Divide and Conquer: A Quick Scheme for Symbolic Regression

2021 ◽  
Author(s):  
Changtong Luo ◽  
Chen Chen ◽  
Zonglin Jiang
Keyword(s):  
Target Function ◽  
Search Space ◽  
Symbolic Regression ◽  
Divide And Conquer ◽  
Model Function ◽  
Quick Scheme ◽  
Special Machine ◽  
Sample Data ◽  
Accurate Expression ◽  
Regression Problems

Symbolic regression (SR), as a special machine learning method, can produce mathematical models with explicit expressions. It has received increasing attention in recent years. However, finding a concise, accurate expression is still challenging because of its huge search space. In this work, a divide and conquer (D&C) scheme is proposed. It tries to divide the search space into a number of orthogonal sub-spaces based on the separability feature inferred from the sample data (dividing process). For each sub-space, a sub-function is learned (conquering process). The target model function is then reconstructed with the sub-functions according to their separability patterns. To this end, a separability pattern detecting technique, bi-correlation test (Bi-CT), is also proposed. Note that the sub-functions could be determined by any of the existing SR methods, which makes D&C easy to use. The D&C powered SR has been tested on many symbolic regression problems, and the study shows that D&C can help SR to get the target function more quickly and reliably.

scholarly journals A NEW LINEAR GENETIC PROGRAMMING APPROACH BASED ON STRAIGHT LINE PROGRAMS: SOME THEORETICAL AND EXPERIMENTAL ASPECTS

2009 ◽  
Vol 18 (05) ◽  
pp. 757-781 ◽  
Author(s):  
CÉSAR L. ALONSO ◽  
JOSÉ LUIS MONTAÑA ◽  
JORGE PUENTE ◽  
CRUZ ENRIQUE BORGES
Keyword(s):  
Data Structure ◽  
Genetic Programming ◽  
Computer Programs ◽  
Symbolic Regression ◽  
Programming Approach ◽  
Linear Genetic Programming ◽  
Straight Line ◽  
Structured Representations ◽  
Regression Problems ◽  
Straight Line Programs

Tree encodings of programs are well known for their representative power and are used very often in Genetic Programming. In this paper we experiment with a new data structure, named straight line program (slp), to represent computer programs. The main features of this structure are described, new recombination operators for GP related to slp's are introduced and a study of the Vapnik-Chervonenkis dimension of families of slp's is done. Experiments have been performed on symbolic regression problems. Results are encouraging and suggest that the GP approach based on slp's consistently outperforms conventional GP based on tree structured representations.

MONTE CARLO METHODS IN FUZZY NON-LINEAR REGRESSION

2008 ◽  
Vol 04 (02) ◽  
pp. 123-141 ◽  
Author(s):  
AREEG ABDALLA ◽  
JAMES BUCKLEY
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Linear Regression ◽  
Fuzzy Numbers ◽  
Random Number ◽  
Random Number Generator ◽  
Search Space ◽  
Triangular Fuzzy Numbers ◽  
Non Linear ◽  
Regression Problems

We apply our new fuzzy Monte Carlo method to certain fuzzy non-linear regression problems to estimate the best solution. The best solution is a vector of triangular fuzzy numbers, for the fuzzy coefficients in the model, which minimizes an error measure. We use a quasi-random number generator to produce random sequences of these fuzzy vectors which uniformly fill the search space. We consider example problems to show that this Monte Carlo method obtains solutions comparable to those obtained by an evolutionary algorithm.

scholarly journals Improved Parallel Legalization Schemes for Standard Cell Placement with Obstacles

Technologies ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 3
Author(s):  
Panagiotis Oikonomou ◽  
Antonios Dadaliaris ◽  
Kostas Kolomvatsos ◽  
Thanasis Loukopoulos ◽  
Athanasios Kakarountas ◽  
...  
Keyword(s):  
Target Function ◽  
Problem Formulation ◽  
Search Space ◽  
Standard Cell ◽  
Chip Area ◽  
Time Performance ◽  
Trade Offs ◽  
Cell Placement ◽  
Placement Algorithm ◽  
Algorithmic Approaches

