e Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) is a recently introduced model-based EA that has been shown to be capable of outperforming state-of-the-art alternative EAs in terms of scalability when solving discrete optimization problems. One of the key aspects of GOMEA's success is a variation operator that is designed to extensively exploit linkage models by e ectively combining partial solutions. Here, we bring the strengths of GOMEA to Genetic Programming (GP), introducing GP-GOMEA. Under the hypothesis of having li le problem-speci c knowledge, and in an e ort to design easy-to-use EAs, GP-GOMEA requires no parameter speci cation. On a set of well-known benchmark problems we nd that GP-GOMEA outperforms standard GP while being on par with more recently introduced, state-of-the-art EAs. We furthermore introduce Input-space Entropy-based Building-block Learning (IEBL), a novel approach to identifying and encapsulating relevant building blocks (subroutines) into new terminals and functions. On problems with an inherent degree of modularity, IEBL can contribute to compact solution representations, providing a large potential for knock-on e ects in performance. On the di cult, but highly modular Even Parity problem, GP-GOMEA+IEBL obtains excellent scalability, solving the 14-bit instance in less than 1 hour.
The Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) is a model-based EA framework that has been shown to perform well in several domains, including Genetic Programming (GP). Differently from traditional EAs where variation acts blindly, GOMEA learns a model of interdependencies within the genotype, i.e., the linkage, to estimate what patterns to propagate. In this article, we study the role of Linkage Learning (LL) performed by GOMEA in Symbolic Regression (SR). We show that the non-uniformity in the distribution of the genotype in GP populations negatively biases LL, and propose a method to correct for this. We also propose approaches to improve LL when ephemeral random constants are used. Furthermore, we adapt a scheme of interleaving runs to alleviate the burden of tuning the population size, a crucial parameter for LL, to SR.We run experiments on 10 real-world datasets, enforcing a strict limitation on solution size, to enable interpretability. We find that the new LL method outperforms the standard one, and that GOMEA outperforms both traditional and semantic GP. We also find that the small solutions evolved by GOMEA are competitive with tuned decision trees, making GOMEA a promising new approach to SR.
Many risk-sensitive applications require Machine Learning (ML) models to be interpretable. Attempts to obtain interpretable models typically rely on tuning, by trial-and-error, hyper-parameters of model complexity that are only loosely related to interpretability. We show that it is instead possible to take a meta-learning approach: an ML model of non-trivial Proxies of Human Interpretability (PHIs) can be learned from human feedback, then this model can be incorporated within an ML training process to directly optimize for interpretability. We show this for evolutionary symbolic regression. We first design and distribute a survey finalized at finding a link between features of mathematical formulas and two established PHIs, simulatability and decomposability. Next, we use the resulting dataset to learn an ML model of interpretability. Lastly, we query this model to estimate the interpretability of evolving solutions within bi-objective genetic programming. We perform experiments on five synthetic and eight real-world symbolic regression problems, comparing to the traditional use of solution size minimization. The results show that the use of our model leads to formulas that are, for a same level of accuracy-interpretability trade-off, either significantly more or equally accurate. Moreover, the formulas are also arguably more interpretable. Given the very positive results, we believe that our approach represents an important stepping stone for the design of next-generation interpretable (evolutionary) ML algorithms.
The recently introduced Gene-pool Optimal Mixing Evolutionary Algorithm for Genetic Programming (GP-GOMEA) has been shown to find much smaller solutions of equally high quality compared to other state-of-the-art GP approaches. This is an interesting aspect as small solutions better enable human interpretation. In this paper, an adaptation of GP-GOMEA to tackle real-world symbolic regression is proposed, in order to find small yet accurate mathematical expressions, and with an application to a problem of clinical interest. For radiotherapy dose reconstruction, a model is sought that captures anatomical patient similarity. This problem is particularly interesting because while features are patient-specific, the variable to regress is a distance, and is defined over patient pairs. We show that on benchmark problems as well as on the application, GP-GOMEA outperforms variants of standard GP. To find even more accurate models, we further consider an evolutionary meta learning approach, where GP-GOMEA is used to construct small, yet effective features for a different machine learning algorithm. Experimental results show how this approach significantly improves the performance of linear regression, support vector machines, and random forest, while providing meaningful and interpretable features.
Purpose: The aim of this study is to establish the first step toward a novel and highly individualized three-dimensional (3D) dose distribution reconstruction method, based on CT scans and organ delineations of recently treated patients. Specifically, the feasibility of automatically selecting the CT scan of a recently treated childhood cancer patient who is similar to a given historically treated child who suffered from Wilms' tumor is assessed. Methods: A cohort of 37 recently treated children between 2-and 6-yr old are considered. Five potential notions of ground-truth similarity are proposed, each focusing on different anatomical aspects. These notions are automatically computed from CT scans of the abdomen and 3D organ delineations (liver, spleen, spinal cord, external body contour). The first is based on deformable image registration, the second on the Dice similarity coefficient, the third on the Hausdorff distance, the fourth on pairwise organ distances, and the last is computed by means of the overlap volume histogram. The relationship between typically available features of historically treated patients and the proposed ground-truth notions of similarity is studied by adopting state-of-the-art machine learning techniques, including random forest. Also, the feasibility of automatically selecting the most similar patient is assessed by comparing ground-truth rankings of similarity with predicted rankings. Results: Similarities (mainly) based on the external abdomen shape and on the pairwise organ distances are highly correlated (Pearson r p ≥ 0.70) and are successfully modeled with random forests based on historically recorded features (pseudo-R 2 ≥ 0.69). In contrast, similarities based on the shape of internal organs cannot be modeled. For the similarities that random forest can reliably model, an estimation of feature relevance indicates that abdominal diameters and weight are the most important. Experiments on automatically selecting similar patients lead to coarse, yet quite robust results: the most similar patient is retrieved only 22% of the times, however, the error in worst-case scenarios is limited, with the fourth most similar patient being retrieved. Conclusions: Results demonstrate that automatically selecting similar patients is feasible when focusing on the shape of the external abdomen and on the position of internal organs. Moreover, whereas the common practice in phantom-based dose reconstruction is to select a representative phantom using age, height, and weight as discriminant factors for any treatment scenario, our analysis on abdominal tumor treatment for children shows that the most relevant features are weight and the anterior-posterior and left-right abdominal diameters.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.