Interval-Valued attention-Based regression with truncated normal distributions over target intervals.
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| Title: | Interval-Valued attention-Based regression with truncated normal distributions over target intervals. |
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| Authors: | Kogan, Stanislav K.1 (AUTHOR) kogan.sk@edu.spbstu.ru, Utkin, Lev V.1 (AUTHOR) utkin_lv@spbstu.ru, Konstantinov, Andrei V.1 (AUTHOR) konstantinov_av@spbstu.ru |
| Source: | Computational Mathematics & Modeling. Oct2026, Vol. 37 Issue 4, p711-730. 20p. |
| Subjects: | Interval analysis, Distribution (Probability theory), Fuzzy algorithms, Monte Carlo method |
| Abstract: | Interval-valued data provides a natural representation for inherent uncertainty in domains ranging from environmental monitoring to predictive analytics. This paper introduces a novel attention-based framework for interval-valued regression that reformulates the task as an imprecise classification problem over "atomic" intervals derived from intersections of all observed training intervals. In contrast to many interval-valued models, predicted target outcome in the framework is represented as a discrete probability distribution over these "atomic" intervals, which are assumed to be constrained to truncated normal distributions with trainable standard deviations. The architecture employs a kernel-based aggregation layer, inspired by dot-product attention, where attention weights computed from input features aggregate probability distributions across instances to produce predictive distributions. We develop two parametric training models: IVT-MC (Interval-Valued Truncated normal-Monte Carlo), which approximates the expected log-likelihood loss via Monte Carlo sampling, and IVT-JL (Interval-Valued Truncated normal-Joint Learning), a more efficient approach that jointly optimizes model parameters and distributional standard deviations. Numerical experiments on synthetic and real datasets illustrate the models. Codes of the models are publicly available. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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