Bayesian cumulative shrinkage for infinite factorizations
The dimension of the parameter space is typically unknown in a variety of models that rely on factorizations. For example, in factor analysis the number of latent factors is not known and has to be inferred from the data. Although classical shrinkage priors are useful in such contexts, increasing sh...
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| Vydáno v: | Biometrika Ročník 107; číslo 3; s. 745 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
01.09.2020
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| ISSN: | 0006-3444 |
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| Abstract | The dimension of the parameter space is typically unknown in a variety of models that rely on factorizations. For example, in factor analysis the number of latent factors is not known and has to be inferred from the data. Although classical shrinkage priors are useful in such contexts, increasing shrinkage priors can provide a more effective approach that progressively penalizes expansions with growing complexity. In this article we propose a novel increasing shrinkage prior, called the cumulative shrinkage process, for the parameters that control the dimension in overcomplete formulations. Our construction has broad applicability and is based on an interpretable sequence of spike-and-slab distributions which assign increasing mass to the spike as the model complexity grows. Using factor analysis as an illustrative example, we show that this formulation has theoretical and practical advantages relative to current competitors, including an improved ability to recover the model dimension. An adaptive Markov chain Monte Carlo algorithm is proposed, and the performance gains are outlined in simulations and in an application to personality data.The dimension of the parameter space is typically unknown in a variety of models that rely on factorizations. For example, in factor analysis the number of latent factors is not known and has to be inferred from the data. Although classical shrinkage priors are useful in such contexts, increasing shrinkage priors can provide a more effective approach that progressively penalizes expansions with growing complexity. In this article we propose a novel increasing shrinkage prior, called the cumulative shrinkage process, for the parameters that control the dimension in overcomplete formulations. Our construction has broad applicability and is based on an interpretable sequence of spike-and-slab distributions which assign increasing mass to the spike as the model complexity grows. Using factor analysis as an illustrative example, we show that this formulation has theoretical and practical advantages relative to current competitors, including an improved ability to recover the model dimension. An adaptive Markov chain Monte Carlo algorithm is proposed, and the performance gains are outlined in simulations and in an application to personality data. |
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| AbstractList | The dimension of the parameter space is typically unknown in a variety of models that rely on factorizations. For example, in factor analysis the number of latent factors is not known and has to be inferred from the data. Although classical shrinkage priors are useful in such contexts, increasing shrinkage priors can provide a more effective approach that progressively penalizes expansions with growing complexity. In this article we propose a novel increasing shrinkage prior, called the cumulative shrinkage process, for the parameters that control the dimension in overcomplete formulations. Our construction has broad applicability and is based on an interpretable sequence of spike-and-slab distributions which assign increasing mass to the spike as the model complexity grows. Using factor analysis as an illustrative example, we show that this formulation has theoretical and practical advantages relative to current competitors, including an improved ability to recover the model dimension. An adaptive Markov chain Monte Carlo algorithm is proposed, and the performance gains are outlined in simulations and in an application to personality data.The dimension of the parameter space is typically unknown in a variety of models that rely on factorizations. For example, in factor analysis the number of latent factors is not known and has to be inferred from the data. Although classical shrinkage priors are useful in such contexts, increasing shrinkage priors can provide a more effective approach that progressively penalizes expansions with growing complexity. In this article we propose a novel increasing shrinkage prior, called the cumulative shrinkage process, for the parameters that control the dimension in overcomplete formulations. Our construction has broad applicability and is based on an interpretable sequence of spike-and-slab distributions which assign increasing mass to the spike as the model complexity grows. Using factor analysis as an illustrative example, we show that this formulation has theoretical and practical advantages relative to current competitors, including an improved ability to recover the model dimension. An adaptive Markov chain Monte Carlo algorithm is proposed, and the performance gains are outlined in simulations and in an application to personality data. |
| Author | Durante, Daniele Dunson, David B Legramanti, Sirio |
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| CitedBy_id | crossref_primary_10_1080_01621459_2025_2546577 crossref_primary_10_1080_07350015_2024_2447302 crossref_primary_10_1016_j_csda_2024_108094 crossref_primary_10_1214_23_BA1410 crossref_primary_10_1002_jae_2966 crossref_primary_10_1007_s11222_025_10703_w crossref_primary_10_1093_jrsssb_qkad062 crossref_primary_10_1007_s11222_024_10454_0 crossref_primary_10_1214_24_BA1499 crossref_primary_10_3390_psych5030054 crossref_primary_10_1214_22_BA1349 crossref_primary_10_1002_sta4_298 crossref_primary_10_1080_10618600_2023_2301072 crossref_primary_10_1080_10618600_2024_2356173 crossref_primary_10_1080_01621459_2024_2408777 crossref_primary_10_1016_j_csda_2024_107974 crossref_primary_10_1007_s42519_021_00188_x crossref_primary_10_1080_03610926_2020_1843055 crossref_primary_10_1214_24_BA1461 crossref_primary_10_1093_jrsssb_qkad010 crossref_primary_10_3390_econometrics11040026 crossref_primary_10_1080_10618600_2025_2551271 crossref_primary_10_1080_01621459_2023_2208390 crossref_primary_10_1080_00401706_2021_1933596 crossref_primary_10_1080_01621459_2023_2220170 crossref_primary_10_1214_25_BA1544 crossref_primary_10_1111_rssc_12589 crossref_primary_10_1007_s10260_025_00779_z crossref_primary_10_1016_j_csda_2023_107783 crossref_primary_10_1093_biomet_asab056 crossref_primary_10_1080_10618600_2025_2509585 |
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