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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.09889 |
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| _version_ | 1866912481001078784 |
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| author | Liu, Wei Zhong, Qingzhi |
| author_facet | Liu, Wei Zhong, Qingzhi |
| contents | Latent factor models that integrate data from multiple sources/studies or modalities have garnered considerable attention across various disciplines. However, existing methods predominantly focus either on multi-study integration or multi-modality integration, rendering them insufficient for analyzing the diverse modalities measured across multiple studies. To address this limitation and cater to practical needs, we introduce a high-dimensional generalized factor model that seamlessly integrates multi-modality data from multiple studies, while also accommodating additional covariates. We conduct a thorough investigation of the identifiability conditions to enhance the model's interpretability. To tackle the complexity of high-dimensional nonlinear integration caused by four large latent random matrices, we utilize a variational lower bound to approximate the observed log-likelihood by employing a variational posterior distribution. By profiling the variational parameters, we establish the asymptotical properties of estimators for model parameters using M-estimation theory. Furthermore, we devise a computationally efficient variational EM algorithm to execute the estimation process and a criterion to determine the optimal number of both study-shared and study-specific factors. Extensive simulation studies and a real-world application show that the proposed method significantly outperforms existing methods in terms of estimation accuracy and computational efficiency. The R package for the proposed method is publicly accessible at https://CRAN.R-project.org/package=MMGFM. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09889 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High-Dimensional Multi-Study Multi-Modality Covariate-Augmented Generalized Factor Model Liu, Wei Zhong, Qingzhi Methodology Latent factor models that integrate data from multiple sources/studies or modalities have garnered considerable attention across various disciplines. However, existing methods predominantly focus either on multi-study integration or multi-modality integration, rendering them insufficient for analyzing the diverse modalities measured across multiple studies. To address this limitation and cater to practical needs, we introduce a high-dimensional generalized factor model that seamlessly integrates multi-modality data from multiple studies, while also accommodating additional covariates. We conduct a thorough investigation of the identifiability conditions to enhance the model's interpretability. To tackle the complexity of high-dimensional nonlinear integration caused by four large latent random matrices, we utilize a variational lower bound to approximate the observed log-likelihood by employing a variational posterior distribution. By profiling the variational parameters, we establish the asymptotical properties of estimators for model parameters using M-estimation theory. Furthermore, we devise a computationally efficient variational EM algorithm to execute the estimation process and a criterion to determine the optimal number of both study-shared and study-specific factors. Extensive simulation studies and a real-world application show that the proposed method significantly outperforms existing methods in terms of estimation accuracy and computational efficiency. The R package for the proposed method is publicly accessible at https://CRAN.R-project.org/package=MMGFM. |
| title | High-Dimensional Multi-Study Multi-Modality Covariate-Augmented Generalized Factor Model |
| topic | Methodology |
| url | https://arxiv.org/abs/2507.09889 |