]
)
pool.close()
pool.join()
else:
results = []
for i in range(chains):
results.append(sample_ns_nfmc_int(*params, random_seed[i], i, _log))
(
traces,
log_evidence,
log_evidences,
likelihood_logp_thresh,
) = zip(*results)
trace = MultiTrace(traces)
trace.report._n_draws = draws
trace.report.log_evidence = np.array(log_evidence)
trace.report._t_sampling = time.time() - t1
return trace
def sample_smc(
draws=2000,
kernel="metropolis",
n_steps=25,
start=None,
tune_steps=True,
p_acc_rate=0.85,
threshold=0.5,
save_sim_data=False,
save_log_pseudolikelihood=True,
model=None,
random_seed=-1,
parallel=False,
chains=None,
cores=None,
):
r"""
Sequential Monte Carlo based sampling.
Parameters
----------
draws: int
The number of samples to draw from the posterior (i.e. last stage). And also the number of
independent chains. Defaults to 2000.
kernel: str
Kernel method for the SMC sampler. Available option are ``metropolis`` (default) and `ABC`.
Use `ABC` for likelihood free inference together with a ``pm.Simulator``.
n_steps: int
The number of steps of each Markov Chain. If ``tune_steps == True`` ``n_steps`` will be used
for the first stage and for the others it will be determined automatically based on the
acceptance rate and `p_acc_rate`, the max number of steps is ``n_steps``.
start: dict, or array of dict
Starting point in parameter space. It should be a list of dict with length `chains`.
When None (default) the starting point is sampled from the prior distribution.
tune_steps: bool
Whether to compute the number of steps automatically or not. Defaults to True
p_acc_rate: float
Used to compute ``n_steps`` when ``tune_steps == True``. The higher the value of
``p_acc_rate`` the higher the number of steps computed automatically. Defaults to 0.85.
It should be between 0 and 1.
threshold: float
Determines the change of beta from stage to stage, i.e.indirectly the number of stages,
the higher the value of `threshold` the higher the number of stages. Defaults to 0.5.
It should be between 0 and 1.
save_sim_data : bool
Whether or not to save the simulated data. This parameter only works with the ABC kernel.
The stored data corresponds to a samples from the posterior predictive distribution.
save_log_pseudolikelihood : bool
Whether or not to save the log pseudolikelihood values. This parameter only works with the
ABC kernel. The stored data can be used to compute LOO or WAIC values. Computing LOO/WAIC
values from log pseudolikelihood values is experimental.
model: Model (optional if in ``with`` context)).
random_seed: int
random seed
parallel: bool
Distribute computations across cores if the number of cores is larger than 1.
Defaults to False.
cores : int
The number of chains to run in parallel. If ``None``, set to the number of CPUs in the
system, but at most 4.
chains : int
The number of chains to sample. Running independent chains is important for some
convergence statistics. If ``None`` (default), then set to either ``cores`` or 2, whichever
is larger.
Notes
-----
SMC works by moving through successive stages. At each stage the inverse temperature
:math:`\beta` is increased a little bit (starting from 0 up to 1). When :math:`\beta` = 0
we have the prior distribution and when :math:`\beta` =1 we have the posterior distribution.
So in more general terms we are always computing samples from a tempered posterior that we can
write as:
.. math::
p(\theta \mid y)_{\beta} = p(y \mid \theta)^{\beta} p(\theta)
A summary of the algorithm is:
1. Initialize :math:`\beta` at zero and stage at zero.
2. Generate N samples :math:`S_{\beta}` from the prior (because when :math `\beta = 0` the
tempered posterior is the prior).
3. Increase :math:`\beta` in order to make the effective sample size equals some predefined
value (we use :math:`Nt`, where :math:`t` is 0.5 by default).
4. Compute a set of N importance weights W. The weights are computed as the ratio of the
likelihoods of a sample at stage i+1 and stage i.
5. Obtain :math:`S_{w}` by re-sampling according to W.
6. Use W to compute the mean and covariance for the proposal distribution, a MVNormal.
7. For stages other than 0 use the acceptance rate from the previous stage to estimate
`n_steps`.
8. Run N independent Metropolis-Hastings (IMH) chains (each one of length `n_steps`),
starting each one from a different sample in :math:`S_{w}`. Samples are IMH as the proposal
mean is the of the previous posterior stage and not the current point in parameter space.
9. Repeat from step 3 until :math:`\beta \ge 1`.
10. The final result is a collection of N samples from the posterior.
References
----------
.. [Minson2013] Minson, S. E. and Simons, M. and Beck, J. L., (2013),
Bayesian inversion for finite fault earthquake source models I- Theory and algorithm.
