A Unified Framework for Feature Dependence: Theory, Algorithms, and Causal Inference
Murali Krishna Pasupuleti · International Journal of Academic and Industrial Research Innovations(IJAIRI) · 2021
Abstract: Concept analysis identifies three pillars of feature relationships—association, conditional dependence, and higher-order interaction (synergy/redundancy)—and motivates the need for coherent definitions, calibrated estimation, and causal interpretability. Building on this analysis, a unified framework is developed that links axiomatic operators to scalable algorithms and causal reasoning. The central problem addressed is the fragmentation of dependence measures and the absence of finite-sample, high-dimensional guarantees and clear connections to causal structure. The methodology formalizes operators with symmetry, invariance, decomposability, and data-processing properties; provides estimators based on kernel embeddings (HSIC/dHSIC), copula models, and information-theoretic functionals; and employs debiased machine learning with cross-fitting for conditional tests. Uncertainty is quantified by permutation and wild-bootstrap procedures with multiple-testing control, while interaction is decomposed via regularized, Shapley-aligned expansions. Integration with causal inference is achieved through conditional independence, invariance across environments, and Markov-blanket diagnostics. Evaluation uses synthetic ground truth and multi-domain case studies under containerized, reproducible protocols. Key results show calibrated Type-I error with competitive power in continuous and mixed-type settings, reliable detection of non-additive interactions without inflated false discoveries, improved alignment with causal graphs when conditioning/invariance are applied, and near-linear computational scaling via randomized sketches. The impact is a decision-grade toolkit that standardizes dependence analysis, strengthens interpretability and robustness of downstream models, and provides transparent evidence to support experimental design, governance, and scientific accumulation. Keywords: feature dependence, conditional independence, interaction, synergy, redundancy, causal inference, invariance, mutual information, HSIC, copulas, Shapley decomposition, cross-fitting, debiased machine learning, bootstrap, multiple testing, kernel methods, high-dimensional statistics, calibration, robustness, reproducibility, Markov blanket, causal discovery ________________________________