The paper proves a variational formula for the mutual information in high-dimensional linear regression with AR(1) dependent rows, and shows empirically that VAMP often reaches the predicted optimal error.
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Information-theoretic limits and approximate message-passing for high-dimensional time series
The paper proves a variational formula for the mutual information in high-dimensional linear regression with AR(1) dependent rows, and shows empirically that VAMP often reaches the predicted optimal error.