Causal models play a vital role in establishing the cause-and-effect associations between variables in complex systems, though they struggle to estimate probabilities associated with multiple interventions and conditions. Two main types of causal models have been the focus of AI research – functional causal models and causal Bayesian networks (CBN).
Functional causal models make it simple to calculate conditional probability where interventions are present. CBNs, on the other hand, have no formal definition or explicit reduction for deriving the probabilities of a characteristic. Knowing how interventions in the model can alter outcomes is crucial in multiple disciplines, from health diagnostics in AI-driven healthcare, understanding the impact of lifestyle on health in epidemiology, to the effects of economic shifts on market behaviour.
In a recent study, researchers at Cornell University’s Computer Science department proposed a technique that could estimate the probability of an interventional formula backed by real, independent assumptions. Included in these interventions are the probabilities of sufficiency and necessity. When these assumptions align with the reality, probabilities can be estimated using observational data, particularly useful where experimental implementation is impracticable.
Researchers explained that the independent assumption suggests, “not only are the equations defining different variables independent, but the equations providing the variable values for different settings of its parents are also independent.” This principle assists them in identifying the odds of the queries in a CBN distinctly rather than deriving a range of values.
The Cornell team’s research included exploring the formality of causal models, explaining the formulas in CBNs, demonstrating that a compatible casual model can form a CBN satisfying given independence assumptions, and simplifying and assessing the probabilities of sufficiency and necessity.
In functional causal models, some variables have causal effects on others, characterised by a series of structured equations. Variables divide into two sets – exogenous variables (EVs) and endogenous variables. EVs evaluate their values using elements external to the model, whereas endogenous variables rely on the EVs to determine their values.
In conclusion, the Cornell researchers provided a new method to estimate the probability of an interventional formula based on specific assumptions. This method is valuable in situations where experiments are impossible. The calculated probabilities use observational data when the assumptions are valid. The study also looked into functional causal models, where sets of structured equations determine the causal effects of variables, further segregating them into EVs and endogenous variables.
