Regression models used in real-world applications are often challenged by noise, outliers, data heterogeneity, and asymmetric error characteristics, which severely limit the effectiveness of conventional point-wise learning models. While twin support vector regression (TSVR) partially addresses these issues through the use of nonparallel regression bounds, it still relies on individual samples as basic learning units. As a result, TSVR remains highly sensitive to noisy and contaminated observations and fails to leverage the underlying structural and regional information inherent in complex datasets, leading to suboptimal robustness and generalization performance. To address these limitations, we introduce granular ball twin support vector regression (GBTSVR) and its quantile extension, granular ball twin support vector quantile regression (GB-TSVQR). The proposed models integrate granular ball computing with TSVR, replacing individual data points with compact, structure-preserving granular balls as fundamental learning units. This region-level representation effectively suppresses noise and outliers while preserving intrinsic data geometry, thereby enhancing robustness, stability, and generalization. GBTSVR constructs nonparallel lower- and upper-bound regression functions over granular balls, significantly reducing sensitivity to sample-level perturbations. Building upon this framework, GB-TSVQR further incorporates quantile regression principles to simultaneously capture heterogeneous trends and asymmetric error distributions across different quantile levels. Extensive experiments on synthetic datasets, time-series benchmarks, and outlier-contaminated data demonstrate that the proposed GBTSVR and GB-TSVQR consistently outperform state-of-the-art regression models.

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