ISR: Invertible Symbolic Regression
<|reference_start|>ISR: Invertible Symbolic Regression: We introduce an Invertible Symbolic Regression (ISR) method. It is a machine learning technique that generates analytical relationships between inputs and outputs of a given dataset via invertible maps (or architectures). The proposed ISR method naturally combines the principles of Invertible Neural Networks (INNs) and Equation Learner (EQL), a neural network-based symbolic architecture for function learning. In particular, we transform the affine coupling blocks of INNs into a symbolic framework, resulting in an end-to-end differentiable symbolic invertible architecture that allows for efficient gradient-based learning. The proposed ISR framework also relies on sparsity promoting regularization, allowing the discovery of concise and interpretable invertible expressions. We show that ISR can serve as a (symbolic) normalizing flow for density estimation tasks. Furthermore, we highlight its practical applicability in solving inverse problems, including a benchmark inverse kinematics problem, and notably, a geoacoustic inversion problem in oceanography aimed at inferring posterior distributions of underlying seabed parameters from acoustic signals.<|reference_end|>
@article{tohme2024isr:,
    title={ISR: Invertible Symbolic Regression},
    author={Tony Tohme, Mohammad Javad Khojasteh, Mohsen Sadr, Florian Meyer,
  Kamal Youcef-Toumi},
    journal={arXiv preprint arXiv:2405.06848},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.06848},
    primaryClass={cs.LG cs.AI cs.IT math.IT stat.ML}
}