Optimizing Causal Objective Functions
A causal objective function scores objects, called units, based on how likely they are to exhibit a certain mode of causal behavior. We discuss the syntax and semantics of causal objective functions (i.e., causal loss functions) and present an exact algorithm for optimizing a broad class of such functions. We also discuss results that bound the complexity of the algorithm and identify the complexity class of this optimization problem. Optimizing causal objective functions is quite related to the "unit selection" problem introduced by Li & Pearl, with two key distinctions: (1) we treat a broad class of causal objective functions that include the "benefit function" used by Li & Pearl as a special case and (2) we take an algorithmic direction that assumes a fully specified causal model---to compute point values of causal objective functions---instead of focusing on computing bounds on the causal objective function using observational and experimental data.
Keynote given by Adnan Darwiche of UCLA at the workshop on causal discovery, Cholula, Mexico, 2023.
00:00 Causal objective functions: What and why?
03:08 The causal hierarchy
08:50 Structural causal models (SCM)
12:08 The identifiability/learning dimension
14:17 Unit selection: The work of Li & Pearl
17:56 The algorithmic dimension of unit selection (optimization)
22:35 Examples of causal objective functions
23:44 Syntax and semantics of causal objective functions
25:25 Sub-models
26:39 Worlds
29:02 Events (associational, interventional, counterfactual)
31:42 Satisfaction of an event by a world
33:54 Example of satisfaction
37:15 Probability of events (associational, interventional, counterfactual)
37:43 Generalized events: conjunctive, disjunctive and negated
38:59 Variable elimination for computing associational queries
40:52 MAR (marginals)
41:27 MAP (maximum a posteriori hypothesis)
43:15 Treewidth & elimination orders
46:15 Optimizing causal objective functions
48:05 Triplet models: evaluating counterfactual queries
50:43 Objective models: optimizing the causal objective function using Reverse-MAP
52:59 Reverse-MAP: Relation to MAP, complexity class of Reverse-MAP and unit selection
55:14 Reverse-MAP: Algorithm, complexity bound, experiments
1:04:10 Elimination orders and treewidth of parallel worlds (twin, triplet, .., models)
1:06:20 Causal treewidth
1:07:03 Main messages
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