The IB problem on (T,C) is exactly equivalent to the IB problem on (φ(T),C) whenever φ is a sufficient statistic for C given T, with the full curve and optimal representations preserved.
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A Sufficient-Statistic Reduction of the Information Bottleneck to a Low-Dimensional Problem
The IB problem on (T,C) is exactly equivalent to the IB problem on (φ(T),C) whenever φ is a sufficient statistic for C given T, with the full curve and optimal representations preserved.