Interpretation for complex equations

[gm89uk]

The ethos behind SR is interpretability.
However, in the event that a complex equation has much better fit to test data, the resulting equation, although much easier to work with than a blackbox model, is difficult to interpret.

How do you tackle this problem?
I have played around with using the SHAP library?

The permutation in SHAP is very slow and I am doubtful this is the best approach, but it does allow for feature importance.

This would give me this example output:

import shap

class CustomModel:
    def __init__(self, equation_str):
        self.equation_str = equation_str

    def predict(self, X):
        results = []
        for _, row in X.iterrows():
            sample_values = get_sample_values(row)
            result = eval(self.equation_str, sample_values)
            results.append(result)
        return np.array(results)

selected_equation_index = 38  # Change this to select a different equation
selected_equation = equation_strs[selected_equation_index]
model = CustomModel(selected_equation)

# Prepare the data using only relevant columns for SHAP
relevant_columns = list(variable_mapping.values())
X = combined_df[relevant_columns]  # Use combined_df instead of df
y_true = combined_df[target_variable]  # Use combined_df instead of df

# Ensure all data types are numeric, coerce errors
X = X.apply(pd.to_numeric, errors='coerce')
y_true = y_true.apply(pd.to_numeric, errors='coerce')

# Drop any remaining rows with NaN values
X = X.dropna()
y_true = y_true.loc[X.index]

# Generate SHAP values using Permutation Explainer
explainer = shap.Explainer(model.predict, X, algorithm="permutation")
shap_values = explainer(X)
shap.summary_plot(shap_values, X, plot_type="bar")
shap.summary_plot(shap_values, X)
shap.plots.beeswarm(shap_values)