Shape-constrained Symbolic Regression -- Improving Extrapolation with Prior Knowledge

• URL: http://arxiv.org/abs/2103.15624v1
• Date: Mon, 29 Mar 2021 14:04:18 GMT
• Title: Shape-constrained Symbolic Regression -- Improving Extrapolation with Prior Knowledge
• Authors: Gabriel Kronberger and Fabricio Olivetti de Fran\c{c}a and Bogdan Burlacu and Christian Haider and Michael Kommenda
• Abstract summary: The aim is to find models which conform to expected behaviour and which have improved capabilities. The algorithms are tested on a set of 19 synthetic and four real-world regression problems. Shape-constrained regression produces the best results for the test set but also significantly larger models.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the addition of constraints on the function image and its derivatives for the incorporation of prior knowledge in symbolic regression. The approach is called shape-constrained symbolic regression and allows us to enforce e.g. monotonicity of the function over selected inputs. The aim is to find models which conform to expected behaviour and which have improved extrapolation capabilities. We demonstrate the feasibility of the idea and propose and compare two evolutionary algorithms for shape-constrained symbolic regression: i) an extension of tree-based genetic programming which discards infeasible solutions in the selection step, and ii) a two population evolutionary algorithm that separates the feasible from the infeasible solutions. In both algorithms we use interval arithmetic to approximate bounds for models and their partial derivatives. The algorithms are tested on a set of 19 synthetic and four real-world regression problems. Both algorithms are able to identify models which conform to shape constraints which is not the case for the unmodified symbolic regression algorithms. However, the predictive accuracy of models with constraints is worse on the training set and the test set. Shape-constrained polynomial regression produces the best results for the test set but also significantly larger models.

Related papers

• Comparative study of regression vs pairwise models for surrogate-based heuristic optimisation [1.2535250082638645]
  This paper addresses the formulation of surrogate problems as both regression models that approximate fitness (surface surrogate models) and a novel way to connect classification models (pairwise surrogate models) The performance of the overall search, when using online machine learning-based surrogate models, depends not only on the accuracy of the predictive model but also on the kind of bias towards positive or negative cases.
  arXiv  Detail & Related papers  (2024-10-04T13:19:06Z)
• Branch and Bound to Assess Stability of Regression Coefficients in Uncertain Models [0.6990493129893112]
  We introduce our algorithm, along with supporting mathematical results, an example application, and a link to our computer code. It helps researchers summarize high-dimensional data and assess the stability of regression coefficients in uncertain models.
  arXiv  Detail & Related papers  (2024-08-19T01:37:14Z)
• Scaling and renormalization in high-dimensional regression [72.59731158970894]
  This paper presents a succinct derivation of the training and generalization performance of a variety of high-dimensional ridge regression models. We provide an introduction and review of recent results on these topics, aimed at readers with backgrounds in physics and deep learning.
  arXiv  Detail & Related papers  (2024-05-01T15:59:00Z)
• Deep Generative Symbolic Regression [83.04219479605801]
  Symbolic regression aims to discover concise closed-form mathematical equations from data. Existing methods, ranging from search to reinforcement learning, fail to scale with the number of input variables. We propose an instantiation of our framework, Deep Generative Symbolic Regression.
  arXiv  Detail & Related papers  (2023-12-30T17:05:31Z)
• A Pseudo-Semantic Loss for Autoregressive Models with Logical Constraints [87.08677547257733]
  Neuro-symbolic AI bridges the gap between purely symbolic and neural approaches to learning. We show how to maximize the likelihood of a symbolic constraint w.r.t the neural network's output distribution. We also evaluate our approach on Sudoku and shortest-path prediction cast as autoregressive generation.
  arXiv  Detail & Related papers  (2023-12-06T20:58:07Z)
• Toward Physically Plausible Data-Driven Models: A Novel Neural Network Approach to Symbolic Regression [2.7071541526963805]
  This paper proposes a novel neural network-based symbolic regression method. It constructs physically plausible models based on even very small training data sets and prior knowledge about the system. We experimentally evaluate the approach on four test systems: the TurtleBot 2 mobile robot, the magnetic manipulation system, the equivalent resistance of two resistors in parallel, and the longitudinal force of the anti-lock braking system.
  arXiv  Detail & Related papers  (2023-02-01T22:05:04Z)
• Using Shape Constraints for Improving Symbolic Regression Models [0.0]
  We describe and analyze algorithms for shape-constrained symbolic regression. We use a set of models from physics textbooks to test the algorithms. The results show that all algorithms are able to find models which conform to all shape constraints.
  arXiv  Detail & Related papers  (2021-07-20T12:53:28Z)
• Goal-directed Generation of Discrete Structures with Conditional Generative Models [85.51463588099556]
  We introduce a novel approach to directly optimize a reinforcement learning objective, maximizing an expected reward. We test our methodology on two tasks: generating molecules with user-defined properties and identifying short python expressions which evaluate to a given target value.
  arXiv  Detail & Related papers  (2020-10-05T20:03:13Z)
• Slice Sampling for General Completely Random Measures [74.24975039689893]
  We present a novel Markov chain Monte Carlo algorithm for posterior inference that adaptively sets the truncation level using auxiliary slice variables. The efficacy of the proposed algorithm is evaluated on several popular nonparametric models.
  arXiv  Detail & Related papers  (2020-06-24T17:53:53Z)
• The data-driven physical-based equations discovery using evolutionary approach [77.34726150561087]
  We describe the algorithm for the mathematical equations discovery from the given observations data. The algorithm combines genetic programming with the sparse regression. It could be used for governing analytical equation discovery as well as for partial differential equations (PDE) discovery.
  arXiv  Detail & Related papers  (2020-04-03T17:21:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.