A parametric assumption specifies how a causal model represents each node’s outcome and maps its parents to that outcome. It chooses, for example, a categorical or numeric outcome and a conditional probability table, regression model, or neural network. section 3.1.9
This choice follows the causal graph rather than defining it. A DAG can encode that age causes education without deciding whether age is represented as classes, an integer, or elapsed time, or whether the relationship uses a categorical distribution or regression. Causal assumptions and parametric assumptions are therefore separate layers of implementation. section 3.1.9
Parametric choices appear in several modeling strategies:
- Use conditional probability tables for categorical variables. section 3.1.9
- Use generalized linear models for categorical outcomes or other regression approaches for numeric outcomes. section 3.1.9
- Use neural network architectures to model individual causal Markov kernels. section 3.1.9
- Recognize that some causal estimands require more than graphical assumptions: instrumental-variable estimation additionally uses a linearity assumption. section 11.3.2
Instrumental-variable estimation
For an instrumental-variable estimand, a linearity assumption lets the treatment and outcome relationships be estimated with linear regression, producing the average treatment effect from model coefficients. The graphical assumptions alone are insufficient for this identification route. section 11.3.2
Listing 3.5 Bayesian point estimation with a Dirichlet conjugate prior
from pgmpy.estimators import BayesianEstimator #1
model.fit(
data,
estimator=BayesianEstimator, #2
prior_type="dirichlet",
pseudo_counts=1 #3
)
causal_markov_kernels = model.get_cpds() #4
cmk_T = causal_markov_kernels[-1] #4
print(cmk_T) #4
Inspect a BayesianEstimator configuration that fits causal Markov kernels with a Dirichlet prior and pseudo-counts. section 3.1.9
