$$\pi $$VAE: a stochastic process prior for Bayesian deep learning with MCMC
Abstract Stochastic processes provide a mathematically elegant way to model complex data. In theory, they provide flexible priors over function classes that can encode a wide range of interesting assumptions. However, in practice efficient inference by optimisation or marginalisation is difficult, a...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Mishra, Swapnil [verfasserIn] |
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| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s) 2022 |
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| Übergeordnetes Werk: |
Enthalten in: Statistics and computing - Springer US, 1991, 32(2022), 6 vom: 17. Okt. |
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| Übergeordnetes Werk: |
volume:32 ; year:2022 ; number:6 ; day:17 ; month:10 |
| Links: |
|---|
| DOI / URN: |
10.1007/s11222-022-10151-w |
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OLC2079748971 |
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| 520 | |a Abstract Stochastic processes provide a mathematically elegant way to model complex data. In theory, they provide flexible priors over function classes that can encode a wide range of interesting assumptions. However, in practice efficient inference by optimisation or marginalisation is difficult, a problem further exacerbated with big data and high dimensional input spaces. We propose a novel variational autoencoder (VAE) called the prior encoding variational autoencoder ($$\pi $$VAE). $$\pi $$VAE is a new continuous stochastic process. We use $$\pi $$VAE to learn low dimensional embeddings of function classes by combining a trainable feature mapping with generative model using a VAE. We show that our framework can accurately learn expressive function classes such as Gaussian processes, but also properties of functions such as their integrals. For popular tasks, such as spatial interpolation, $$\pi $$VAE achieves state-of-the-art performance both in terms of accuracy and computational efficiency. Perhaps most usefully, we demonstrate an elegant and scalable means of performing fully Bayesian inference for stochastic processes within probabilistic programming languages such as Stan. | ||
| 650 | 4 | |a Bayesian inference | |
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| 700 | 1 | |a Flaxman, Seth |4 aut | |
| 700 | 1 | |a Berah, Tresnia |4 aut | |
| 700 | 1 | |a Zhu, Harrison |4 aut | |
| 700 | 1 | |a Pakkanen, Mikko |4 aut | |
| 700 | 1 | |a Bhatt, Samir |4 aut | |
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10.1007/s11222-022-10151-w doi (DE-627)OLC2079748971 (DE-He213)s11222-022-10151-w-p DE-627 ger DE-627 rakwb eng 004 620 VZ Mishra, Swapnil verfasserin (orcid)0000-0002-8759-5902 aut $$\pi $$VAE: a stochastic process prior for Bayesian deep learning with MCMC 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2022 Abstract Stochastic processes provide a mathematically elegant way to model complex data. In theory, they provide flexible priors over function classes that can encode a wide range of interesting assumptions. However, in practice efficient inference by optimisation or marginalisation is difficult, a problem further exacerbated with big data and high dimensional input spaces. We propose a novel variational autoencoder (VAE) called the prior encoding variational autoencoder ($$\pi $$VAE). $$\pi $$VAE is a new continuous stochastic process. We use $$\pi $$VAE to learn low dimensional embeddings of function classes by combining a trainable feature mapping with generative model using a VAE. We show that our framework can accurately learn expressive function classes such as Gaussian processes, but also properties of functions such as their integrals. For popular tasks, such as spatial interpolation, $$\pi $$VAE achieves state-of-the-art performance both in terms of accuracy and computational efficiency. Perhaps most usefully, we demonstrate an elegant and scalable means of performing fully Bayesian inference for stochastic processes within probabilistic programming languages such as Stan. Bayesian inference MCMC VAE Spatio-temporal Flaxman, Seth aut Berah, Tresnia aut Zhu, Harrison aut Pakkanen, Mikko aut Bhatt, Samir aut Enthalten in Statistics and computing Springer US, 1991 32(2022), 6 vom: 17. Okt. (DE-627)131007963 (DE-600)1087487-2 (DE-576)052732894 0960-3174 nnns volume:32 year:2022 number:6 day:17 month:10 https://doi.org/10.1007/s11222-022-10151-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT AR 32 2022 6 17 10 |
