Custom subexpressions within final expressions

[janzenchoi]

Hello,

Currently, I have been able to specify the operators in the final expression.

However, I would like to introduce a custom function (of input variables and constants) that is made optionally-available for the regressor to use as an element in the final expression.

For instance, I would like to introduce the power law, A*x^n, where A and n are constants to be fine tuned by the regressor, and x is one of the input variables. The final expression would ideally look something like the equation below, where the custom function (15.6*x^2.4) is merely an element.

y = 1/x - (15.6*x^2.4) / (x+4.2) 

I tried to implement this in TemplateExpressionSpec, but it fixes a specific structure and number of inputs/coefficients. Is there an alternate approach that could allow me to achieve these custom functions?

Thanks for the help.

Regards,
Janzen

[MilesCranmer]

@janzenchoi could you perhaps give additional examples of what you mean? Essentially, what would "candidate" expressions look like for a single search? I think there's a way to make TemplateExpressionSpec work for this.

[janzenchoi]

Hello @MilesCranmer,

Thanks for the response. The candidate expressions could have the power law somewhere inside them, though they may omit it if it provides a worse fit. Ideally, the candidate expressions would look something like:

1. y = 12.4*x^3.4 + 17.4
2. y = (6.7*x^2.7) / (x+1.5)
3. y = 23.5 * exp(1.8*x^4.2) + 0.5

Where the regressor is allowed to place the power law (A*x^n) anywhere in the expression.

[MilesCranmer]

Thanks. In this case you can do it with a template expression like this:

template = TemplateExpressionSpec(
    expressions=["f",],
    variable_names=["x"],
    parameters={"p": 2}
    combine="""
        A, n = p[1], p[2]
        axn = A * x ^ n
        f(x, axn)
    """
)
model = PySRRegressor(
    expression_spec=template,
    binary_operators=["+", "*", "-", "/"],
)

[janzenchoi]

Oh, that is wonderful. Thank you!