Estimating the fundamental limits is easier than achieving the fundamental limits
IEEE Transactions on Information Theory, 2019•ieeexplore.ieee.org
We show through case studies that it is easier to estimate the fundamental limits of data
processing than to construct the explicit algorithms to achieve those limits. Focusing on
binary classification, data compression, and prediction under logarithmic loss, we show that
in the finite space setting, when it is possible to construct an estimator of the limits with
vanishing error with n samples, it may require at least n ln n samples to construct an explicit
algorithm to achieve the limits.
processing than to construct the explicit algorithms to achieve those limits. Focusing on
binary classification, data compression, and prediction under logarithmic loss, we show that
in the finite space setting, when it is possible to construct an estimator of the limits with
vanishing error with n samples, it may require at least n ln n samples to construct an explicit
algorithm to achieve the limits.
We show through case studies that it is easier to estimate the fundamental limits of data processing than to construct the explicit algorithms to achieve those limits. Focusing on binary classification, data compression, and prediction under logarithmic loss, we show that in the finite space setting, when it is possible to construct an estimator of the limits with vanishing error with n samples, it may require at least n ln n samples to construct an explicit algorithm to achieve the limits.
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