A-secret I-projection
The KL-divergence-nearest element obtained by projecting a target distribution onto an A-equivalence class; it is indistinguishable from the original distribution under A, but its support in the original space may be entirely different.
Timeline (last 90 days)
For any target distribution T, there exists a unique KL-divergence-nearest element Q* in the A-equivalence class, called the A-secret I-projection, whose density has the explicit expression q*(z) = t(z)p_S(A(z))/t_S(A(z)).
The KL divergence between T and P can be decomposed into the divergence from T to Q* plus the divergence from Q* to P, where the first term corresponds to the detectable component and the second term corresponds to the secret component.
The explicit construction of the A-secret I-projection provides a computable tool for assessing the size of the blind spot of existing CTMs, helping to quantify risk in distribution shift detection scenarios.
All Facts (3)
For any target distribution T, there exists a unique KL-divergence-nearest element Q* in the A-equivalence class, called the A-secret I-projection, whose density has the explicit expression q*(z) = t(z)p_S(A(z))/t_S(A(z)).
50%UnverifiedThe KL divergence between T and P can be decomposed into the divergence from T to Q* plus the divergence from Q* to P, where the first term corresponds to the detectable component and the second term corresponds to the secret component.
50%UnverifiedThe explicit construction of the A-secret I-projection provides a computable tool for assessing the size of the blind spot of existing CTMs, helping to quantify risk in distribution shift detection scenarios.
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