Structured Basis Function Networks: Loss-Centric Multi-Hypothesis Ensembles with Controllable Diversity
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| Format: | Preprint |
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2025
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| _version_ | 1866918134890364928 |
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| author | Dominguez, Alejandro Rodriguez Shahzad, Muhammad Hong, Xia |
| author_facet | Dominguez, Alejandro Rodriguez Shahzad, Muhammad Hong, Xia |
| contents | Existing approaches to predictive uncertainty rely either on multi-hypothesis prediction, which promotes diversity but lacks principled aggregation, or on ensemble learning, which improves accuracy but rarely captures the structured ambiguity. This implicitly means that a unified framework consistent with the loss geometry remains absent. The Structured Basis Function Network addresses this gap by linking multi-hypothesis prediction and ensembling through centroidal aggregation induced by Bregman divergences. The formulation applies across regression and classification by aligning predictions with the geometry of the loss, and supports both a closed-form least-squares estimator and a gradient-based procedure for general objectives. A tunable diversity mechanism provides parametric control of the bias-variance-diversity trade-off, connecting multi-hypothesis generalisation with loss-aware ensemble aggregation. Experiments validate this relation and use the mechanism to study the complexity-capacity-diversity trade-off across datasets of increasing difficulty with deep-learning predictors. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_02792 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structured Basis Function Networks: Loss-Centric Multi-Hypothesis Ensembles with Controllable Diversity Dominguez, Alejandro Rodriguez Shahzad, Muhammad Hong, Xia Machine Learning 68T05, 68U10, 68T45 I.2.1; I.2.6; I.5.2; I.5.4 Existing approaches to predictive uncertainty rely either on multi-hypothesis prediction, which promotes diversity but lacks principled aggregation, or on ensemble learning, which improves accuracy but rarely captures the structured ambiguity. This implicitly means that a unified framework consistent with the loss geometry remains absent. The Structured Basis Function Network addresses this gap by linking multi-hypothesis prediction and ensembling through centroidal aggregation induced by Bregman divergences. The formulation applies across regression and classification by aligning predictions with the geometry of the loss, and supports both a closed-form least-squares estimator and a gradient-based procedure for general objectives. A tunable diversity mechanism provides parametric control of the bias-variance-diversity trade-off, connecting multi-hypothesis generalisation with loss-aware ensemble aggregation. Experiments validate this relation and use the mechanism to study the complexity-capacity-diversity trade-off across datasets of increasing difficulty with deep-learning predictors. |
| title | Structured Basis Function Networks: Loss-Centric Multi-Hypothesis Ensembles with Controllable Diversity |
| topic | Machine Learning 68T05, 68U10, 68T45 I.2.1; I.2.6; I.5.2; I.5.4 |
| url | https://arxiv.org/abs/2509.02792 |