Is “Capacity” Defined for Source Recovery & Learning Problems?
نویسنده
چکیده
This paper presents “strong” limits on the number of samples required for recovery in the domains of compressive sensing, matrix-completion and model-selection. In other words, the paper determines lower-bounds on systems parameters; where if these lower bounds are not met, then any recovery algorithm will be guaranteed to be erroneous with high probability. A common mathematical framework is presented which is subsequently used to develop such lower bounds for each of these three domains. These lower bounds, along with existing achievability arguments is used to argue that a notion of “capacity” analogous to Shannon capacity of communication systems exists for certain recovery/learning problems.
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