def rand_additive_basis(dag: DAG,
basis: list,
snr_dict: Optional[dict] = None,
rand_weight_fn: RandWeightFn = unif_away_zero,
noise=lambda: np.random.normal(0, 1),
internal_variance: int = 1,
num_monte_carlo: int = 10000,
progress=False):
"""
Generate a random structural causal model (SCM), using `dag` as the structure, and with each variable
being a general additive model (GAM) of its parents.
Parameters
----------
dag:
A DAG to use as the structure for the model.
basis:
Basis functions for the GAM.
snr_dict:
A dictionary mapping each number of parents to the desired signal-to-noise ratio (SNR) for nodes
with that many parents. By default, 1/2 for any number of parents.
rand_weight_fn:
A function to generate random weights for each parent.
noise:
A function to generate random internal noise for each node.
internal_variance:
The variance of the above noise function.
num_monte_carlo:
The number of Monte Carlo samples used when computing coefficients to achieve the desired SNR.
Examples
--------
>>> import causaldag as cd
>>> import numpy as np
>>> d = cd.DAG(arcs={(1, 2), (2, 3), (1, 3)})
>>> basis = [np.sin, np.cos, np.exp]
>>> snr_dict = {1: 1/2, 2: 2/3}
>>> g = cd.rand.rand_additive_basis(d, basis, snr_dict)
"""
if snr_dict is None:
snr_dict = {nparents: 1 / 2 for nparents in range(dag.nnodes)}
sample_dag = SampleDAG(dag._nodes, arcs=dag._arcs)
top_order = dag.topological_sort()
sample_dict = defaultdict(list)
# for each node, create the conditional
node_iterator = top_order if not progress else tqdm(top_order)
for node in node_iterator:
parents = dag.parents_of(node)
nparents = dag.indegree(node)
parent_bases = random.choices(basis, k=nparents)
parent_weights = rand_weight_fn(size=nparents)
c_node = None
if nparents > 0:
values_from_parents = []
for i in range(num_monte_carlo):
val = sum([
weight * base(sample_dict[parent][i]) for weight, base,
parent in zip(parent_weights, parent_bases, parents)
])
values_from_parents.append(val)
variance_from_parents = np.var(values_from_parents)
try:
desired_snr = snr_dict[nparents]
except ValueError:
raise Exception(
f"`snr_dict` does not specify a desired SNR for nodes with {nparents} parents"
)
c_node = internal_variance / variance_from_parents * desired_snr / (
1 - desired_snr)
conditional = partial(_cam_conditional,
c_node=c_node,
parent_weights=parent_weights,
parent_bases=parent_bases,
noise=noise)
for i in range(num_monte_carlo):
val = conditional([sample_dict[parent][i] for parent in parents])
sample_dict[node].append(val)
sample_dag.set_conditional(node, conditional)
return sample_dag
def rand_additive_basis(dag: DAG,
basis: list,
r2_dict: Optional[Union[Dict[int, float],
float]] = None,
rand_weight_fn: RandWeightFn = unif_away_zero,
noise=lambda size: np.random.normal(0, 1, size=size),
internal_variance: int = 1,
num_monte_carlo: int = 10000,
progress=False):
"""
Generate a random structural causal model (SCM), using `dag` as the structure, and with each variable
being a general additive model (GAM) of its parents.
Parameters
----------
dag:
A DAG to use as the structure for the model.
basis:
Basis functions for the GAM.
r2_dict:
A dictionary mapping each number of parents to the desired signal-to-noise ratio (SNR) for nodes
with that many parents. By default, 1/2 for any number of parents.
rand_weight_fn:
A function to generate random weights for each parent.
noise:
A function to generate random internal noise for each node.
internal_variance:
The variance of the above noise function.
num_monte_carlo:
The number of Monte Carlo samples used when computing coefficients to achieve the desired SNR.
Examples
--------
>>> import causaldag as cd
>>> import numpy as np
>>> d = cd.DAG(arcs={(1, 2), (2, 3), (1, 3)})
>>> basis = [np.sin, np.cos, np.exp]
>>> r2_dict = {1: 1/2, 2: 2/3}
>>> g = cd.rand.rand_additive_basis(d, basis, r2_dict)
"""
if r2_dict is None:
r2_dict = {nparents: 1 / 2 for nparents in range(dag.nnodes)}
if isinstance(r2_dict, float):
r2_dict = {nparents: r2_dict for nparents in range(dag.nnodes)}
cam_dag = CamDAG(dag._nodes, arcs=dag._arcs)
top_order = dag.topological_sort()
sample_dict = dict()
# for each node, create the conditional
node_iterator = top_order if not progress else tqdm(top_order)
for node in node_iterator:
parents = dag.parents_of(node)
nparents = dag.indegree(node)
parent2base = dict(zip(parents, random.choices(basis, k=nparents)))
parent_weights = rand_weight_fn(size=nparents)
parent_vals = np.array([
sample_dict[parent] for parent in parents
]).T if nparents > 0 else np.zeros([num_monte_carlo, 0])
c_node = 1
if nparents > 0:
mean_function_no_c = partial(_cam_mean_function,
c_node=1,
parent_weights=parent_weights,
parent2base=parent2base)
values_from_parents = mean_function_no_c(parent_vals, parents)
variance_from_parents = np.var(values_from_parents)
try:
desired_r2 = r2_dict[nparents]
except ValueError:
raise Exception(
f"`snr_dict` does not specify a desired R^2 for nodes with {nparents} parents"
)
c_node = internal_variance / variance_from_parents * desired_r2 / (
1 - desired_r2)
if np.isnan(c_node):
raise ValueError
print(node, parents, variance_from_parents, parent_weights, c_node)
mean_function = partial(_cam_mean_function,
c_node=c_node,
parent_weights=parent_weights,
parent2base=parent2base)
mean_vals = mean_function(parent_vals, parents)
sample_dict[node] = mean_vals + noise(size=num_monte_carlo)
cam_dag.set_mean_function(node, mean_function)
cam_dag.set_noise(node, noise)
return cam_dag