There are multiple features, your approach doesn't take that in consideration.

For polynomial with degree 2, 3 features, we need:
['bias', 'X1', 'X2', 'X3', 'X1^2', 'X1*X2', 'X1*X3', 'X2^2', 'X2*X3', 'X3^2']

I generated it with:

@property
def feature_names_(self):
    check_is_fitted(self, 'n_input_features_')

    def pstr(p):
        if np.count_nonzero(p)==0:
            return 'bias'
        vars, exps = np.nonzero(p)[0], p[np.nonzero(p)]
        vstrs = ['X'+str(v+1) for v in vars]
        estrs = [('^'+str(e) if e>1 else '') for e in exps]
        terms = [v+e for v,e in zip(vstrs, estrs)]
        return '*'.join(terms)

    return [pstr(power) for power in self.powers_]

Thanks for clarifying. So the property expected is the output feature mapping in terms of the polynomials of input features. Will do that and let you know.

Hi everyone, the suggestion by @aniryou seems to be solving the use case here. I don't think I have enough exposure in this domain to decide on the best approach to take. Please let me know if it would be ideal to go ahead with his idea. I will proceed as per the consensus reached here. Thanks.

I think @aniryou's version is the better one to use. Also I agree that this should be a get_feature_names function, as this is already used in a couple other places in the package, and is expected in a transformer by the pipeline code.

Thanks for clarifying. It would indeed be better if someone experienced completes it. Sorry I didn't get to do the right thing here. Closing this as it is superseded by #6372.