Fitting Discontinuous Expressions

[janzenchoi]

Hello,

I am using TemplateExpressionSpec to fit two expressions, z0 and z1. The z0 expression is undefined/complex after x0 > z1. The template returns the sum of the relative errors, which the loss function interprets as the loss. The following is a snippet of my code to fit the discontinuous expression.

expression_spec = TemplateExpressionSpec(
    expressions    = ["f0", "fA", "fn", "fM", "fphi", "fchi"],
    variable_names = ["x0", "x1", "x2", "y0", "y1"],
    combine        = """
        A = 10^fA(x2); n = abs(fn(x2)); M = 10^fM(x2); phi = abs(fphi(x2)); chi = abs(fchi(x2));
        z0 = A*x1^n * ((1-(phi+1)*M*x1^chi*x0)^((phi+1-n)/(phi+1))-1) / (M*x1^chi*(n-phi-1)) + f0(x0,x1,x2);
        z1 = 1/((phi+1)*M*x1^chi);
        ((y0-z0)/y0)^2 + ((y1-z1)/y1)^2
    """
)

regressor = PySRRegressor(
    expression_spec  = expression_spec,
    populations      = 32,
    population_size  = 32,
    maxsize          = 16,
    niterations      = 128,
    precision        = 64,
    verbosity        = 0,
    binary_operators = ["+", "*", "/"],
    unary_operators  = ["log"],
    elementwise_loss = "take_first(p, t, w) = p",
)

In fitting the expressions, the loss function may try to evaluate the relative error where the z0 is undefined (i.e., x0 > z1).

Is there any way to have the loss function only calculate the loss for defined / real z0 values (i.e., when x0 < z1 )?

Thanks again for the help.

[MilesCranmer]

Not sure if I follow butiIt should automatically do this already. The NaNs will propagate and the expression will receive an infinite loss. Therefore the genetic algorithm will avoid expression that give such terms.

But yes, it will consider all points in the dataset. If any point is NaN, it will be thrown out.

[janzenchoi]

For my problem, a solution can be good even if there are NaNs when x0 > z1. Is there a way for the solution to not be thrown out if there are NaNs? Instead, the loss function would only calculate the error for x0 < z1.

[MilesCranmer]

what happens if all x0 > z1? Or if only one point is safe? I guess you’d have to set some threshold.

but you can get the underlying arrays with .x and the validity with .valid. Just be sure to propagate the validity and return a ValidVector(x, valid) from the code block.

[janzenchoi]

I included the relative error for z1 in the loss function, so I'm thinking that having only one safe point wouldn't be a big issue.

I'm not very familiar with Julia. Where would I access the .x and .valid values? And how would one do such propagation?

[MilesCranmer]

All of the variables in the combine code are ValidVector types. They each have .valid and .x