A unified generalization of inverse regression via adaptive column selection
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910538731094016 |
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| author | Jin, Yin Luo, Wei |
| author_facet | Jin, Yin Luo, Wei |
| contents | A bottleneck of sufficient dimension reduction (SDR) in the modern era is that, among numerous methods, only the sliced inverse regression (SIR) is generally applicable under the high-dimensional settings. The higher-order inverse regression methods, which form a major family of SDR methods that are superior to SIR in the population level, suffer from the dimensionality of their intermediate matrix-valued parameters that have an excessive number of columns. In this paper, we propose the generic idea of using a small subset of columns of the matrix-valued parameter for SDR estimation, which breaks the convention of using the ambient matrix for the higher-order inverse regression methods. With the aid of a quick column selection procedure, we then generalize these methods as well as their ensembles towards sparsity under the ultrahigh-dimensional settings, in a uniform manner that resembles sparse SIR and without additional assumptions. This is the first promising attempt in the literature to free the higher-order inverse regression methods from their dimensionality, which facilitates the applicability of SDR. The gain of column selection with respect to SDR estimation efficiency is also studied under the fixed-dimensional settings. Simulation studies and a real data example are provided at the end. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08284 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A unified generalization of inverse regression via adaptive column selection Jin, Yin Luo, Wei Methodology A bottleneck of sufficient dimension reduction (SDR) in the modern era is that, among numerous methods, only the sliced inverse regression (SIR) is generally applicable under the high-dimensional settings. The higher-order inverse regression methods, which form a major family of SDR methods that are superior to SIR in the population level, suffer from the dimensionality of their intermediate matrix-valued parameters that have an excessive number of columns. In this paper, we propose the generic idea of using a small subset of columns of the matrix-valued parameter for SDR estimation, which breaks the convention of using the ambient matrix for the higher-order inverse regression methods. With the aid of a quick column selection procedure, we then generalize these methods as well as their ensembles towards sparsity under the ultrahigh-dimensional settings, in a uniform manner that resembles sparse SIR and without additional assumptions. This is the first promising attempt in the literature to free the higher-order inverse regression methods from their dimensionality, which facilitates the applicability of SDR. The gain of column selection with respect to SDR estimation efficiency is also studied under the fixed-dimensional settings. Simulation studies and a real data example are provided at the end. |
| title | A unified generalization of inverse regression via adaptive column selection |
| topic | Methodology |
| url | https://arxiv.org/abs/2404.08284 |