Paper: arXiv 2212.04235

Authors: Matthias Feiler

Abstract

The paper addresses the problem of finding the causal direction between two associated variables. The proposed solution is to build an autoencoder of their joint distribution and to maximize its estimation capacity relative to both the marginal distributions. It is shown that the resulting two capacities cannot, in general, be equal. This leads to a new criterion for causal discovery: the higher capacity is consistent with the unconstrained choice of a distribution representing the cause while the lower capacity reflects the constraints imposed by the mechanism on the distribution of the effect. Estimation capacity is defined as the ability of the auto-encoder to represent arbitrary datasets. A regularization term forces it to decide which one of the variables to model in a more generic way i.e., while maintaining higher model capacity. The causal direction is revealed by the constraints encountered while encoding the data instead of being measured as a property of the data itself. The idea is implemented and tested using a restricted Boltzmann machine.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 4.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces a novel theoretical framework using restricted Boltzmann machines and autoencoder capacity regularization to infer causal direction. While mathematically sound and original in concept, it lacks extensive empirical validation on standard financial benchmark datasets and relies heavily on theoretical formulations.

Research Flowchart

  flowchart TD
    A["Research Goal: Identify Causal Direction X → Y vs Y → X"] --> B["Input: Joint Bivariate Data P(X,Y)"]
    B --> C["Train RBM Autoencoder on Joint Distribution"]
    C --> D["Apply Capacity Regularization to Force Asymmetric Modeling"]
    D --> E["Evaluate Estimation Capacity for Marginal/Conditional Directions"]
    E --> F["Outcome: Higher Capacity Direction Identifies the Cause (Unconstrained Variable)"]