Symbolic Regression of Conditional Target Expressions

Korns, Michael F.

doi:10.1007/978-1-4419-1626-6_13

Cited by 11 publications

(13 citation statements)

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“…For example, forecasting benchmarks are often based on chaotic attractors (e.g., [156]) thus uncertainty regarding concept shift/drift. Likewise, some of the most challenging regression tasks include a 'switch' between different model generating processes and dummy attributes [108]. Indeed, similar challenges exist in related fields, such as regime switching in econometrics (e.g., [116]).…”

Section: Resultsmentioning

confidence: 98%

Evolutionary model building under streaming data for classification tasks: opportunities and challenges

Heywood

2014

Genet Program Evolvable Mach

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Streaming data analysis potentially represents a significant shift in emphasis from schemes historically pursued for offline (batch) approaches to the classification task. In particular, a streaming data application implies that: (1) the data itself has no formal 'start' or 'end'; (2) the properties of the process generating the data are non-stationary, thus models that function correctly for some part(s) of a stream may be ineffective elsewhere; (3) constraints on the time to produce a response, potentially implying an anytime operational requirement; and (4) given the prohibitive cost of employing an oracle to label a stream, a finite labelling budget is necessary. The scope of this article is to provide a survey of developments for model building under streaming environments from the perspective of both evolutionary and non-evolutionary frameworks. In doing so, we bring attention to the challenges and opportunities that developing solutions to streaming data classification tasks are likely to face using evolutionary approaches.

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Section: Resultsmentioning

confidence: 98%

Evolutionary model building under streaming data for classification tasks: opportunities and challenges

Heywood

2014

Genet Program Evolvable Mach

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“…The previously published results (Korns, 2009) of training on the nine base training models on 10,000 rows and five columns with no random noise and only 20 generations allowed, are shown in Table 7-1 1 .…”

Section: Previous Results On Nine Base Problemsmentioning

confidence: 99%

“…out of sample testing). Our two fitness measures are described in detail in (Korns, 2009) and consist of a standard least squared error which is normalized by dividing LSE by the standard deviation of Y (dependent variable). This normalization allows us to meaningfully compare the normalized least squared error (NLSE) between different problems.…”

Section: Testing Regimen and Fitness Measurementioning

confidence: 99%

“…In previous papers (Korns, 2006;Korns, 2007;Korns and Nunez, 2008;Korns, 2009), our pursuit of industrial scale performance with large-scale, symbolic regression problems, required us to reexamine many commonly held beliefs and to borrow a number of techniques from disparate schools of genetic programming and recombine them in ways not normally seen in the published literature. The techniques of abstract expression grammars were developed, but expored only tangentially.…”

Section: Introductionmentioning

confidence: 99%

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Abstract Expression Grammar Symbolic Regression

Korns¹

2010

Genetic and Evolutionary Computation

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This chapter examines the use of Abstract Expression Grammars to perform the entire Symbolic Regression process without the use of Genetic Programming per se. The techniques explored produce a symbolic regression engine which has absolutely no bloat, which allows total user control of the search space and output formulas, which is faster, and more accurate than the engines produced in our previous papers using Genetic Programming. The genome is an all vector structure with four chromosomes plus additional epigenetic and constraint vectors, allowing total user control of the search space and the final output formulas. A combination of specialized compiler techniques, genetic algorithms, particle swarm, aged layered populations, plus discrete and continuous differential evolution are used to produce an improved symbolic regression sytem. Nine base test cases, from the literature, are used to test the improvement in speed and accuracy. The improved results indicate that these techniques move us a big step closer toward future industrial strength symbolic regression systems. While the techniques, described in detail in (Korns, 2009), produce a symbolic regression system of breadth and strength, lack of user control of the search space, bloated unreadable output formulas, accuracy, and slow convergence speed are all issues keeping an industrial strength symbolic regression system tantalizingly out of reach. In this chapter abstract expression grammars become the main focus and are promoted as the sole means of performing symbolic regression. Using the nine base test cases from (Korns, 2007) as a training set, to test for improvements in accuracy, we constructed our symbolic regression system using these important techniques:Abstract expression grammars Universal abstract goal expression Standard single point vector-based mutation Standard two point vector-based cross over Continuous vector differential evolution Discrete vector differential evolution Continuous particle swarm evolution Pessimal vertical slicing and out-of-sample scoring during training Age-layered populations User defined epigenetic factors User defined constraints

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“…Our fitness measure is normalized least squared error (NLSE) as defined in (Korns, 2009). Normalized least squared error is the least squared error value divided by the standard deviation of Y.…”

Section: Testing Regimenmentioning

confidence: 99%

Accuracy in Symbolic Regression

Korns

2011

Genetic and Evolutionary Computation

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This chapter asserts that, in current state-of-the-art symbolic regression engines, accuracy is poor. That is to say that state-of-the-art symbolic regression engines return a champion with good fitness; however, obtaining a champion with the correct formula is not forthcoming even in cases of only one basis function with minimally complex grammar depth.Ideally, users expect that for test problems created with no noise, using only functions in the specified grammar, with only one basis function and some minimal grammar depth, that state-of-the-art symbolic regression systems should return the exact formula (or at least an isomorph) used to create the test data. Unfortunately, this expectation cannot currently be achieved using published state-of-the-art symbolic regression techniques.Several classes of test formulas, which prove intractable, are examined and an understanding of why they are intractable is developed. Techniques in Abstract Expression Grammars are employed to render these problems tractable, including manipulation of the epigenome during the evolutionary process, together with breeding of multiple targeted epigenomes in separate population islands.A selected set of currently intractable problems are shown to be solvable, using these techniques, and a proposal is put forward for a discipline-wide program of improving accuracy in state-of-the-art symbolic regression systems.

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Symbolic Regression of Conditional Target Expressions

Cited by 11 publications

References 1 publication

Evolutionary model building under streaming data for classification tasks: opportunities and challenges

Evolutionary model building under streaming data for classification tasks: opportunities and challenges

Abstract Expression Grammar Symbolic Regression

Accuracy in Symbolic Regression

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