Year: 2026
Type: preprint
Abstract: We consider a generalization of the Gaussian information bottleneck problem to jointly stable variables $X$ and $Y$. Specifically, for $X = Y + A$, where $A$ is stable and independent of $Y$, we find optimal stable linear encoders of the form $T = kX + N$, with $N$ stable and independent of $X$. We characterize the linear stable information bottleneck in closed-form and its critical value. Furthermore, we show that, except for the Gaussian case, such stochastic linear encoders are strictly suboptimal, while becoming asymptotically optimal at large compression rates. Our linear solution recovers the Gaussian information bottleneck for jointly Gaussian variables as a special case.
Source: arXiv (Cornell University)
Authors: Park, Dongmin, Fahs, Jihad, Assaad, Mohamad
Language: English
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221046862