[Paper Review] Probabilistic Variational Causal Approach in Observational Studies

Usef Faghihi, Amir Saki|arXiv (Cornell University)|Aug 12, 2022

Bayesian Modeling and Causal Inference4 citations

TL;DR

This paper introduces Probabilistic Variational Causal Effect (PACE), a novel causal inference framework that integrates intervention via total variation with the natural availability of changing exposure values given background variables. By parameterizing this availability through a degree $d$, PACE produces a causal effect vector rather than a single value, enabling robust handling of both rare-event and probabilistic causal problems, with identifiable counterfactuals and extensions like PEACE and SPACE for positive/negative effects.

ABSTRACT

In this paper, we introduce a new causal methodology that accounts for the rarity and frequency of events in observational studies based on their relevance to the underlying problem. Specifically, we propose a direct causal effect metric called the Probabilistic vAriational Causal Effect (PACE) and its variations adhering to certain postulates applicable to both non-binary and binary treatments. The PACE metric is derived by integrating the concept of total variation, representing the purely causal component, with interventions on the treatment value, combined with the probabilities of hypothetical transitioning between treatment levels. PACE features a parameter $d$, where lower values of $d$ correspond to scenarios emphasizing rare treatment values, while higher values of $d$ focus on situations where the causal impact of more frequent treatment levels is more relevant. Thus, instead of a single causal effect value, we provide a causal effect function of the degree $d$. Additionally, we introduce positive and negative PACE to measure the respective positive and negative causal changes in the outcome as exposure values shift. We also consider normalized versions of PACE, referred to MEAN PACE. Furthermore, we provide an identifiability criterion for PACE to handle counterfactual challenges in observational studies, and we define several generalizations of our methodology. Lastly, we compare our framework with other well-known causal frameworks through the analysis of various examples.

Motivation & Objective

• To develop a causal inference framework that accounts for the natural availability of changing exposure values in real-world settings.
• To address limitations in existing frameworks—like Pearl’s and information-theoretic models—when rare events or non-probabilistic scenarios are central.
• To provide a unified approach for both probabilistic and non-probabilistic causal problems using a single parameterized formula.
• To enable measurement of positive and negative causal effects via PEACE and SPACE variants.
• To establish an identifiability criterion for counterfactuals in observational data using the PACE framework.

Proposed method

• Proposes PACE as a causal effect formula based on the total variation of a function integrated with probability theory.
• Introduces a degree parameter $d$ to control the sensitivity to rare or common exposure changes, enabling a vector of causal effects.
• Defines PEACE and SPACE as variants to separately measure positive and negative causal changes under intervention.
• Uses the natural availability of changing exposure values $\mathbb{P}(X=1|\bm{Z}=\bm{z})$ as a core component of the causal effect computation.
• Applies a structural equation model $Y = g(X, \bm{Z})$ to formalize direct causal effects while conditioning on confounders $\bm{Z}$.
• Establishes an identifiability criterion for PACE in observational studies using conditional probabilities and counterfactual reasoning.

Experimental results

Research questions

• RQ1 How can causal inference be improved in scenarios where rare exposure changes significantly affect outcomes?
• RQ2 In what way does the natural availability of changing exposure values influence the estimation of direct causal effects?
• RQ3 How can a single causal effect formula handle both probabilistic and non-probabilistic causal problems?
• RQ4 What is the role of the parameter $d$ in shaping the causal effect vector and its sensitivity to rare events?
• RQ5 How does PACE compare to established frameworks like Pearl’s do-calculus, mutual information, and Janzing et al. in capturing causal strength?

Key findings

• PACE produces a causal effect vector by discretizing the degree parameter $d$, allowing sensitivity analysis across different levels of exposure change availability.
• For the wet grass example, PACE identified $\mathbb{I}(R;W|S) \approx 0.4936$ and $\mathbb{I}(S;W|R) \approx 0.3707$, showing stronger indirect causal influence from rain via sprinkler.
• In the rare disease example, low $\mathbb{P}(N=1|\bm{o})$ values were shown to reduce the causal effect, reflecting real-world scarcity.
• The framework successfully identified that $W \sim \mathbb{B}(0.6509)$, with entropy $\mathbb{H}(W) \approx 0.9333$, and conditional entropy $\mathbb{H}(W|R) \approx 0.6849$, supporting causal strength quantification.
• PACE’s identifiability criterion enables counterfactual reasoning in observational data by leveraging conditional probabilities and structural models.
• The framework outperforms traditional models in capturing causal effects where rare cases or asymmetric exposure availability matter, as demonstrated in the binary symmetric channel and disease examples.