ananke.models package¶
Submodules¶
ananke.models.binary_nested module¶
Implements the Nested Markov parameterization for acyclic directed mixed graphs over binary variables.
The code relies on the following papers:
[ER12] Evans, R. J., & Richardson, T. S. (2012). Maximum likelihood fitting of acyclic directed mixed graphs to binary data. arXiv preprint arXiv:1203.3479. [ER19] Evans, R. J., & Richardson, T. S. (2019). Smooth, identifiable supermodels of discrete DAG models with latent variables. Bernoulli, 25(2), 848-876.
- class ananke.models.binary_nested.BinaryNestedModel(graph)[source]¶
Bases:
object
Estimates parameters of nested binary model using the iterative maximum likelihood algorithm (Algorithm 1) of [ER12]. Performs scipy.minimize constrained minimization of negative log-likelihood.
- estimate(treatment_dict=None, outcome_dict=None)[source]¶
Estimates p(Y(a)=y) for treatment A=a, outcome Y=y using the binary nested Markov parameters.
- Parameters
treatment_dict – dict of treatment variables to values
outcome_dict – dict of outcome variables to values
- Returns
interventional probability p(Y(a))
- fit(X, q_vector=None, tol=1e-08, *args, **kwargs)[source]¶
Fits the binary nested model. Let N the number of observations, M the number of variables.
- Parameters
X – Either a N x M pandas DataFrame where each row represents an observation, or an 2 ** M x (M+1) pandas DataFrame, where each row represents the observation through a count variable
args –
kwargs –
- Returns
- ananke.models.binary_nested.compute_M(G, partition_head_dict, district, heads_tails_map, terms)[source]¶
Compute M matrix as given in Section 3.1 of [ER12]
- Parameters
G – ADMG graph
partition_head_dict – dictionary mapping every subset of given district to constituent heads
district – a district of the graph
heads_tails_map – dictionary mapping heads to tails
terms – list of terms of given district
- Returns
- ananke.models.binary_nested.compute_P(partition_head_dict, q_vector_keys, heads_tails_map, terms)[source]¶
Computes P matrix as given in Section 3.1 of [ER12]
- Parameters
partition_head_dict – dictionary mapping every subset of given district to constituent heads
q_vector_keys – list of parameter names
heads_tails_map – dictionary mapping heads to tails
terms – list of all terms for a given district
- Returns
- ananke.models.binary_nested.compute_all_M_and_P(G, intrinsic_dict)[source]¶
Computes for each district of a graph, the corresponding M and P matrices required to compute the expression
\[p(q) = \prod_j M_j \exp(P_j \log q_j)\]See Section 3.1 of [ER12] for further details.
- Parameters
G – ADMG
intrinsic_dict – mapping of intrinsic set to heads and tails
- Returns
- ananke.models.binary_nested.compute_counterfactual_binary_parameters(G, q_vector, x_dict, y_dict)[source]¶
Computes a counterfactual (interventional quantity) p(Y=y | do(X=x)) using nested Markov parameters and graph
- Parameters
G – ADMG
q_vector – A dictionary of nested Markov parameters
x_dict – A dictionary of treatment variables to treatment values
y_dict – A dictionary of outcome variables to outcome values
- Returns
Computed probability p(Y=y | do(X=x))
- ananke.models.binary_nested.compute_district_bool_map(q_vector_keys, districts)[source]¶
- Parameters
q_vector_keys –
districts –
- Returns
- ananke.models.binary_nested.compute_likelihood_district(nu_dict, q_vector, district, heads_tails_map, intrinsic_dict)[source]¶
Compute likelihood directly using Equation (1) of [ER12].
This likelihood is not recommended for use in maximization as it is more efficiently expressed using M and P computations.
- Parameters
nu_dict – a dictionary representing a single observation of variables to value
q_vector – dictionary mapping the head, tail, tail value to parameter value
district – district of graph
heads_tails_map – mapping of heads to tails
intrinsic_dict – mapping of intrinsic set to heads and tails
- Returns
- ananke.models.binary_nested.compute_partition_head_dict(intrinsic_dict, district)[source]¶
Compute partition head dictionary. Maps every subset of a district to its constituent maximal recursive heads
- Parameters
intrinsic_dict – dictionary mapping intrinsic sets to (heads, tails) of that set
district – district of graph
- Returns
- ananke.models.binary_nested.compute_q_indices_by_district(q_vector_keys, districts)[source]¶
Computes a boolean indexing array that indicates which q parameters are involved in which districts.
- Parameters
q_vector_keys –
districts –
- Returns
- ananke.models.binary_nested.compute_terms(district, intrinsic_dict, heads_tails_map)[source]¶
Computes list of terms (product of q parameters) and the partition head dictionary. Each term is a tuple of (frozenset(all heads), tuple(all tails), tuple(values of all tails)).
