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@article{184365,
        author = {Harsh Agarwal},
        title = {Mathematical Trade-offs between Bias and Variance in Ensemble Learning and their influence on Model Generalization in High-Dimensional data},
        journal = {International Journal of Innovative Research in Technology},
        year = {2025},
        volume = {12},
        number = {4},
        pages = {1229-1234},
        issn = {2349-6002},
        url = {https://ijirt.org/article?manuscript=184365},
        abstract = {The bias–variance trade-off is a fundamental principle that shapes the generalization ability of machine learning models. In high-dimensional data environments, this trade-off becomes particularly challenging: the sparsity of data inflates variance, while dimensionality reduction or regularization may increase bias. This paper explores the mathematical foundations of bias and variance, presents their decomposition in the context of prediction error, and examines how ensemble learning methods address these challenges. Bagging is shown to reduce variance through decorrelation of base learners, boosting reduces bias by sequentially refining predictions, and stacking combines multiple models to leverage their complementary strengths. The analysis further highlights how ensembles mitigate the curse of dimensionality, where traditional models fail due to distance concentration and instability. Through theoretical discussion and mathematical formulations, the study demonstrates that ensembles provide a balanced approach to error minimization, enabling more robust and reliable generalization in complex, high-dimensional spaces.},
        keywords = {},
        month = {September},
        }