[
    {
        "id": "osp-21707",
        "type": "article-journal",
        "title": "Mutual Information Constrained Chernoff Bottleneck",
        "author": [
            {
                "family": "Tang",
                "given": "Dier"
            },
            {
                "family": "Han",
                "given": "Guangyue"
            }
        ],
        "URL": "https://omanscience.com/ar/articles/mutual-information-constrained-chernoff-bottleneck",
        "language": "en",
        "issued": {
            "date-parts": [
                [
                    2026
                ]
            ]
        },
        "abstract": "The classical information bottleneck (IB) measures the relevance of a representation $U$ of $X$ to a target $Y$ by $I(U;Y)$, which does not directly characterize the error of downstream decisions. For a binary hypothesis $Y$ inferred from many separately encoded observations, the optimal error exponent is the Chernoff information between the two conditional distributions of $U$ given $Y$. We study the mutual information constrained Chernoff bottleneck, which seeks an encoder that maximizes this Chernoff information subject to a rate constraint $I(U;X) \\leq R$. We show that its optimal value $C(R)$ increases strictly up to $R = H(V)$, where $V$ merges the symbols of $X$ with equal likelihood ratio, remains at the uncompressed exponent beyond, and, unlike the IB curve, need not be concave. We further show that $k+1$ outputs suffice to attain $C(R)$, where $k$ is the cardinality of $V$. We propose an alternating algorithm that updates the encoder via a generalized Blahut--Arimoto algorithm and the Chernoff parameter $s$ via a nonlinear equation, and prove that its iterates remain feasible, with nondecreasing and convergent Chernoff information. Numerical experiments confirm the theory, and on real topic-detection data from the 20 Newsgroups corpus, compressing each word to only $17\\%$ of its entropy retains $90\\%$ of the error exponent and nearly the accuracy of the uncompressed classifier."
    }
]