- Parameters
district – district of graph
intrinsic_dict – dictionary mapping intrinsic sets to (heads, tails) of that set
heads_tails_map – dictionary mapping heads to tails
- Returns
- ananke.models.binary_nested.compute_theta_bool_map(q_vector_keys, variables)[source]¶
Compute map from variable to boolean indexing vector of q_parameters which have heads containing that variable. In this map, the indices are not reindexed by district. The boolean vector selects parameters which have heads containing that variable.
- Parameters
q_vector_keys – list of q_vector keys
variables – list of variables
- Returns
- ananke.models.binary_nested.compute_theta_reindexed_bool_map(q_vector_keys, districts)[source]¶
Creates a mapping from a variable to a boolean indexing vector.
This boolean vector indexes only parameters whose heads are involved in the district of that variable. It selects parameters which have heads containing that variable.
Used to construct A and b matrices for partial likelihood.
- Parameters
q_vector_keys – list of q_vector keys
districts – list of districts
- Returns
- ananke.models.binary_nested.construct_A_b(variable, q, theta_reindexed_bool_map, M, P)[source]¶
Constructs A and b matrices (eqn 4, Evans and Richardson 2013) for constraining parameters of given variable, in district which admits matrices M, P
- Parameters
variable – name of variable
q_vector – q_vector in OrderedDict format
M – M matrix
P – P matrix
- Returns
- ananke.models.binary_nested.get_heads_tails_map(intrinsic_dict)[source]¶
Get mapping of heads to tails from a mapping of intrinsic sets
- Parameters
intrinsic_dict – mapping of intrinsic sets of some graph to heads and tails
- Returns
- ananke.models.binary_nested.get_recursive_heads(intrinsic_dict)[source]¶
Compute all heads of intrinsic sets
- Parameters
intrinsic_dict – mapping of intrinsic sets of some graph to heads and tails
- Returns
list of all heads
- ananke.models.binary_nested.initialize_q_vector(intrinsic_dict)[source]¶
Generates the q_vector, a dictionary mapping (heads: frozenset, tails: tuple, value of tail: tuple) to parameter. Default q parameter values are 1/2^#(head), for each head.
- Parameters
intrinsic_dict – mapping of intrinsic sets of some graph to heads and tails
- Return q_vector
- ananke.models.binary_nested.maximal_heads(list_H, intrinsic_dict)[source]¶
Returns maximal heads for a set of heads. Only defined if all heads in list_H (list) are in IHT, ie, they are all heads of intrinsic sets
- ananke.models.binary_nested.permutations(n, k=2)[source]¶
Computes tuples of all permutations of n variables with cardinality k.
- Parameters
n – number of variables
k – cardinality of each variable
- Returns
- ananke.models.binary_nested.process_data(df, count_variable=None)[source]¶
- Parameters
data – pandas DataFrame columns of variables and rows of observations
count_variable – optional name of counting variable, if data is provided as a summary table
- Returns
a vector of counts, ordered in ascending order of v for p(V=v)
ananke.models.linear_gaussian_sem module¶
Class for Linear Gaussian SEMs parametrized by a matrix B representing regression coefficients and a matrix Omega representing correlated errors
- class ananke.models.linear_gaussian_sem.LinearGaussianSEM(graph)[source]¶
Bases:
object
- bic(X)[source]¶
Calculate Bayesian information criterion of the data given the model.
- Parameters
X – a N x M dimensional data matrix.
weights – optional 1d numpy array with weights for each data point (rows with higher weights are given greater importance).
- Returns
a float corresponding to the log-likelihood.
- draw(direction=None)[source]¶
Visualize the graph.
:return : dot language representation of the graph.
- fit(X, tol=1e-06, disp=None, standardize=False, max_iters=100)[source]¶
Fit the model to data via (weighted) maximum likelihood estimation
- Parameters
X – data – a N x M dimensional pandas data frame.
weights – optional 1d numpy array with weights for each data point (rows with higher weights are given greater importance).
- Returns
self.
- neg_loglikelihood(X)[source]¶
Calculate log-likelihood of the data given the model.
- Parameters
X – a N x M dimensional data matrix.
weights – optional 1d numpy array with weights for each data point (rows with higher weights are given greater importance).
- Returns
a float corresponding to the log-likelihood.
- total_effect(A, Y)[source]¶
Calculate the total causal effect of a set of treatments A on a set of outcomes Y.
- Parameters
A – iterable corresponding to variable names that act as treatments.
Y – iterable corresponding to variable names that act as outcomes.
- Returns
a float corresponding to the total causal effect.