O NADEZhNOM VOSSTANOVLENII SIGNALOV PO NEPRYaMYM NABLYuDENIYaM

Мұқаба

Дәйексөз келтіру

Толық мәтін

Ашық рұқсат Ашық рұқсат
Рұқсат жабық Рұқсат берілді
Рұқсат жабық Рұқсат ақылы немесе тек жазылушылар үшін

Аннотация

Рассматривается линейная обратная задача с неопределенностью, где требуется восстановить неизвестный сигнал по зашумленным наблюдениям. Исследуются свойства устойчивых полиэдральных оценок для случаев ограниченного и разреженного загрязнения. Показано, как такие оценки могут быть построены с помощью процедур выпуклой оптимизации.

Әдебиет тізімі

  1. Juditsky A., Nemirovski A. On polyhedral estimation of signals via indirect observations // Electronic Journal of Statistics. 2020. V. 14. No. 1. P. 458–502.
  2. Juditsky A., Nemirovski A. Statistical Inference via Convex Optimization. Princeton: Princeton University Press, 2020.
  3. Tukey J.W. A survey of sampling from contaminated distributions / Contributions to Probability and Statistics. 1960. P. 448–485.
  4. Huber P.J. Robust Statistics. New York: Wiley, 1981.
  5. Yu C., Yao W. Robust linear regression: A review and comparison // Communications in Statistics – Simulation and Computation. 2017. V. 46. No. 8. P. 6261–6282.
  6. Поляк В.Т., Цыпкин Я.З. Адаптивные алгоритмы оценивания (сходимость, оптимальность, стабильность) // АиТ. 1979. № 3. С. 71–84.
  7. Polyak B.T., Tsypkin Ya.Z. Robust identification // Automatica. 1980. V. 16. No. 1. P. 53–63.
  8. Поляк В.Т., Цыпкин Я.З. Робастные псевдоградиентные алгоритмы адаптации // АиТ. 1980. № 10. С. 91–97.
  9. Polyak B.T., Tsypkin Ya.Z. Optimal and robust methods for unconditional optimization // IFAC Proceedings Volumes. 1981. V. 14. No. 2. P. 519–523.
  10. Поляк В.Т., Цыпкин Я.З. Критериальные алгоритмы стохастической оптимизации // АиТ. 1984. № 6. С. 95–104.
  11. Polyak B.T., Tsypkin Ya.Z. Optimal recurrent algorithms for identification of nonstationary plants // Computers & Electrical Engineering. 1992. V. 18. No. 5. P. 365–371.
  12. Chen Y., Caramanis C., Mannor Sh. Robust sparse regression under adversarial corruption // International Conference on Machine Learning. PMLR, 2013. P. 774–782.
  13. Balakrishnan S., Du Simon S., Li J., Singh A. Computationally efficient robust sparse estimation in high dimensions // Conference on Learning Theory. PMLR, 2017. P. 169–212.
  14. Diakonikolas I., Kong W., Stewart A. Efficient algorithms and lower bounds for robust linear regression // Proceedings of the Thirtieth Annual ACM–SIAM Symposium on Discrete Algorithms. SIAM, 2019. P. 2745–2754.
  15. Liu L., Shen Y., Li T., Caramanis C. High dimensional robust sparse regression // International Conference on Artificial Intelligence and Statistics. PMLR, 2020. P. 411–421.
  16. Minsker S., Ndaoud M., Wang L. Robust and tuning-free sparse linear regression via square-root slope // SIAM J. Math. Data Sci. 2024. V. 6. No. 2. P. 428–453
  17. Foygel R., Mackey L. Corrupted sensing: Novel guarantees for separating structured signals // IEEE Transactions on Information Theory. 2014. V. 60. No. 2. P. 1223–1247.
  18. Dalalyan A., Thompson Ph. Outlier-robust estimation of a sparse linear model using l1-penalized Huber’s M-estimator // Advances in Neural Information Processing Systems. 2019. V. 32.
