Numerical precision problem in the outputted expression

[folivetti]

Running some experiments with SBP using this dataset:

Pagie.csv

And by running this script:

from pyGPGOMEA import GPGOMEARegressor as GPG

def standardNotation(expr):
    expr = (expr.replace("X0", "x0")
            .replace("X1", "x1")
            .replace("X2", "x2")
            .replace("_", "")
            .replace("+-", "-")
            .replace("--", "+")
            .replace("^", "**")
            )
    expr = re.sub(r"/(-\d+\.\d+)", r"/(\1)", expr)
    return re.sub(r"\*(-\d+\.\d+)", r"*(\1)", expr)

est = GPG( popsize=500, generations=200,
    linearscaling=True, functions='+_-_*_div_log_exp', erc=True,
    initmaxtreeheight=6, maxtreeheight=20, maxsize=1000,
    subcross=0.0, sbagx=False,
    sbrdo=0.75, submut=0.25,
    unifdepthvar=True,
    tournament=4,
    sblibtype='p_10_9999_l_n',
    caching=False,
    gomea=False, ims=False, silent=True, parallel=False, seed=1 )

z = np.loadtxt("Pagie.csv", delimiter=",")
x = z[:,:-1]
y = z[:,-1]
x0 = x[:,0]
x1 = x[:,1]

est.fit(x,y)
eq = standardNotation(model(est))
yhat = eval(eq)
yhat2 = est.predict(x)
print(np.square(yhat-yhat2).mean()) # squared error between the predicted output from `predict` method and from evaluating the symbolic model

I get a mean squared error of 5624673608570.937, as discussed it is possibly due to truncation of the coefficient values.

[marcovirgolin]

Thank you @folivetti . This is indeed a rounding problem because C++ uses double precision but the output displays only the first (I think) 5 digits.

A way to fix this is to restrict the evolution to work up to a certain numerical precision, another (which you suggested and I report in order to remember) is to try to use scientific notation for the output.

Gotta find some time to do that, though. For now, I suggest using est.predict instead of re-interpreting the formula, to get the correct prediction.