Temporal Causal Discovery

The PCMCI (Peter-Clark Momentary Conditional Independence) algorithm is a two-stage constraint-based method. It first uses conditional independence tests to prune irrelevant links, then applies Momentary Conditional Independence (MCI) to control for autocorrelation and indirect paths. This effectively removes spurious correlations that plague standard Granger causality, isolating only direct causal parents for each variable at specific time lags.

VAR-LiNGAM (Vector Autoregressive Linear Non-Gaussian Acyclic Model) combines structural equation modeling with time-series analysis. It exploits the non-Gaussianity of data distributions to break the symmetry of correlations and identify the direction of causal arrows. Unlike constraint-based methods, it estimates a fully directed acyclic graph where the causal ordering of variables is uniquely determined, making it powerful for distinguishing instantaneous from lagged effects.

Granger causality is the foundational statistical test for temporal causation: a variable X 'Granger-causes' Y if past values of X improve the forecast of Y beyond using only past values of Y. However, it is a predictive, not structural, concept. It fails in the presence of latent confounders or deterministic dynamics. Modern causal discovery treats Granger causality as a baseline, applying stricter controls to infer true mechanistic causation.

The inferred causal graph serves as a ground-truth mask for model explanations. Feature attributions from a predictive model are validated by checking if they align with the discovered causal parents. A feature receiving high SHAP importance but absent from the causal graph is flagged as a spurious attribution. This process bridges the gap between post-hoc explainability and structural causal understanding, ensuring explanations reflect the system's true data-generating process.

Causal discovery enables in silico interventions. By learning the structural equations, one can simulate the effect of setting a variable to a fixed value at a specific time step, breaking its natural dependencies. This answers counterfactual questions like, 'What would the forecast be if we had changed the marketing spend at t-3?' This moves attribution from passive observation to active causal reasoning, critical for decision-making systems.

Advanced methods like LPCMCI (Latent PCMCI) extend constraint-based discovery to scenarios with unobserved common causes. By detecting specific conditional independence patterns, they can identify when a latent confounder is driving apparent causal links between observed variables. This prevents the discovery of false positive causal edges that would otherwise mislead downstream attribution and policy decisions in complex industrial systems.

The Peter-Clark Momentary Conditional Independence algorithm is the gold standard for time-series causal discovery. It operates in two stages: first, a modified PC algorithm identifies a superset of potential causal parents by testing for conditional independence; second, a Momentary Conditional Independence (MCI) test is applied to eliminate false positives from autocorrelation and contemporaneous links. This robustly handles high-dimensional, autocorrelated data common in climate science and finance.

A Vector Autoregressive Linear Non-Gaussian Acyclic Model combines a classic VAR model with the LiNGAM framework. It exploits the non-Gaussianity of data distributions to break the symmetry of correlations and identify the full causal structure, including both lagged (temporal) and contemporaneous (instantaneous) causal effects. Unlike Granger causality, it can distinguish between direct and indirect causes, providing a complete causal graph rather than just predictive utility.

A foundational statistical hypothesis test where a time series X is said to 'Granger-cause' Y if past values of X provide statistically significant information about future values of Y, beyond the information contained in past values of Y alone. It is a test of predictive causality, not true structural causality. It is widely used as a baseline and for feature validation in econometrics and neuroscience, but is limited to linear, bivariate relationships without intervention modeling.

Inferred causal graphs must be rigorously validated. Key methods include:

• Intervention Analysis: Comparing the graph's predictions against real-world A/B tests or natural experiments.
• Sensitivity Analysis: Testing graph stability by bootstrapping data or adding synthetic noise.
• Domain Expert Review: Having subject-matter experts confirm that discovered edges align with known physical or economic mechanisms.
• Predictive Performance: Using the learned causal features to improve a downstream forecasting model, proving the graph's utility.

An SCM is the formal mathematical framework underlying causal discovery. It represents a system as a set of structural equations where each variable is a function of its direct causes and an independent noise term. Unlike a simple probabilistic model, an SCM supports the do-operator, allowing us to formally reason about the outcome of an intervention. Temporal SCMs explicitly model time-lagged dependencies, making them the target output of algorithms like PCMCI.

The core statistical engine of causal discovery. A test determines if two variables are independent given a conditioning set of other variables. For temporal data, common tests include:

• ParCorr: Linear partial correlation.
• GPDC: Gaussian Process Distance Correlation for non-linear dependencies.
• CMIknn: A k-nearest-neighbor estimator for Conditional Mutual Information, capturing any functional relationship. The choice of test is critical and must match the data's assumed distribution and dimensionality.