Geophysical Journal International, 2013, 194(3), pp.1701-1726,
`link <https://gji.oxfordjournals.org/content/194/3/1701.full>`__
.. [Ching2007] Ching, J. and Chen, Y. (2007).
Transitional Markov Chain Monte Carlo Method for Bayesian Model Updating, Model Class
Selection, and Model Averaging. J. Eng. Mech., 10.1061/(ASCE)0733-9399(2007)133:7(816),
816-832. `link <http://ascelibrary.org/doi/abs/10.1061/%28ASCE%290733-9399
%282007%29133:7%28816%29>`__
"""
_log = logging.getLogger("pymc3")
_log.info("Initializing SMC sampler...")
model = modelcontext(model)
if model.name:
raise NotImplementedError(
"The SMC implementation currently does not support named models. "
"See https://github.com/pymc-devs/pymc3/pull/4365.")
if cores is None:
cores = _cpu_count()
if chains is None:
chains = max(2, cores)
elif chains == 1:
cores = 1
_log.info(f"Sampling {chains} chain{'s' if chains > 1 else ''} "
f"in {cores} job{'s' if cores > 1 else ''}")
if random_seed == -1:
random_seed = None
if chains == 1 and isinstance(random_seed, int):
random_seed = [random_seed]
if random_seed is None or isinstance(random_seed, int):
if random_seed is not None:
np.random.seed(random_seed)
random_seed = [np.random.randint(2**30) for _ in range(chains)]
if not isinstance(random_seed, Iterable):
raise TypeError(
"Invalid value for `random_seed`. Must be tuple, list or int")
if kernel.lower() == "abc":
if len(model.observed_RVs) != 1:
warnings.warn(
"SMC-ABC only works properly with models with one observed variable"
)
if model.potentials:
_log.info("Potentials will be added to the prior term")
params = (
draws,
kernel,
n_steps,
start,
tune_steps,
p_acc_rate,
threshold,
save_sim_data,
save_log_pseudolikelihood,
model,
)
t1 = time.time()
if parallel and chains > 1:
loggers = [_log] + [None] * (chains - 1)
pool = mp.Pool(cores)
results = pool.starmap(sample_smc_int,
[(*params, random_seed[i], i, loggers[i])
for i in range(chains)])
pool.close()
pool.join()
else:
results = []
for i in range(chains):
results.append(sample_smc_int(*params, random_seed[i], i, _log))
(
traces,
sim_data,
log_marginal_likelihoods,
log_pseudolikelihood,
betas,
accept_ratios,
nsteps,
) = zip(*results)
trace = MultiTrace(traces)
trace.report._n_draws = draws
trace.report._n_tune = 0
trace.report.log_marginal_likelihood = np.array(log_marginal_likelihoods)
trace.report.log_pseudolikelihood = log_pseudolikelihood
trace.report.betas = betas
trace.report.accept_ratios = accept_ratios
trace.report.nsteps = nsteps
trace.report._t_sampling = time.time() - t1
if save_sim_data:
return trace, {
modelcontext(model).observed_RVs[0].name: np.array(sim_data)
}
else:
return trace
def sample_nf_smc(
draws=2000,
start=None,
threshold=0.5,
frac_validate=0.1,
iteration=5,
alpha=(0, 0),
k_trunc=0.25,
pareto=False,
epsilon=1e-3,
local_thresh=3,
local_step_size=0.1,
local_grad=True,
nf_local_iter=0,
max_line_search=2,
verbose=False,
n_component=None,
interp_nbin=None,
KDE=True,
bw_factor=0.5,
edge_bins=None,
ndata_wT=None,
MSWD_max_iter=None,
NBfirstlayer=True,
logit=False,
Whiten=False,
batchsize=None,
nocuda=False,
patch=False,
shape=[28, 28, 1],
model=None,
random_seed=-1,
parallel=False,
chains=None,
cores=None,
):
r"""
Sequential Monte Carlo based sampling.
Parameters
----------
draws: int
The number of samples to draw from the posterior (i.e. last stage). And also the number of
independent chains. Defaults to 2000.
start: dict, or array of dict
Starting point in parameter space. It should be a list of dict with length `chains`.
When None (default) the starting point is sampled from the prior distribution.
threshold: float
Determines the change of beta from stage to stage, i.e.indirectly the number of stages,
the higher the value of `threshold` the higher the number of stages. Defaults to 0.5.
It should be between 0 and 1.
model: Model (optional if in ``with`` context)).
random_seed: int
random seed
parallel: bool
Distribute computations across cores if the number of cores is larger than 1.
Defaults to False.
cores : int
The number of chains to run in parallel. If ``None``, set to the number of CPUs in the
system, but at most 4.
chains : int
The number of chains to sample. Running independent chains is important for some
convergence statistics. If ``None`` (default), then set to either ``cores`` or 2, whichever
is larger.
