2020 Fiscal Year Research-status Report
Parsimonious statistical modelling for high-dimensional problems
| Project/Area Number |
19K23193
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| Research Institution | Osaka University |
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Principal Investigator |
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| Project Period (FY) |
2019-08-30 – 2022-03-31
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| Keywords | High dimension / M-estimation / Sparsity |
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| Outline of Annual Research Achievements |
The research was dedicated to high-dimensional statistics and its applications with a focus on the parsimonious modelling to tackle the so-called curse of dimensionality, to fix over-fitting issues and to gain prediction accuracy for prediction purposes. A significant part of the work was devoted to deriving the theoretical properties of such high-dimensional techniques and to assessing the performances of such modelling through simulated experiments and real data.
One work focused on non-linear feature selection methods. Another work concentrated on factor modelling. One paper focused on sparse techniques for M-estimation with pseudo-observations. Finally one study was devoted to the sparse modelling of high-dimensional variance covariance processes.
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| Current Status of Research Progress |
Current Status of Research Progress
1: Research has progressed more than it was originally planned.
Reason
Due to the sanitary situation arising from the spread of coronavirus-19, all face-to-face research conferences, seminars, meetings (both domestic and international) have been cancelled. Thus, a significant part of the budget that was originally dedicated for conference/seminars/research meetings has not been used.
Research progress is going well (3 international publications in 2020, 1 international publication in March 2021) and due to the broad range of open subjects and existing problems in the proposed research "Parsimonious statistical modelling for high-dimensional problems", new research papers are currently under development.
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| Strategy for Future Research Activity |
Several projects within the area of the proposed research are currently under development.
More precisely, one work is dedicated to non-linear feature selection using Distance Covariance with the treatment of the redundancy using sparsity.
Another study focuses on the development of new association measures for feature selection and their ability to correctly identify the covariates.
Another work completes the publication related to factor modelling. Sparsity is now specified for the factor loading matrix. The key problem is the identifiability issue in factor modelling, since the factor loading matrix enters the variance covariance matrix as a quadratic product. A penalized estimating equation setting is thus considered to derive the theoretical properties. Algorithms are also developed.
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| Causes of Carryover |
In face of the sanitary situation arising from coronavirus-19, all face-to-face research conferences, seminars, meetings (both domestic and international) have been cancelled. So a large part of the budget has not been used.
If the sanitary situation improves, I plan to make a visiting period for a new research project with Prof Fermanian in France this September 2021 or March 2022.
In addition, a significant part of the research is dedicated to the applications to real-world problems so that computational issues are important matters. Thus, I plan to purchase a multi-core computer.
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Research Products
(9 results)