In standard cell placement, a circuit is given consisting of cells with a standard height, (different widths) and the problem is to place the cells in the standard rows of a chip area so that no overlaps occur and some target function is optimized. The process is usually split into at least two phases. In a first pass, a global placement algorithm distributes the cells across the circuit area, while in the second step, a legalization algorithm aligns the cells to the standard rows of the power grid and alleviates any overlaps. While a few legalization schemes have been proposed in the past for the basic problem formulation, few obstacle-aware extensions exist. Furthermore, they usually provide extreme trade-offs between time performance and optimization efficiency. In this paper, we focus on the legalization step, in the presence of pre-allocated modules acting as obstacles. We extend two known algorithmic approaches, namely Tetris and Abacus, so that they become obstacle-aware. Furthermore, we propose a parallelization scheme to tackle the computational complexity. The experiments illustrate that the proposed parallelization method achieves a good scalability, while it also efficiently prunes the search space resulting in a superlinear speedup. Furthermore, this time performance comes at only a small cost (sometimes even improvement) concerning the typical optimization metrics.

scholarly journals Cluster Analysis of a Symbolic Regression Search Space

2019 ◽  
pp. 85-102 ◽  
Author(s):  
Gabriel Kronberger ◽  
Lukas Kammerer ◽  
Bogdan Burlacu ◽  
Stephan M. Winkler ◽  
Michael Kommenda ◽  
...  
Keyword(s):  
Cluster Analysis ◽  
Search Space ◽  
Symbolic Regression

Convergence analysis of distributed multi-penalty regularized pairwise learning

2019 ◽  
Vol 18 (01) ◽  
pp. 109-127
Author(s):  
Ting Hu ◽  
Jun Fan ◽  
Dao-Hong Xiang
Keyword(s):  
Single Machine ◽  
Learning Algorithm ◽  
Target Function ◽  
Distributed Learning ◽  
Divide And Conquer ◽  
Learning Performance ◽  
Manifold Regularization ◽  
Optimal Learning ◽  
Pairwise Learning ◽  
Optimal Learning Rate

In this paper, we establish the error analysis for distributed pairwise learning with multi-penalty regularization, based on a divide-and-conquer strategy. We demonstrate with [Formula: see text]-error bound that the learning performance of this distributed learning scheme is as good as that of a single machine which could process the whole data. With semi-supervised data, we can relax the restriction of the number of local machines and enlarge the range of the target function to guarantee the optimal learning rate. As a concrete example, we show that the work in this paper can apply to the distributed pairwise learning algorithm with manifold regularization.

ON LABEL INFORMATION INCORPORATED METRIC LEARNING FOR REGRESSIONS

2010 ◽  
Vol 09 (04) ◽  
pp. 339-351 ◽  
Author(s):  
CHENG JIN ◽  
YANGJING LONG
Keyword(s):  
Optimization Problem ◽  
Learning Algorithm ◽  
Metric Learning ◽  
Gaussian Process Regression ◽  
Test Sample ◽  
Optimization Method ◽  
Distance Metric ◽  
Sample Data ◽  
Label Information ◽  
Regression Problems

We present a distance metric learning algorithm for regression problems, which incorporates label information to form a biased distance metric in the process of learning. We use Newton's optimization method to solve an optimization problem for the sake of learning this biased distance metric. Experiments show that this method can find the intrinsic variation trend of data in a regression model by a relative small amount of samples without any prior assumption of the structure or distribution of data. In addition, the test sample data can be projected to this metric by a simple linear transformation and it is easy to be combined with manifold learning algorithms to improve the performance. Experiments are conducted on the FG-NET aging database, the UIUC-IFP-Y aging database, and the CHIL head pose database by Gaussian process regression based on the learned metric, which shows that our method is competitive among the start-of-art.

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