Question about the output of Hall of Frame

[qizzhao]

Hi, I am new to the SymbolicRegression. I have questions about how to control the output in hall of frame.

Q1: Is that possible to control the number of output in HOF? (I tried to change the number of topn . It seems not working.) If yes, how?

Q2: It seems that each complexity has an unique result. Is that possible to give as many good results as possible , even that they have the same complexity.

Q3: Sometimes, HOF will return formula like this y = constant_number, which is not I want. I want formula which has at least one variable x. How could I fix this?

Q4: I am training on a timeseries dataset and use custom loss function on Symbolic Regression Model. How could I input extra parameter (list of datetime) to my custom loss function?

Thank you.

[MilesCranmer]

Q1-3 => It's a bit hard to do this because of things like the fact that $x + 1.0$ and $x + 1.000000001$ are technically different expressions with perhaps identical losses. And also things like $x / 2.0$ compared to $x * 0.5$. So the thing done right now is that only the first expression to hit a particular (loss, complexity) threshold is taken for each complexity from 1 to maxsize. I confess I'm not really sure how to do otherwise – would you create some way of gauging diversity of expressions stored at each complexity.

Q4 => can you convert them to floating point numbers for this?

[tlmakinen]

been thinking about this as well -- would it be possible to implement a minsize or minimum complexity threshold for an expression to induct it into the hall of fame ?

[qizzhao]

Sorry for the late reply. For Q4, yes, I could convert them to floating point number and tried to input them as weight parameter.
For Q3, is there any possible way I could avoid the case that final regression is a constant number. ( for example, y = 1.0 ). I have tried to add constraint in my custom loss function that if regression's prediction is all same number or the variance of prediction is equal to zero, the loss would be inf. But sometimes HOF will still return constant-number-only regression.

[MilesCranmer]

Just wondering — why do you need to avoid the constant expression? It does correctly express the most accurate expression at that given complexity. But why not simply only consider the .equation_ with complexity 3 and above? All of the operations, like predict, sympy, latex, latex_table , etc, all have an argument that let you pick which equation to evaluate. So you can choose the index to avoid the simplest one.

[tlmakinen]

Yeah I've been thresholding after the search -- is there an easy way to get the HOF output file to save more equations (perhaps ~100 or so) ? i'm doing a post-search pruning with a different criterion and it'd be helpful to have more candidate expressions on hand

[MilesCranmer]

I'm not sure how to build that list of expressions though as they might be identical to the original expression (maybe you swap a+b to b+a). Maybe there's some diversity criterion for building it?

I guess you could look at diversity in predictions outside the domain. But it seems pretty hard to write a general approach for this. Maybe the user could provide something...