Symbolic Regression searches for a function form that approximates a dataset
often using Genetic Programming.
Since there is usually no restriction to what form the function can have,
Genetic Programming may return a hard to understand model due to non-linear
function chaining or long expressions. A novel representation called
Interaction-Transformation was recently proposed to alleviate this problem. In
this representation, the function form is restricted to an affine combination
of terms generated as the application of a single univariate function to the
interaction of selected variables. This representation obtained competing
solutions on standard benchmarks. Despite the initial success, a broader set of
benchmarking functions revealed the limitations of the constrained
representation.
In this paper we propose an extension to this representation, called
Transformation-Interaction-Rational representation that defines a new function
form as the rational of two Interaction-Transformation functions. Additionally,
the target variable can also be transformed with an univariate function. The
main goal is to improve the approximation power while still constraining the
overall complexity of the expression.
We tested this representation with a standard Genetic Programming with
crossover and mutation. The results show a great improvement when compared to
its predecessor and a state-of-the-art performance for a large benchmark.

本文提出一种扩展 Interaction-Transformation 方法的新函数形式，称为 Transformation-Interaction-Rational representation，通过对目标变量的变换，并使用两个 Interaction-Transformation 函数的有理数形式，提高了模型的近似能力。在大型基准测试中取得了与尖端性能相当的结果。

符号回归的变换 - 交互 - 理性表示

Transformation-Interaction-Rational Representation for Symbolic  Regression

The Interaction-Transformation (IT) is a new representation for Symbolic
Regression that restricts the search space into simpler, but expressive,
function forms. This representation has the advantage of creating a smoother
search space unlike the space generated by Expression Trees, the common
representation used in Genetic Programming. This paper introduces an
Evolutionary Algorithm capable of evolving a population of IT expressions
supported only by the mutation operator. The results show that this
representation is capable of finding better approximations to real-world data
sets when compared to traditional approaches and a state-of-the-art Genetic
Programming algorithm.

本文提出一种基于交互转换（IT）的进化算法，通过限制搜索空间到更简单但表达能力更强的函数形式，相对于遗传编程中常用的表达式树，该表示法具有创建更平滑的搜索空间的优点，并在真实数据集的逼近方面比传统方法和最先进的遗传编程算法表现更好。