multinomial logistic regression

Conventional statistical software frequently encounters infeasibility issues in estimating cumulative link model (CLM) parameters, and standard CLMs lack flexibility in handling missing responses, longitudinal binary outcomes, and non-proportional odds structures. Method: We propose a novel family of regression models for ordinal responses—comprising mixed-link, two-group, conditional-link, and PO–NPO hybrid specifications—that rigorously characterize the feasible parameter space of CLMs for the first time, providing necessary and sufficient feasibility conditions. We develop a verifiable maximum likelihood estimation (MLE) feasibility algorithm, derive closed-form expressions for the Fisher information matrix, and construct a comprehensive model selection framework incorporating AIC and BIC. Contributions/Results: Our approach relaxes the proportional odds assumption, enabling category-specific modeling. Empirical results demonstrate substantially improved goodness-of-fit, correction of misclassification induced by missing responses (NA), resolution of CLM convergence failures in mainstream software, and more robust and accurate statistical inference.

This study addresses variable selection for binary-response generalized linear models in high-dimensional settings by proposing a novel method, termed Boosting with Multiple Testing correction (BMT), which integrates multiple testing adjustment within a nonlinear boosting framework. At each iteration, BMT incorporates only the covariate exhibiting the strongest conditional significance while progressively constructing a sparse model through rigorous control of the multiplicity-induced error rate. The approach uniquely embeds a formal multiple hypothesis testing procedure into the boosting paradigm, offering theoretical guarantees of selection consistency and oracle properties for parameter estimation. Empirical evaluations demonstrate that BMT outperforms existing methods in both variable selection accuracy and estimation precision, and it achieves superior out-of-sample predictive performance in forecasting U.S. inflation.

This paper addresses binary classification under partial identification, where covariates follow a discrete distribution and model parameters are not fully identified. We propose a novel classification method grounded in Manski’s maximum score framework. Our key innovation is the first reformulation of maximum score estimation as two tractable linear programs—bypassing the computational complexity and convergence issues inherent in conventional iterative algorithms. The method retains minimal distributional assumptions (requiring neither conditional distribution continuity nor smoothness), thereby unifying computational efficiency with theoretical robustness. We establish a nontrivial finite-sample lower bound on classification accuracy and corroborate our approach via Monte Carlo simulations and empirical analysis. Results demonstrate that, relative to leading parametric and nonparametric methods, our estimator achieves superior predictive accuracy, enhanced small-sample stability, and greater robustness to model misspecification.

This work investigates the asymptotic generalization performance of overparameterized linear multiclass classifiers under a Gaussian covariate bilevel model, where sample size, feature dimension, and number of classes all diverge simultaneously. Addressing Subramanian et al. (2022)’s conjecture on the suboptimality of interpolating classifiers, we provide the first rigorous theoretical confirmation: in a specific high-dimensional regime, the minimum-norm interpolating classifier exhibits an asymptotically higher misclassification rate than non-interpolating counterparts—demonstrating a phase transition in relative performance. Technically, we introduce a novel variant of the Hanson–Wright inequality tailored to sparse label settings, and integrate it with asymptotic random matrix theory and information-theoretic strong converse bounds to derive tight upper and lower bounds on generalization error—establishing that the misclassification rate must converge almost surely to either zero or one. Our framework further extends successfully to multi-label classification.

To address the limited discriminative capability of naïve Bayes stemming from its strong conditional independence (isotropic) assumption, this paper proposes Projection Naïve Bayes (PNB), which learns an optimal linear subspace via discriminative projection optimization and performs naïve Bayes factorization of class-conditional densities within this low-dimensional projected space. PNB is the first framework to deeply integrate discriminative projection learning with naïve Bayes modeling, simultaneously enabling dimensionality reduction, visualization, and theoretical interpretability; it is further shown to be equivalent to class-conditional independent component analysis. Extensive experiments across 162 public benchmark datasets demonstrate that PNB significantly outperforms classical probabilistic discriminative models—including Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA)—and matches the accuracy of Support Vector Machines (SVM), while retaining the statistical interpretability and computational efficiency inherent to generative models.

Generalized linear models (GLMs) are widely used in actuarial modeling, yet their nonlinear link functions render existing fairness diagnostics—typically grounded in linear intuition—inapplicable. This work proposes the first fairness decomposition framework tailored to GLMs by extending the Wasserstein barycenter criterion to the distributional level and integrating moment decomposition with curvature analysis of the inverse link function. The resulting interpretable “four-channel plus dual-curvature” effect decomposition yields explicit formulas for logistic, Poisson, and Tweedie models. Empirical application to healthcare expenditure data demonstrates that the method effectively disentangles sources of prediction disparities, including the direct effect of sensitive attributes, mediation through proxy variables, differences in covariance structure, and amplification effects induced by nonlinear link coupling, thereby offering a practical tool for fairness auditing in actuarial practice.

This study addresses the arbitrariness in recidivism risk prediction arising from model multiplicity by leveraging a judicial system with over 15 years of operational history. The authors formalize legal rules into algorithmic labels to construct a high-quality dataset, train interpretable models, and analyze how structural diversity among models influences predictive disagreement. For the first time in a real-world judicial setting, they quantify the relationship between model multiplicity and prediction arbitrariness, establish a theoretical lower bound, and demonstrate that actual inter-model consistency substantially exceeds worst-case expectations. Innovatively adopting a “minimum risk score across multiple models” strategy, the approach simultaneously safeguards individual rights and reduces decision arbitrariness. The resulting models not only achieve superior predictive performance and more equitable error distributions across demographic groups but also effectively capture inmates’ rehabilitation progress.

This study addresses the limitations of covariate logistic models in latent class analysis, specifically their difficulty in capturing complex interactions and providing sufficient interpretability. To overcome these challenges, this work proposes a novel framework that directly integrates decision trees into latent class analysis. By leveraging interpretable tree structures combined with pruning and binary splitting techniques, the method effectively models covariate effects without requiring additional assumptions. Empirical validation demonstrates the approach's efficacy, yielding highly interpretable classification paths. Consequently, this research significantly expands the methodological toolkit for latent class analysis, establishing a new paradigm for handling complex covariate relationships while enhancing model transparency and practical utility.

This work addresses the potential nonexistence of a global optimum in linear ensembles of multiple binary classifiers by proposing a theoretical framework grounded in truth-table logical structuring and equivalence class partitioning, which establishes sufficient conditions for the existence of a convexified empirical risk minimizer. By introducing a multidimensional generalization of classification-calibrated loss functions and the notion of φ-frontiers, the study analyzes solution stability in relation to data quality. Under exponential (Boost) and logistic (Logit) losses, the authors derive, for the first time, explicit closed-form expressions for the optimal ensemble weights and fully characterize all solution regimes in the three-classifier setting. This approach circumvents iterative optimization, thereby substantially enhancing both the interpretability and computational efficiency of ensemble models.

This study addresses the challenge of simultaneously controlling both types of error in binary classification tasks, where overlapping class distributions inherently hinder such control. Within the Neyman-Pearson framework, this work introduces a rejection mechanism and proposes a model-agnostic joint calibration strategy to achieve selective dual error rate control. Furthermore, by leveraging martingale theory to precisely compute finite-sample crossing probabilities, the method ensures strict statistical validity without requiring multiple testing corrections. This approach overcomes the limitations of conventional threshold search procedures by guaranteeing that both error types strictly satisfy their predefined bounds. Its effectiveness is empirically validated in high-stakes applications, including recidivism prediction and credit default assessment, thereby providing reliable statistical safeguards for critical decision-making scenarios.