  19. Bruce A.G., Donoho D.L., Gao H.-Y., Martin R.D. Denoising and robust nonlinear wavelet analysis // Wavelet Applications. SPIE, 1994. V. 2242. P. 325–336.
  20. Sardy S., Tseng P., Bruce A. Robust wavelet denoising // IEEE Transactions on Signal Processing. 2001. V. 49. No. 6. P. 1146–1152.
  21. Diakonikolas I., Kane D.M. Algorithmic High-Dimensional Robust Statistics. Cambridge: Cambridge University Press, 2023.
  22. Juditsky A., Nemirovski A. Near-optimality of linear recovery from indirect observations // Mathematical Statistics and Learning. 2018. V. 1. No. 2. P. 171–225.
  23. Donoho D.L. Statistical estimation and optimal recovery // The Annals of Statistics. 1994. V. 22. No. 1. P. 238–270.
  24. Juditsky A.B., Nemirovski A.S. Nonparametric estimation by convex programming // The Annals of Statistics. 2009. V. 37. No. 5A. P. 2278–2300.
  25. Juditsky A., Nemirovski A. Near-optimality of linear recovery in Gaussian observation scheme under ∥·∥2-loss // The Annals of Statistics. 2018. V. 46. No. 4. P. 1603–1629.
  26. Grant M., Boyd S. The CVX Users’ Guide. Release 2.1, 2014. https://web.cvxr.com/cvx/doc/CVX.pdf
  27. Micchelli C.A., Rivlin T.J. A Survey of optimal recovery / Optimal Estimation in Approximation Theory. Micchelli C.A., Rivlin T.J. (Eds.). Boston, MA: Springer, 1977. P. 1–54.
  28. Micchelli C.A., Rivlin T.J. Lectures on optimal recovery / Numerical Analysis Lancaster 1984. Lecture Notes in Mathematics. Turner P.R. (Ed.). Berlin–Heidelberg: Springer, 1985. V. 1129. P. 21–93.
  29. Черноусоко Ф.Л. Оценивание фазового состояния динамических систем. М.: Наука, 1988.
  30. Fogel E., Huang Y.-F. On the value of information in system identification-bounded noise case // Automatica. 1982. V. 18. No. 2. P. 229–238.
  31. Граничин О.Н., Поляк Б.Т. Рандомизированные алгоритмы оценивания и оптимизации при почти произвольных помехах. М.: Наука, 2003.
  32. Kurzhanski A.B. Identification – a theory of guaranteed estimates // From Data to Model. Willems J.C. (Ed.). Berlin–Heidelberg: Springer, 1989. P. 135–214.
  33. Kurzhanski A., Vályi I. Ellipsoidal Calculus for Estimation and Control. Boston, MA: Birkhäuser, 1997.
  34. Milanese M., Vicino A. Optimal estimation theory for dynamic systems with set membership uncertainty: An overview // Automatica. 1991. V. 27. No. 6. P. 997–1009.
  35. Schwerpe F.C. Uncertain Dynamic Systems. Englewood Cliffs, NJ: Prentice-Hall, 1973.
  36. Juditsky A., Nemirovski A. On design of polyhedral estimates in linear inverse problems // SIAM Journal on Mathematics of Data Science. 2024. V. 6. No. 1. P. 76–96.
  37. Candes E.J., Tao T. Decoding by linear programming // IEEE Transactions on Information Theory. 2005. V. 51. No. 12. P. 4203–4215.
  38. Bickel P.J., Ritov Ya., Tsybakov A.B. Simultaneous analysis of Lasso and Dantzig selector // The Annals of Statistics. 2009. V. 37. No. 4. P. 1705–1732.
  39. Donoho D.L., Huo X. Uncertainty principles and ideal atomic decomposition // IEEE Transactions on Information Theory. 2001. V. 47. No. 7. P. 2845–2862.
  40. van de Geer S. Estimation and Testing under Sparsity. Cham: Springer, 2016.
  41. Mosek ApS. The MOSEK optimization toolbox for MATLAB manual. Version 8.0, 2015. http://docs.mosek.com/8.0/toolbox/

Қосымша файлдар

Қосымша файлдар
Әрекет
1. JATS XML

© The Russian Academy of Sciences, 2025