ISR: Invertible Symbolic Regression

• URL: http://arxiv.org/abs/2405.06848v1
• Date: Fri, 10 May 2024 23:20:46 GMT
• Title: ISR: Invertible Symbolic Regression
• Authors: Tony Tohme, Mohammad Javad Khojasteh, Mohsen Sadr, Florian Meyer, Kamal Youcef-Toumi,
• Abstract summary: Invertible Symbolic Regression is a machine learning technique that generates analytical relationships between inputs and outputs of a given dataset via invertible maps. We transform the affine coupling blocks of INNs into a symbolic framework, resulting in an end-to-end differentiable symbolic invertible architecture. We show that ISR can serve as a (symbolic) normalizing flow for density estimation tasks.
• Score: 7.499800486499609
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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