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Feature Neutral Correlation
Motivation
Feature neutral correlation (FNC) is the correlation of a model with the target, after its predictions have been neutralized to all of Numerai’s features.
A model that is overly reliant on a small set of features will have a low FNC, but might still have a high correlation in the short term. However, it is also more likely to burn significantly in the long term.
A model that uses a diverse set of features and is still correlated with the targets will have a high FNC, and is more likely to have consistent performance over the long term.
Calculation
To calculate a user's FNC for a given round we
- Normalize the predictions in their submission
- Neutralize their submission to Numerai's features for that round
- Calculate the Spearman rank-order correlation of their neutralized submission to the target
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def calculate_fnc(sub, targets, features):
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"""
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Args:
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sub (pd.Series)
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targets (pd.Series)
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features (pd.DataFrame)
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"""
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# Normalize submission
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sub = (sub.rank(method="first").values - 0.5) / len(sub)
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# Neutralize submission to features
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f = features.values
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sub -= f.dot(np.linalg.pinv(f).dot(sub))
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sub /= sub.std()
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sub = pd.Series(np.squeeze(sub)) # Convert np.ndarray to pd.Series
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# FNC: Spearman rank-order correlation of neutralized submission to target
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fnc = np.corrcoef(sub.rank(pct=True, method="first"), targets)[0, 1]
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return fnc
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