GP for Symbolic Regression

In this problem, we use GP to search for an analytical expression that fits the data.

For example, given a target example:

$$y=x^4+x^3+x^2+x$$

Given samples $(x_i,y_i)$, GP must discover $\hat{f}(x)\approx y$.

The GP system only sees input-output samples:

We aim to minimize MSE:

$$\text{MSE}=\frac{1}{N}\sum _{i=1}^N(\hat{f}(x_i)-y_i{)}^2$$

With parsimony pressure, our objective becomes becomes:

$$J=\text{MSE}+\lambda \cdot \text{size}(T)$$

Tracing the progress:

Despite its strengths, symbolic regression with GP has challenges:

• Large computational cost
• Potential overfitting
• Sensitivity to function set design
• Multiple semantically equivalent expressions