- author = "Baligh Al-Helali and Qi Chen and Bing Xue and Mengjie Zhang",
- title = "Hessian Complexity Measure for Genetic Programming-based Imputation Predictor Selection in Symbolic Regression with Incomplete Data",
- booktitle = "EuroGP 2020: Proceedings of the 23rd European Conference on Genetic Programming",
- year = "2020",
- month = "15-17 " # apr,
- editor = "Ting Hu and Nuno Lourenco and Eric Medvet",
- series = "LNCS",
- volume = "12101",
- publisher = "Springer Verlag",
- address = "Seville, Spain",
- pages = "1--17",
- organisation = "EvoStar, Species",
- keywords = "genetic algorithms, genetic programming, Symbolic regression, Incomplete data, Feature selection, Imputation, Model complexity",
- isbn13 = "978-3-030-44093-0",
-
video_url = "
https://www.youtube.com/watch?v=zeZvFJElkBM",
-
DOI = "
doi:10.1007/978-3-030-44094-7_1",
- abstract = "Missing values bring several challenges when learning from real-world data sets. Imputation is a widely adopted approach to estimating missing values. However, it has not been adequately investigated in symbolic regression. When imputing the missing values in an incomplete feature, the other features that are used in the prediction process are called imputation predictors. In this work, a method for imputation predictor selection using regularized genetic programming (GP) models is presented for symbolic regression tasks on incomplete data. A complexity measure based on the Hessian matrix of the phenotype of the evolving models is proposed. It is employed as a regularizer in the fitness function of GP for model selection and the imputation predictors are selected from the selected models. In addition to the baseline which uses all the available predictors, the proposed selection method is compared with two GP-based feature selection variations: the standard GP feature selector and GP with feature selection pressure. The trends in the results reveal that in most cases, using the predictors selected by regularized GP models could achieve a considerable reduction in the imputation error and improve the symbolic regression performance as well.",
-
notes = "fitness = error + lamda * complexity. (Lamda fixed
linear weighting)
Model complexity based on second order partial derivaties (not tree size). Form n by n Hessian matrix, where n is number of inputs (terminal set size). Each element is 2nd order partial dertivative of GP tree with respect to input i and input j. Hessian is symetric matrix. Matrix C is Hessian with all constant terms set to zero.
Complexity = determinant of C divided by the determinant of H. (calculated with python package SymPy). Division replaced by analytic quotiant \cite{Ni:2012:ieeeTEC}.
Data missing at random.
Five OpenML benchmarks. Compare python DEAP with Linear Regression, PMM, KNN (R package Simpulation).
http://www.evostar.org/2020/cfp_eurogp.php Part of \cite{Hu:2020:GP} EuroGP'2020 held in conjunction with EvoCOP2020, EvoMusArt2020 and EvoApplications2020",
