145,334 research outputs found
On the Limits of Sequential Testing in High Dimensions
This paper presents results pertaining to sequential methods for support
recovery of sparse signals in noise. Specifically, we show that any sequential
measurement procedure fails provided the average number of measurements per
dimension grows slower then log s / D(f0||f1) where s is the level of sparsity,
and D(f0||f1) the Kullback-Leibler divergence between the underlying
distributions. For comparison, we show any non-sequential procedure fails
provided the number of measurements grows at a rate less than log n /
D(f1||f0), where n is the total dimension of the problem. Lastly, we show that
a simple procedure termed sequential thresholding guarantees exact support
recovery provided the average number of measurements per dimension grows faster
than (log s + log log n) / D(f0||f1), a mere additive factor more than the
lower bound.Comment: Asilomar 201
Adaptive sensing performance lower bounds for sparse signal detection and support estimation
This paper gives a precise characterization of the fundamental limits of
adaptive sensing for diverse estimation and testing problems concerning sparse
signals. We consider in particular the setting introduced in (IEEE Trans.
Inform. Theory 57 (2011) 6222-6235) and show necessary conditions on the
minimum signal magnitude for both detection and estimation: if is a sparse vector with non-zero components then it
can be reliably detected in noise provided the magnitude of the non-zero
components exceeds . Furthermore, the signal support can be exactly
identified provided the minimum magnitude exceeds . Notably
there is no dependence on , the extrinsic signal dimension. These results
show that the adaptive sensing methodologies proposed previously in the
literature are essentially optimal, and cannot be substantially improved. In
addition, these results provide further insights on the limits of adaptive
compressive sensing.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ555 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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