This paper presents an estimation framework to assess the performance of the sorting function over data that is perturbed. In particular, the performance is measured in terms of the Minimum Mean Square Error (MMSE) between the values of the sorting function computed on the data without perturbation and the estimate that uses the sorting function applied to the perturbed data. It is first shown that, under certain conditions satisfied by the practically relevant Gaussian noise perturbation, the optimal estimator can be expressed as a linear combination of estimators on the unsorted data. Then, a suboptimal estimator is proposed, and its performance is evaluated and compared to the optimal estimator. Finally, a lower bound on the desired MMSE is derived when data is i.i.d. and has a Gaussian distribution. This is accomplished by solving a new problem that consists of estimating the norm of an unsorted vector from a noisy observation of it.
|Original language||English (US)|
|Title of host publication||2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|Number of pages||5|
|State||Published - Jul 2019|
|Event||2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, France|
Duration: Jul 7 2019 → Jul 12 2019
|Name||IEEE International Symposium on Information Theory - Proceedings|
|Conference||2019 IEEE International Symposium on Information Theory, ISIT 2019|
|Period||7/7/19 → 7/12/19|
Bibliographical noteFunding Information:
The work of A. Dytso and H. V. Poor was supported in part by the U.S. National Science Foundation under Grants CCF-0939370 and CCF-1513915. The work of M. Cardone was supported in part by the U.S. National Science Foundation under Grant CCF-1849757.