Mathematical Equation-based Model Fitting Task
A Mathematical Equation-based Model Fitting Task is a model fitting task that produces a mathematical expression.
- AKA: Symbolic Regression, Equation Discovery.
- Context:
- It can be solved by a Mathematical Equation-based Model Fitting System (that implements a mathematical model fitting algorithm).
- …
- Counter-Example(s):
- See: Inductive Process Modeling; Learning as Search; Measurement Scales; Analytic Function.
References
2021
- (Wikipedia, 2021) ⇒ https://en.wikipedia.org/wiki/symbolic_regression Retrieved:2021-3-22.
- Symbolic Regression (SR) is a type of regression analysis that searches the space of mathematical expressions to find the model that best fits a given dataset, both in terms of accuracy and simplicity. No particular model is provided as a starting point to the algorithm. Instead, initial expressions are formed by randomly combining mathematical building blocks such as mathematical operators, analytic functions, constants, and state variables. Usually, a subset of these primitives will be specified by the person operating it, but that's not a requirement of the technique. The symbolic regression problem for mathematical functions has been tackled with a variety of methods, including recombining equations most commonly using genetic programming, as well as more recently methods utilizing Bayesian methods and physics inspired AI. The other non-classical alternative method to SR is called Universal Functions Originator (UFO), which has a different mechanism, search-space, and building strategy.
By not requiring a priori specification of a model, symbolic regression isn't affected by human bias, or unknown gaps in domain knowledge. It attempts to uncover the intrinsic relationships of the dataset, by letting the patterns in the data itself reveal the appropriate models, rather than imposing a model structure that is deemed mathematically tractable from a human perspective. The fitness function that drives the evolution of the models takes into account not only error metrics (to ensure the models accurately predict the data), but also special complexity measures, thus ensuring that the resulting models reveal the data's underlying structure in a way that's understandable from a human perspective. This facilitates reasoning and favors the odds of getting insights about the data-generating system.
- Symbolic Regression (SR) is a type of regression analysis that searches the space of mathematical expressions to find the model that best fits a given dataset, both in terms of accuracy and simplicity. No particular model is provided as a starting point to the algorithm. Instead, initial expressions are formed by randomly combining mathematical building blocks such as mathematical operators, analytic functions, constants, and state variables. Usually, a subset of these primitives will be specified by the person operating it, but that's not a requirement of the technique. The symbolic regression problem for mathematical functions has been tackled with a variety of methods, including recombining equations most commonly using genetic programming, as well as more recently methods utilizing Bayesian methods and physics inspired AI. The other non-classical alternative method to SR is called Universal Functions Originator (UFO), which has a different mechanism, search-space, and building strategy.
2011
- (Todorovski, 2011a) ⇒ Ljupco Todorovski. (2011). “Equation Discovery.” In: (Sammut & Webb, 2011) p.327
2004
- http://www.mafy.lut.fi/EcmiNL/older/ecmi35/node70.html
- KEYWORDS: analytic programming, genetic programming, grammar evolution, evolution algorithms, symbolic regression.
- QUOTE: Term “symbolic regression” (SR) represents process during which are measured data fitted by suitable mathematical formula like “[math]\displaystyle{ x^2 + C }[/math], [math]\displaystyle{ \sin(x)+1/e^x }[/math], etc. This process is amongst mathematician quite well known and used when some data of unknown process are obtained.