Causal Discovery Algorithm

These algorithms use conditional independence tests to prune edges between variables. If two variables are independent given a conditioning set, the edge is removed. The PC algorithm (named after Peter and Clark) is the canonical example, systematically testing all possible conditioning sets. In supply chains, this can identify that Supplier Lead Time and Defect Rate are conditionally independent given Raw Material Quality, revealing the true causal structure without prior knowledge.

Instead of testing independencies, score-based methods search over the space of possible Directed Acyclic Graphs (DAGs) and assign a score to each, such as the Bayesian Information Criterion (BIC) or Minimum Description Length (MDL). The algorithm optimizes for the graph that best balances fit and complexity. Greedy Equivalence Search (GES) is a prominent example. This approach is valuable for finding the most plausible causal model explaining why a Logistics Delay and a Warehouse Capacity spike co-occur.

FCM-based discovery goes beyond conditional independence by assuming a specific functional form for the causal mechanism, such as non-linear additive noise models. This allows the algorithm to distinguish between X → Y and Y → X even when they are statistically dependent. For instance, if the noise in a Demand Forecast Error is independent of the Promotional Spend, but not vice versa, the algorithm infers that spend causes the error. This breaks the symmetry that constraint-based methods cannot resolve.

Hybrid algorithms combine constraint-based and score-based approaches to improve computational efficiency and accuracy. A common pattern uses conditional independence tests to restrict the search space of possible graphs, then applies a score-based search on the reduced space. The Max-Min Hill-Climbing (MMHC) algorithm is a classic example. This is particularly effective in high-dimensional supply chain settings with hundreds of variables like SKU velocity, port congestion indices, and weather data.

Advanced discovery algorithms explicitly model unobserved common causes. The Fast Causal Inference (FCI) algorithm and its variants output a Partial Ancestral Graph (PAG), which represents a set of possible causal graphs that include latent variables. In disruption analysis, a latent confounder like Global Geopolitical Instability might simultaneously cause delays at multiple unrelated suppliers. FCI can detect this hidden influence without measuring it directly, preventing a spurious causal link between the suppliers.

For temporal data, algorithms like Granger Causality and its non-linear extensions (e.g., using Recurrent Neural Networks) or PCMCI (Peter and Clark Momentary Conditional Independence) are used. PCMCI is specifically designed for high-dimensional, time-lagged data, iterating through a condition-selection step and a momentary conditional independence test. This is crucial for discovering that a Production Line Sensor Anomaly at time t-3 is the root cause of a Quality Control Failure at time t, filtering out autocorrelation effects.

The formal mathematical framework that defines a system's data-generating mechanism. An SCM consists of a set of endogenous variables, exogenous noise variables, and structural equations that map causes to effects.

• Represents the world as a collection of autonomous mechanisms
• Enables counterfactual reasoning by modifying individual equations
• The output of a causal discovery algorithm is often an SCM or its graphical skeleton

A visual representation of causal assumptions where nodes represent variables and directed edges encode direct causal relationships. The 'acyclic' constraint prohibits feedback loops.

• Encodes conditional independence relationships via d-separation
• Causal discovery algorithms search the space of possible DAGs
• The Markov equivalence class defines the set of DAGs indistinguishable by observational data alone

A complete set of three inference rules developed by Judea Pearl for transforming expressions involving the do-operator—which represents an intervention—into standard conditional probabilities.

• Bridges the gap between observational and interventional distributions
• Determines if a causal effect can be estimated from non-experimental data
• Provides the theoretical backbone for identification strategies in causal discovery

A graphical rule for selecting a sufficient set of covariates to block all spurious paths between a treatment and an outcome. Conditioning on a set that satisfies the backdoor criterion eliminates confounding bias.

• Blocks non-causal associations flowing through common causes
• Must avoid conditioning on colliders to prevent opening new bias paths
• Causal discovery helps identify valid adjustment sets when domain knowledge is incomplete

The process of estimating what would have happened to an outcome if a specific intervention had been different, given what actually occurred. This is the highest rung of Pearl's Causal Hierarchy.

• Requires a fully specified SCM, not just a DAG
• Answers 'what if' questions like: 'Would the disruption have occurred if the supplier had been different?'
• Essential for root cause attribution and recourse analysis in supply chains

The property that a predictive relationship remains stable across different environments or interventions because it captures a genuine causal mechanism rather than a spurious correlation.

• A model relying on causal parents of a target variable generalizes robustly
• Invariant prediction is a modern principle used in algorithms like ICP (Invariant Causal Prediction)
• Contrasts sharply with brittle correlational features that fail under distribution shift