High-dimensional regression with outcomes of mixed-type using the multivariate spike-and-slab LASSO
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arXiv
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| Formato: | Preprint |
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2025
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| author | Ghosh, Soham Deshpande, Sameer K. |
| author_facet | Ghosh, Soham Deshpande, Sameer K. |
| contents | We consider a high-dimensional multi-outcome regression in which $q,$ possibly dependent, binary and continuous outcomes are regressed onto $p$ covariates. We model the observed outcome vector as a partially observed latent realization from a multivariate linear regression model. Our goal is to estimate simultaneously a sparse matrix ($B$) of latent regression coefficients (i.e., partial covariate effects) and a sparse latent residual precision matrix ($Ω$), which induces partial correlations between the observed outcomes. To this end, we specify continuous spike-and-slab priors on all entries of $B$ and off-diagonal elements of $Ω$ and introduce a Monte Carlo Expectation-Conditional Maximization algorithm to compute the maximum a posterior estimate of the model parameters. Under a set of mild assumptions, we derive the posterior contraction rate for our model in the high-dimensional regimes where both $p$ and $q$ diverge with the sample size $n$ and establish a sure screening property, which implies that, as $n$ increases, we can recover all truly non-zero elements of $B$ with probability tending to one. We demonstrate the excellent finite-sample properties of our proposed method, which we call mixed-mSSL, using extensive simulation studies and three applications spanning medicine to ecology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13007 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High-dimensional regression with outcomes of mixed-type using the multivariate spike-and-slab LASSO Ghosh, Soham Deshpande, Sameer K. Methodology We consider a high-dimensional multi-outcome regression in which $q,$ possibly dependent, binary and continuous outcomes are regressed onto $p$ covariates. We model the observed outcome vector as a partially observed latent realization from a multivariate linear regression model. Our goal is to estimate simultaneously a sparse matrix ($B$) of latent regression coefficients (i.e., partial covariate effects) and a sparse latent residual precision matrix ($Ω$), which induces partial correlations between the observed outcomes. To this end, we specify continuous spike-and-slab priors on all entries of $B$ and off-diagonal elements of $Ω$ and introduce a Monte Carlo Expectation-Conditional Maximization algorithm to compute the maximum a posterior estimate of the model parameters. Under a set of mild assumptions, we derive the posterior contraction rate for our model in the high-dimensional regimes where both $p$ and $q$ diverge with the sample size $n$ and establish a sure screening property, which implies that, as $n$ increases, we can recover all truly non-zero elements of $B$ with probability tending to one. We demonstrate the excellent finite-sample properties of our proposed method, which we call mixed-mSSL, using extensive simulation studies and three applications spanning medicine to ecology. |
| title | High-dimensional regression with outcomes of mixed-type using the multivariate spike-and-slab LASSO |
| topic | Methodology |
| url | https://arxiv.org/abs/2506.13007 |