Marginal Independence
A concept in probability theory whereby two random variables satisfy P(z,c)=P(z)P(c) over the joint distribution, which is equivalent to zero mutual information. This constraint is stronger than conditional independence.
Timeline (last 90 days)
The conditional autoencoder's objective function simultaneously constrains reconstruction quality (preserving task-relevant information) and the population-level independence of the sensitive attribute from the representation (removing sensitive information).
The paper proves that, under the given assumptions, perfect reconstruction plus population independence is sufficient to achieve perfect nonlinear guardedness.
Population independence means the representation z and the sensitive attribute c satisfy P(z,c)=P(z)P(c), which is equivalent to mutual information I(z;c)=0 and is a stronger constraint than conditional independence.
All Facts (3)
The conditional autoencoder's objective function simultaneously constrains reconstruction quality (preserving task-relevant information) and the population-level independence of the sensitive attribute from the representation (removing sensitive information).
50%UnverifiedThe paper proves that, under the given assumptions, perfect reconstruction plus population independence is sufficient to achieve perfect nonlinear guardedness.
50%UnverifiedPopulation independence means the representation z and the sensitive attribute c satisfy P(z,c)=P(z)P(c), which is equivalent to mutual information I(z;c)=0 and is a stronger constraint than conditional independence.
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