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info.json
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{
"abstract": "In this paper, the problem of one-bit compressed sensing (OBCS) is formulated as a problem in probably approximately correct (PAC) learning. It is shown that the Vapnik-Chervonenkis (VC-) dimension of the set of half-spaces in $\\R^n$ generated by $k$-sparse vectors is bounded below by $k ( \\lfloor\\lg (n/k) \\rfloor +1 )$ and above by $\\lfloor 2k \\lg (en) \\rfloor $. By coupling this estimate with well-established results in PAC learning theory, we show that a consistent algorithm can recover a $k$-sparse vector with $O(k \\lg n)$ measurements, given only the signs of the measurement vector. This result holds for \\textit{all} probability measures on $\\R^n$. The theory is also applicable to the case of noisy labels, where the signs of the measurements are flipped with some unknown probability.",
"authors": [
"Mehmet Eren Ahsen",
"Mathukumalli Vidyasagar"
],
"emails": [
"mehmeteren.ahsen@mssm.edu",
"m.vidyasagar@utdallas.edu",
"m.vidyasagar@iith.ac.in"
],
"id": "17-504",
"issue": 11,
"pages": [
1,
23
],
"title": "An Approach to One-Bit Compressed Sensing Based on Probably Approximately Correct Learning Theory ",
"volume": 20,
"year": 2019
}