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Robust Causal Directionality Inference in Quantum Inference under MNAR Observation and High-Dimensional Noise

Joonsung Kang

TL;DR

<3-5 sentence high-level summary> The paper develops a principled framework for robust causal directionality inference in quantum systems subject to MNAR observation and high-dimensional noise. By integrating MNAR-aware selection, CVAE-based latent constraints, GEE stabilization, robust regression with Penalized Empirical Likelihood, and Bayesian optimization, it achieves double robustness, perturbation stability, and minimax-optimal performance. Theoretical guarantees are provided for double robustness, asymptotic normality, HDLSS stability, and PEL oracle inequalities, with extensive simulations and real-data validation on HDLSS genomics and proteomics datasets. This work offers a rigorous methodology for reliable causal structure discovery in quantum contexts where measurement processes actively shape observed data.

Abstract

In quantum mechanics, observation actively shapes the system, paralleling the statistical notion of Missing Not At Random (MNAR). This study introduces a unified framework for \textbf{robust causal directionality inference} in quantum engineering, determining whether relations are system$\to$observation, observation$\to$system, or bidirectional. The method integrates CVAE-based latent constraints, MNAR-aware selection models, GEE-stabilized regression, penalized empirical likelihood, and Bayesian optimization. It jointly addresses quantum and classical noise while uncovering causal directionality, with theoretical guarantees for double robustness, perturbation stability, and oracle inequalities. Simulation and real-data analyses (TCGA gene expression, proteomics) show that the proposed MNAR-stabilized CVAE+GEE+AIPW+PEL framework achieves lower bias and variance, near-nominal coverage, and superior quantum-specific diagnostics. This establishes robust causal directionality inference as a key methodological advance for reliable quantum engineering.

Robust Causal Directionality Inference in Quantum Inference under MNAR Observation and High-Dimensional Noise

TL;DR

<3-5 sentence high-level summary> The paper develops a principled framework for robust causal directionality inference in quantum systems subject to MNAR observation and high-dimensional noise. By integrating MNAR-aware selection, CVAE-based latent constraints, GEE stabilization, robust regression with Penalized Empirical Likelihood, and Bayesian optimization, it achieves double robustness, perturbation stability, and minimax-optimal performance. Theoretical guarantees are provided for double robustness, asymptotic normality, HDLSS stability, and PEL oracle inequalities, with extensive simulations and real-data validation on HDLSS genomics and proteomics datasets. This work offers a rigorous methodology for reliable causal structure discovery in quantum contexts where measurement processes actively shape observed data.

Abstract

In quantum mechanics, observation actively shapes the system, paralleling the statistical notion of Missing Not At Random (MNAR). This study introduces a unified framework for \textbf{robust causal directionality inference} in quantum engineering, determining whether relations are systemobservation, observationsystem, or bidirectional. The method integrates CVAE-based latent constraints, MNAR-aware selection models, GEE-stabilized regression, penalized empirical likelihood, and Bayesian optimization. It jointly addresses quantum and classical noise while uncovering causal directionality, with theoretical guarantees for double robustness, perturbation stability, and oracle inequalities. Simulation and real-data analyses (TCGA gene expression, proteomics) show that the proposed MNAR-stabilized CVAE+GEE+AIPW+PEL framework achieves lower bias and variance, near-nominal coverage, and superior quantum-specific diagnostics. This establishes robust causal directionality inference as a key methodological advance for reliable quantum engineering.
Paper Structure (38 sections, 5 theorems, 51 equations, 3 figures, 2 tables)

This paper contains 38 sections, 5 theorems, 51 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Theoretical Background
  3. MNAR and Quantum Observation
  4. Limitations of QEC/QEM
  5. Importance of Causal Directionality
  6. Methodology
  7. CVAE-based Latent Space Constraints
  8. MNAR-aware Selection Models and Quantum Inference Noise Handling
  9. Definition of $\mathcal{O}$ with explicit two-stage error/noise handling.
  10. Outcome Regression and GEE Stabilization
  11. Robust Sparse Regression and Penalized Empirical Likelihood
  12. Minimal Error-rate Conditions via Bayesian Optimization and Causal Directionality
  13. Causal Directionality Evaluation.
  14. Theoretical Guarantees
  15. Setup and Assumptions
  16. ...and 23 more sections

Key Result

Theorem 1

Under Assumptions asm:pos--asm:nuis, the estimator is doubly robust: if either (i) $e$ is consistently estimated or (ii) both $m_0,m_1$ are consistently estimated, then $\hat{\tau}\to_p \tau$.

Figures (3)

  • Figure 1: Performance under contamination ratio $\epsilon = 0.0$.
  • Figure 2: Performance under contamination ratio $\epsilon = 0.1$.
  • Figure 3: Performance under contamination ratio $\epsilon = 0.2$.

Theorems & Definitions (6)

  • Theorem 1: Double robustness
  • Theorem 2: Asymptotic normality
  • Theorem 3: HDLSS perturbation stability
  • Proposition 4: Oracle inequality for PEL
  • Theorem 5: Identifiable and uniquely recoverable causal direction
  • Definition 6: Directional MNAR Robustness Error (DMRE)