Information-Theoretic Lower Bound
A theoretical lower bound characterizing the optimal performance achievable by any algorithm, even one running in exponential time, when there is no constraint on computational resources and only the amount of data is limited.
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Information-theoretic lower bounds characterize the best performance achievable by any algorithm (even exponential-time) without computational resource constraints, corresponding in this problem to Õ(md+k); computational lower bounds, by contrast, assume the algorithm must run in polynomial time, and the resulting bounds are usually larger.
The authors provide new information-theoretic lower bounds, proving in a minimax sense that the complex dependence of the error on q is fundamental rather than an artifact of the algorithm design.
All Facts (2)
Information-theoretic lower bounds characterize the best performance achievable by any algorithm (even exponential-time) without computational resource constraints, corresponding in this problem to Õ(md+k); computational lower bounds, by contrast, assume the algorithm must run in polynomial time, and the resulting bounds are usually larger.
50%UnverifiedThe authors provide new information-theoretic lower bounds, proving in a minimax sense that the complex dependence of the error on q is fundamental rather than an artifact of the algorithm design.
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