# What is Symbolic Regression in the Context of Machine Learning?

by Stephen M. Walker II, Co-Founder / CEO

## What is Symbolic Regression in the Context of Machine Learning?

Symbolic Regression is a form of regression analysis that seeks to find a mathematical expression, in symbolic form, that best fits a set of data points. Unlike traditional regression methods that fit data to a pre-specified model (like linear or polynomial regression), Symbolic Regression does not assume any particular model structure. Instead, it explores a potentially infinite space of mathematical expressions to uncover the underlying model that most accurately represents the data.

In the context of machine learning, Symbolic Regression is used as a powerful tool for model discovery. It can identify complex relationships between variables that are not apparent through standard regression techniques. This method is particularly useful in fields such as system identification, where the form of the system's dynamics is unknown, and in data-driven science, where discovering the governing equations from observations can be invaluable.

### How Does Symbolic Regression Work?

Symbolic Regression typically employs genetic programming or evolutionary algorithms to explore the space of mathematical expressions. These algorithms simulate the process of natural selection to evolve expressions over time, aiming to improve their fit to the data with each generation.

The process involves the following steps:

1. Initialization — Generate an initial population of random mathematical expressions.
2. Evaluation — Assess the fitness of each expression by how well it fits the data.
3. Selection — Choose the fittest expressions to be parents of the next generation.
4. Crossover and Mutation — Create a new generation of expressions by combining parts of parent expressions and introducing random changes.
5. Termination — Repeat the evaluation, selection, and reproduction steps until a satisfactory expression is found or a maximum number of generations is reached.

### What are the Benefits of Symbolic Regression?

Symbolic Regression offers several benefits in machine learning:

1. Model Interpretability — The resulting expressions are explicit and can be easily interpreted, which is valuable for understanding the underlying phenomena.
2. Flexibility — It can model a wide range of nonlinear and complex relationships without prior assumptions about the data structure.
3. Simplicity — The best-fitting expressions can often be simpler and more parsimonious than models produced by other non-linear regression methods.

### What are the Limitations of Symbolic Regression?

Despite its advantages, Symbolic Regression also has limitations:

1. Computational Complexity — Searching through an infinite space of expressions can be computationally intensive and time-consuming.
2. Overfitting — There is a risk of overfitting the data, especially if the search process is not carefully controlled.
3. Scalability — Symbolic Regression may not scale well to very large datasets or high-dimensional problems without significant modifications.

### How is Symbolic Regression Applied in AI Research?

In AI research, Symbolic Regression is applied in several ways:

1. Discovering Physical Laws — It has been used to rediscover known physical laws from experimental data, demonstrating its potential in automated scientific discovery.
2. Feature Engineering — Symbolic Regression can be used to create new features from raw data, which can improve the performance of other machine learning models.
3. Hybrid Models — Combining Symbolic Regression with other machine learning techniques can lead to hybrid models that leverage the strengths of both approaches.

### What is the Future of Symbolic Regression in Machine Learning?

The future of Symbolic Regression in machine learning looks promising, with ongoing research into improving its efficiency, scalability, and integration with other AI techniques. Advances in computing power and algorithm design are likely to expand its applicability and effectiveness in various domains, from scientific discovery to industrial process optimization. As interpretability becomes increasingly important in AI, Symbolic Regression's ability to provide understandable models will only grow in value.

## More terms

### What is combinatorial optimization?

Combinatorial optimization is a subfield of mathematical optimization that focuses on finding the optimal solution from a finite set of objects. The set of feasible solutions is discrete or can be reduced to a discrete set.

### What is approximation error?

Approximation error refers to the difference between an approximate value or solution and its exact counterpart. In mathematical and computational contexts, this often arises when we use an estimate or an algorithm to find a numerical solution instead of an analytical one. The accuracy of the approximation depends on factors like the complexity of the problem at hand, the quality of the method used, and the presence of any inherent limitations or constraints in the chosen approach.