Notes
-----
SMC works by moving through successive stages. At each stage the inverse temperature
:math:`\beta` is increased a little bit (starting from 0 up to 1). When :math:`\beta` = 0
we have the prior distribution and when :math:`\beta` =1 we have the posterior distribution.
So in more general terms we are always computing samples from a tempered posterior that we can
write as:
.. math::
p(\theta \mid y)_{\beta} = p(y \mid \theta)^{\beta} p(\theta)
A summary of the algorithm is:
1. Initialize :math:`\beta` at zero and stage at zero.
2. Generate N samples :math:`S_{\beta}` from the prior (because when :math `\beta = 0` the
tempered posterior is the prior).
3. Increase :math:`\beta` in order to make the effective sample size equals some predefined
value (we use :math:`Nt`, where :math:`t` is 0.5 by default).
4. Compute a set of N importance weights W. The weights are computed as the ratio of the
likelihoods of a sample at stage i+1 and stage i.
5. Obtain :math:`S_{w}` by re-sampling according to W.
6. Use W to compute the mean and covariance for the proposal distribution, a MVNormal.
7. For stages other than 0 use the acceptance rate from the previous stage to estimate
`n_steps`.
8. Run N independent Metropolis-Hastings (IMH) chains (each one of length `n_steps`),
starting each one from a different sample in :math:`S_{w}`. Samples are IMH as the proposal
mean is the of the previous posterior stage and not the current point in parameter space.
9. Repeat from step 3 until :math:`\beta \ge 1`.
10. The final result is a collection of N samples from the posterior.
References
----------
.. [Minson2013] Minson, S. E. and Simons, M. and Beck, J. L., (2013),
Bayesian inversion for finite fault earthquake source models I- Theory and algorithm.
Geophysical Journal International, 2013, 194(3), pp.1701-1726,
`link <https://gji.oxfordjournals.org/content/194/3/1701.full>`__
.. [Ching2007] Ching, J. and Chen, Y. (2007).
Transitional Markov Chain Monte Carlo Method for Bayesian Model Updating, Model Class
Selection, and Model Averaging. J. Eng. Mech., 10.1061/(ASCE)0733-9399(2007)133:7(816),
816-832. `link <http://ascelibrary.org/doi/abs/10.1061/%28ASCE%290733-9399
%282007%29133:7%28816%29>`__
"""
_log = logging.getLogger("pymc3")
_log.info("Initializing SMC+SINF sampler...")
model = modelcontext(model)
if model.name:
raise NotImplementedError(
"The SMC implementation currently does not support named models. "
"See https://github.com/pymc-devs/pymc3/pull/4365.")
if cores is None:
cores = _cpu_count()
if chains is None:
chains = max(2, cores)
elif chains == 1:
cores = 1
_log.info(f"Sampling {chains} chain{'s' if chains > 1 else ''} "
f"in {cores} job{'s' if cores > 1 else ''}")
if random_seed == -1:
random_seed = None
if chains == 1 and isinstance(random_seed, int):
random_seed = [random_seed]
if random_seed is None or isinstance(random_seed, int):
if random_seed is not None:
np.random.seed(random_seed)
random_seed = [np.random.randint(2**30) for _ in range(chains)]
if not isinstance(random_seed, Iterable):
raise TypeError(
"Invalid value for `random_seed`. Must be tuple, list or int")
params = (
draws,
start,
threshold,
frac_validate,
iteration,
alpha,
k_trunc,
pareto,
epsilon,
local_thresh,
local_step_size,
local_grad,
nf_local_iter,
max_line_search,
verbose,
n_component,
interp_nbin,
KDE,
bw_factor,
edge_bins,
ndata_wT,
MSWD_max_iter,
NBfirstlayer,
logit,
Whiten,
batchsize,
nocuda,
patch,
shape,
model,
)
t1 = time.time()
if parallel and chains > 1:
loggers = [_log] + [None] * (chains - 1)
pool = mp.Pool(cores)
results = pool.starmap(sample_nf_smc_int,
[(*params, random_seed[i], i, loggers[i])
for i in range(chains)])
pool.close()
pool.join()
else:
results = []
for i in range(chains):
results.append(sample_nf_smc_int(*params, random_seed[i], i, _log))
(
traces,
log_marginal_likelihood,
q_samples,
q_log_weights,
betas,
) = zip(*results)
trace = MultiTrace(traces)
trace.report._n_draws = draws
trace.report.log_marginal_likelihood = log_marginal_likelihood
trace.report.q_samples = q_samples
trace.report.q_log_weights = q_log_weights
trace.report.betas = betas
trace.report._t_sampling = time.time() - t1
return trace