spearman correlation

This paper addresses the rank verification problem—determining whether the observed top-ranked unit corresponds to the true maximum mean—under heteroscedastic Gaussian distributions. It introduces the first systematic selective inference framework for this task, circumventing power loss from conventional multiple testing correction. Methodologically, it unifies Top-K set validation and partial order identification via conditional hypothesis testing and exact p-value construction. Compared to standard approaches, it achieves substantially higher statistical power and accuracy while preserving rigorous type-I error control, as empirically validated on NHANES real-world data. Key contributions are: (1) the first theoretical framework and algorithm for rank verification under heteroscedasticity; (2) integration of selective inference principles to relax the homoscedasticity assumption; and (3) an open-source, reproducible, and interpretable software package implementing the method.

Canonical Correlation Analysis (CCA) lacks a unified theoretical exposition bridging its historical foundations with modern high-dimensional and random matrix–theoretic developments, hindering deep conceptual understanding and pedagogical coherence. Method: This survey systematically traces CCA’s century-long evolution—from Jordan’s and Hotelling’s foundational work to contemporary advances—within an integrated framework unifying linear algebra, high-dimensional statistics, and random matrix theory. It introduces a modular pedagogical architecture featuring six progressive exercise sets designed to reinforce conceptual internalization and cross-chapter integration. Contribution/Results: The work establishes the most comprehensive, theoretically rigorous, and pedagogically viable CCA reference system to date. By achieving strict interdisciplinary unification and embedding principled instructional design, it significantly enhances graduate students’ and researchers’ conceptual mastery and practical application capabilities in CCA.

This study investigates whether pairwise comparisons genuinely reflect model accuracy or are confounded by stylistic preferences and annotator biases. The authors reformulate five standard benchmarks as open-ended generation tasks and integrate pairwise comparisons, Elo rating aggregation, and Spearman correlation analysis with causal inference techniques. Their systematic evaluation—conducted in settings where ground-truth labels are available—demonstrates for the first time that Elo rankings exhibit strong alignment with accuracy-based rankings (Spearman correlation > 0.9), significantly outperforming direct scoring, especially under weak annotator conditions. Furthermore, they identify “answer repetition at the end” as a key causal factor driving human preference, while finding that stylistic variation and annotator bias exert only minimal influence on overall model rankings.

Black-box classifiers suffer from degraded generalization—especially under out-of-distribution settings—due to spurious correlations. To address this, we propose a counterfactual (CF) alignment method that generates CF images perturbed with respect to a target classifier and evaluates the consistency of output responses across multiple heterogeneous classifiers. This enables unsupervised, model-agnostic localization and quantification of spurious correlation instances. Crucially, we introduce cross-model CF response consistency as a novel, principled criterion for identifying spurious correlations—a first in the literature—and demonstrate its utility for evaluating robustness interventions such as GroupDRO, JTT, and FLAC. We validate our approach on the Face-Attribute and Waterbird benchmarks, achieving high detection accuracy. Both visualizations and quantitative metrics exhibit strong agreement, confirming that our method reliably identifies spurious correlations and accurately measures their strength.

Existing feature attribution methods for learning-to-rank (LTR) lack ranking-aware theoretical foundations, often yielding contradictory or counterintuitive results that undermine interpretability. Method: This paper introduces the first game-theoretic, axiomatized framework for ranking—formally specifying ranking-specific axioms including ranking consistency and efficiency—and derives Rank-SHAP, the first axiomatic extension of Shapley values to ranking tasks. Contribution/Results: We evaluate Rank-SHAP on MSLR-WEB30K and Istella with state-of-the-art LTR models (e.g., LambdaMART, DeepRank) and validate it via user studies. Results demonstrate significant improvements in attribution consistency and alignment with human judgment. Axiomatic analysis further reveals that most existing attribution methods violate fundamental ranking axioms. This work establishes the first rigorous, axiom-based foundation for explainable LTR.

Chatterjee’s rank correlation coefficient lacks a rigorous theoretical foundation clarifying its underlying probabilistic structure. Method: We rigorously analyze the local averaging process in the ε → 0 limit, revealing that the coefficient’s intrinsic ε–δ structure arises from local dependence between random variables. We reformulate it as a natural empirical L₁ residual measure and develop the first formal ε–δ–based interpretive framework. We prove that the probability integral transform serves only a normalization role and does not contribute to the core structural definition; we further propose an L₂ variant that recovers Pearson’s R² under Gaussianity. Contribution/Results: Our work decouples distribution-freeness from model interpretability, unifies multiple dependence measures—including Spearman, Kendall, and Pearson—under a common local-to-global dependency lens, and establishes a theoretical bridge from local dependence to global correlation. The framework provides both statistical robustness and transparent geometric intuition, enabling principled extensions to multivariate and conditional settings.

Existing interpretability methods lack standardized data benchmarks and struggle to assess whether model explanations genuinely reflect the intrinsic structure of training data. Method: We propose a model-agnostic framework for evaluating model-data consistency, grounded in Rubin’s potential outcomes framework to construct a model-free, data-driven baseline. This baseline quantifies the true separative effect of each feature on binary classification tasks. Model explanations are then diagnosed by comparing feature importance rankings against this causal, data-derived baseline. Contribution/Results: Our approach efficiently detects when models deviate from fundamental data-generating mechanisms. It offers strong interpretability, low computational overhead, and cross-model applicability. To our knowledge, it is the first causally grounded, feature-effect-based tool for validating model-data consistency—providing a foundational method for trustworthy AI evaluation.

This paper addresses the problem of model-free inference of global rankings from noisy pairwise comparisons (e.g., tennis match outcomes), where both the latent object strengths and the functional mapping from strengths to win probabilities are unknown. To overcome the limitations of parametric models—such as Bradley–Terry—which impose strong prior assumptions on the link function (e.g., logistic), we propose the first Bayesian nonparametric framework that jointly infers latent strength parameters and an unknown response function. Our method integrates variational adaptive function modeling with MCMC sampling and incorporates empirical calibration to enhance robustness. Evaluated on real-world datasets spanning sports and academic citation networks, our approach significantly outperforms baselines relying on prespecified link functions, demonstrating superior ranking accuracy and generalization stability even under model misspecification.

Deep learning models are prone to shortcut learning—exploiting spurious correlations between non-semantic features and labels or sensitive attributes—leading to biased predictions, particularly in domains like medical imaging where human interpretability is limited and quantitative, pixel-level diagnostic tools are lacking. To address this, we propose the first model-agnostic framework for quantifying and localizing shortcut learning at the pixel level. Our method constructs a dataset-level regional ranking spectrum from attribution maps and employs ordinal correlation analysis, partial correlation, and bias correlation metrics across three complementary models (BA, TS, SA). We further introduce a test-time shortcut region attenuation strategy. Extensive experiments on CelebA, CheXpert, and ADNI demonstrate superior stability, sensitivity, and spatial localization accuracy compared to baselines, while significantly narrowing performance gaps across worst-case subgroups.

This study addresses the challenge of distinguishing directional asymmetry from tail-ratio deviations in multivariate distributions by proposing a quantile-based projection diagnostic framework that avoids reliance on higher-order moments. The method integrates directional skewness and tail-ratio measures through one-dimensional projections, sparse rank-one computations, and directional search to robustly classify heavy-tailed multivariate distributions into four categories: symmetric baseline tails, symmetric tail deviations, skewed baseline tails, and skewed tail deviations. Theoretical analysis establishes population-level properties, finite-sample uniform bounds, and classifier consistency, while revealing the complementary roles of coordinate and random directions in high dimensions, thereby offering a reliable foundation for multivariate modeling choices.