A self-calibrated direct approach to precision matrix estimation and linear discriminant analysis in high dimensions
A self-calibrated direct estimation algorithm based on ℓ1-regularized quadratic programming is proposed. The self-calibration is achieved by an iterative algorithm for finding the regularization parameter simultaneously with the estimation target. The proposed algorithm is free of cross-validation....
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2022
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| Online Access: | https://hdl.handle.net/10356/154897 |
| _version_ | 1811691518200643584 |
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| author | Pun, Chi Seng Hadimaja, Matthew Zakharia |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Pun, Chi Seng Hadimaja, Matthew Zakharia |
| author_sort | Pun, Chi Seng |
| collection | NTU |
| description | A self-calibrated direct estimation algorithm based on ℓ1-regularized quadratic programming is proposed. The self-calibration is achieved by an iterative algorithm for finding the regularization parameter simultaneously with the estimation target. The proposed algorithm is free of cross-validation. Two applications of this algorithm are proposed, namely precision matrix estimation and linear discriminant analysis. It is proven that the proposed estimators are consistent under different matrix norm errors and misclassification rate. Moreover, extensive simulation and empirical studies are conducted to evaluate the finite-sample performance and examine the support recovery ability of the proposed estimators. With the theoretical and empirical evidence, it is shown that the proposed estimator is better than its competitors in statistical accuracy and has clear computational advantages. |
| first_indexed | 2024-10-01T06:21:10Z |
| format | Journal Article |
| id | ntu-10356/154897 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T06:21:10Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1548972022-01-13T04:08:34Z A self-calibrated direct approach to precision matrix estimation and linear discriminant analysis in high dimensions Pun, Chi Seng Hadimaja, Matthew Zakharia School of Physical and Mathematical Sciences Science::Mathematics High-Dimensional Statistics Precision Matrix Estimation A self-calibrated direct estimation algorithm based on ℓ1-regularized quadratic programming is proposed. The self-calibration is achieved by an iterative algorithm for finding the regularization parameter simultaneously with the estimation target. The proposed algorithm is free of cross-validation. Two applications of this algorithm are proposed, namely precision matrix estimation and linear discriminant analysis. It is proven that the proposed estimators are consistent under different matrix norm errors and misclassification rate. Moreover, extensive simulation and empirical studies are conducted to evaluate the finite-sample performance and examine the support recovery ability of the proposed estimators. With the theoretical and empirical evidence, it is shown that the proposed estimator is better than its competitors in statistical accuracy and has clear computational advantages. Nanyang Technological University Chi Seng Pun gratefully acknowledges Data Science and Artificial Intelligence Research Centre and Start-up Grant at Nanyang Technological University, Singapore [No.: M4082115 & 04INS000248C230] for the funding of this research. 2022-01-13T04:08:34Z 2022-01-13T04:08:34Z 2021 Journal Article Pun, C. S. & Hadimaja, M. Z. (2021). A self-calibrated direct approach to precision matrix estimation and linear discriminant analysis in high dimensions. Computational Statistics and Data Analysis, 155, 107105-. https://dx.doi.org/10.1016/j.csda.2020.107105 0167-9473 https://hdl.handle.net/10356/154897 10.1016/j.csda.2020.107105 2-s2.0-85092076330 155 107105 en M4082115 04INS000248C230 Computational Statistics and Data Analysis © 2020 Elsevier B.V. All rights reserved. |
| spellingShingle | Science::Mathematics High-Dimensional Statistics Precision Matrix Estimation Pun, Chi Seng Hadimaja, Matthew Zakharia A self-calibrated direct approach to precision matrix estimation and linear discriminant analysis in high dimensions |
| title | A self-calibrated direct approach to precision matrix estimation and linear discriminant analysis in high dimensions |
| title_full | A self-calibrated direct approach to precision matrix estimation and linear discriminant analysis in high dimensions |
| title_fullStr | A self-calibrated direct approach to precision matrix estimation and linear discriminant analysis in high dimensions |
| title_full_unstemmed | A self-calibrated direct approach to precision matrix estimation and linear discriminant analysis in high dimensions |
| title_short | A self-calibrated direct approach to precision matrix estimation and linear discriminant analysis in high dimensions |
| title_sort | self calibrated direct approach to precision matrix estimation and linear discriminant analysis in high dimensions |
| topic | Science::Mathematics High-Dimensional Statistics Precision Matrix Estimation |
| url | https://hdl.handle.net/10356/154897 |
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