Conditional Causal Discovery Interface

The Causality Challenge

• Traditional approach: Single causal graph (DirectLiNGAM)
• Wide Learning™: Multiple graphs under different conditions
• Problem: Too many graphs to comprehend effectively

The "Spaghetti Graph" Problem

Complex causal graphs are inherently difficult to interpret

CVD: Our Design Framework

CV/CD/VD

We consider the pairwise interaction of these concepts:

• CV - we explore by explanation of elements of the Rashomon set with similarities
• CD - we explore by understanding how and why these causalities came to be through independent or directed evaluation of evidence
• VD - we explore by choosing elements from the Rashomon set that have new or unexpected results

Understanding the Background and Necessary Tools

Directed Acyclic Graphs (DAGs)

Mathematical foundation for representing causal structures

• Nodes: Variables in the system
• Directed edges: Causal relationships
• Acyclic: No variable causes itself
• Constraint: Prevents circular causality

Causal Discovery

Recovering DAG representations from observational data

Key Challenge: Given only probability distributions, you can identify a Markov equivalence class — multiple DAGs that are statistically indistinguishable

Structural Equation Model (SEM)

Structural equation modeling (SEM) is a multivariate statistical framework for specifying and testing systems of relationships among observed and latent variables in a single, integrated model

\(M_{SEM} = (U, V, F, P)\)

• U: Exogenous variables (external factors)
• V: Endogenous variables (observed)
• F: Functions defining relationships
• P: Joint probability distribution

Direct Linear Non-Gaussian Acyclic Model

Resolves ambiguity by exploiting non-Gaussianity

Result: Identifies a unique DAG rather than an equivalence class

DirectLiNGAM: Algorithm

Iterative process to identify causal ordering

1. Find exogenous variables (no parents)
2. Test which variable's residuals are most independent
3. Remove that variable and repeat
4. Build unique causal structure

DirectLiNGAM: Example

Variables: Temperature, Ice Cream Sales, Drowning Deaths

• Step 1: Test all variables — Temperature's residuals are most independent → no parents
• Step 2: Remove Temperature, test remaining — Ice Cream Sales is independent
• Step 3: Only Drowning Deaths left
• Result: Temperature → Ice Cream Sales, Temperature → Drowning Deaths

Both caused by temperature, but don't cause each other!

Wide Learning (WL)

Symbolic classification model for causal discovery

\(M_{WL} = (\text{features}, \text{combinator}, \text{evaluation})\)

Generates multiple causal graphs under different conditions

Wide Learning: Example

Student Performance Study

DirectLiNGAM:

Study hours → Performance (one global graph)

Wide Learning discovers:

• High stress, low sleep: Study hours have little effect
• Low stress, adequate sleep: Study hours strongly affect performance
• With tutoring: Study hours → understanding → performance

Rashomon Sets

Set of unique, equally good explanations/models

Model Multiplicity: Many structurally different models achieve nearly identical performance

Named after the film where the same event has multiple plausible accounts

Model Evaluation Metrics

Assess fit and select among competing DAG structures

AIC: Akaike Information Criterion

\(\text{AIC} = 2k - 2\ln(L)\)

• k: Number of parameters
• L: Likelihood
• Balances fit against complexity
• Lower AIC = better model

CFI & RMSEA

Graph Hierarchies

Solution for navigating spaghetti graphs

• Input: Complex graph structures
• Output: Numerical grades for comparison
• Metrics: Incoherence and Democracy
• Enable discovery by properties

Interface Design Principles

1. Minimize overwhelmingness - Present information in digestible subsets
2. Storytelling approach - Build understanding progressively
3. Guided & unguided discovery - Balance exploration and direction
4. Accessibility features - Color, navigation, responsiveness
5. "Don't think, feel!" - Intuitive, interactive design

Feature 1: Data Visualization

• Data cleaning suggestions
• Descriptive statistics
• Correlation analysis (heatmap & scatterplots)
• Distribution histograms

Data Visualization Dashboard

Raw data, descriptive statistics, and data quality checks

Correlation Analysis

Pairwise correlations revealed through heatmap and scatterplots

Wine Dataset Insights

Feature 2: Prior Knowledge Survey

• -1 (Default): No prior knowledge
• 0 (Add): x causes y (specify sinks/outcomes)
• 1 (Add): y causes x (specify sources/actions)

Prior Knowledge Interface

Interactive matrix for specifying causal relationships

Feature 3: Hierarchical Metrics

Democracy Coefficient

• Measures "balance" of influence
• High: Many features equally important
• Low: Few features dominate

Incoherence Score

• Measures graph complexity
• High: Many contradictory paths
• Low: Clear, coherent structure

Hierarchical Visualization

Democracy vs. Incoherence scatter plot reveals graph clusters

Feature 4: Model Builder for Guided Discovery

• Step-by-step exploration from parent to children nodes
• Path tracking and undo functionality
• Edge weight threshold filtering
• Child node preview on hover

Guided Discovery in Action

Building causal paths interactively

Path Tracking

Selected nodes form a clear causal path

Feature 5: Model Builder - Unguided Discovery

Dynamic Graph View

Interactive exploration with full graph visibility

Static Graph View

Clean, exportable representation with color-coded nodes

Feature 6: Insights & Analysis

• Summary Statistics: Feature ranges, averages, modes for each condition
• Statistical Validity: CFI, AIC, RMSEA indices
• Recipe for Success: Actionable recommendations based on models

Statistical Validity

Quantitative details add convincingness to discoveries

Decision-Making Support

Translating causal discoveries into strategic actions

Future Directions

1. Bootstrapping: Report which causal relationships are most supported across samples
2. Learning by playing: Touchscreen, tablet, VR integration
3. Model supplementation: Integrate latent variable models, handle confounding
4. Generative AI themes: Customize interface design based on dataset domain

Research Extensions

• Prior Knowledge: Advanced identification techniques for chains, forks, and colliders
• Accessibility: Full WCAG compliance, multi-modal interaction
• Domain Expertise: Customized interfaces for different user types (scientists, managers, regulators)
• Statistical Enhancements: Automated model comparison and selection