Reducing Learner Redundancy in Boosting via Residual Orthogonalization

While sequential residual fitting is the bedrock of standard boosting frameworks, it inherently breeds learner redundancy by repeatedly revisiting correlated error components. To address this bottleneck, we propose a shift from residual fitting to \textit{residual orthogonalization} and introduce SCBoost. Our framework tackles redundancy through two complementary mechanisms: Spectral Residual Projection (SRP) and Covariance-Regularized Weighting (CRW). During training, SRP projects each residual target onto the orthogonal complement of the historical prediction subspace, forcing successive learners to capture only novel empirical innovations. During aggregation, CRW optimizes ensemble weights on a validation set with an explicit covariance penalty to mitigate remaining correlations. Theoretically, we provide a finite-sample geometric characterization proving that SRP yields an exact additive residual-energy decomposition. Furthermore, under an isotropic-noise assumption, we rigorously establish the conditions under which this projection improves the effective Signal-to-Noise Ratio. Extensive experiments across ten benchmark datasets demonstrate that SCBoost delivers strong out-of-the-box performance, particularly in accuracy and F1 score. This work reinterprets boosting through a geometric lens, suggesting that explicit redundancy control is a principled and necessary step toward more efficient ensemble architectures.

ITBoost: Information-Theoretic Trust for Robust Boosting

Gradient boosting remains a strong and widely used method for tabular data learning, but its performance often degrades when training labels are noisy. This behavior is largely related to the way boosting algorithms emphasize samples with large gradients, without explicitly accounting for whether such errors originate from informative hard cases or from unreliable labels. We address this issue by reconsidering how sample reliability is evaluated during boosting. Instead of relying on instantaneous error, we examine the evolution of each sample's residuals across iterations. Based on this insight, we propose Information-Theoretic Trust Boosting (ITBoost), which uses the Minimum Description Length principle to measure the complexity of residual trajectories. Samples whose residual patterns fluctuate in an irregular manner are treated as less trustworthy and are down-weighted during learning. Theoretically, we derive a tighter generalization bound for ITBoost under label noise. Empirical results on various tabular benchmarks indicate that ITBoost provides improved robustness in noisy environments over leading boosting and deep tabular models, while retaining best average performance on clean data.