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10.1007/s11222-022-10151-w doi (DE-627)OLC2079748971 (DE-He213)s11222-022-10151-w-p DE-627 ger DE-627 rakwb eng 004 620 VZ Mishra, Swapnil verfasserin (orcid)0000-0002-8759-5902 aut $$\pi $$VAE: a stochastic process prior for Bayesian deep learning with MCMC 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2022 Abstract Stochastic processes provide a mathematically elegant way to model complex data. In theory, they provide flexible priors over function classes that can encode a wide range of interesting assumptions. However, in practice efficient inference by optimisation or marginalisation is difficult, a problem further exacerbated with big data and high dimensional input spaces. We propose a novel variational autoencoder (VAE) called the prior encoding variational autoencoder ($$\pi $$VAE). $$\pi $$VAE is a new continuous stochastic process. We use $$\pi $$VAE to learn low dimensional embeddings of function classes by combining a trainable feature mapping with generative model using a VAE. We show that our framework can accurately learn expressive function classes such as Gaussian processes, but also properties of functions such as their integrals. For popular tasks, such as spatial interpolation, $$\pi $$VAE achieves state-of-the-art performance both in terms of accuracy and computational efficiency. Perhaps most usefully, we demonstrate an elegant and scalable means of performing fully Bayesian inference for stochastic processes within probabilistic programming languages such as Stan. Bayesian inference MCMC VAE Spatio-temporal Flaxman, Seth aut Berah, Tresnia aut Zhu, Harrison aut Pakkanen, Mikko aut Bhatt, Samir aut Enthalten in Statistics and computing Springer US, 1991 32(2022), 6 vom: 17. Okt. (DE-627)131007963 (DE-600)1087487-2 (DE-576)052732894 0960-3174 nnns volume:32 year:2022 number:6 day:17 month:10 https://doi.org/10.1007/s11222-022-10151-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT AR 32 2022 6 17 10 |
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10.1007/s11222-022-10151-w doi (DE-627)OLC2079748971 (DE-He213)s11222-022-10151-w-p DE-627 ger DE-627 rakwb eng 004 620 VZ Mishra, Swapnil verfasserin (orcid)0000-0002-8759-5902 aut $$\pi $$VAE: a stochastic process prior for Bayesian deep learning with MCMC 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2022 Abstract Stochastic processes provide a mathematically elegant way to model complex data. In theory, they provide flexible priors over function classes that can encode a wide range of interesting assumptions. However, in practice efficient inference by optimisation or marginalisation is difficult, a problem further exacerbated with big data and high dimensional input spaces. We propose a novel variational autoencoder (VAE) called the prior encoding variational autoencoder ($$\pi $$VAE). $$\pi $$VAE is a new continuous stochastic process. We use $$\pi $$VAE to learn low dimensional embeddings of function classes by combining a trainable feature mapping with generative model using a VAE. We show that our framework can accurately learn expressive function classes such as Gaussian processes, but also properties of functions such as their integrals. For popular tasks, such as spatial interpolation, $$\pi $$VAE achieves state-of-the-art performance both in terms of accuracy and computational efficiency. Perhaps most usefully, we demonstrate an elegant and scalable means of performing fully Bayesian inference for stochastic processes within probabilistic programming languages such as Stan. Bayesian inference MCMC VAE Spatio-temporal Flaxman, Seth aut Berah, Tresnia aut Zhu, Harrison aut Pakkanen, Mikko aut Bhatt, Samir aut Enthalten in Statistics and computing Springer US, 1991 32(2022), 6 vom: 17. Okt. (DE-627)131007963 (DE-600)1087487-2 (DE-576)052732894 0960-3174 nnns volume:32 year:2022 number:6 day:17 month:10 https://doi.org/10.1007/s11222-022-10151-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT AR 32 2022 6 17 10 |
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10.1007/s11222-022-10151-w doi (DE-627)OLC2079748971 (DE-He213)s11222-022-10151-w-p DE-627 ger DE-627 rakwb eng 004 620 VZ Mishra, Swapnil verfasserin (orcid)0000-0002-8759-5902 aut $$\pi $$VAE: a stochastic process prior for Bayesian deep learning with MCMC 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2022 Abstract Stochastic processes provide a mathematically elegant way to model complex data. In theory, they provide flexible priors over function classes that can encode a wide range of interesting assumptions. However, in practice efficient inference by optimisation or marginalisation is difficult, a problem further exacerbated with big data and high dimensional input spaces. We propose a novel variational autoencoder (VAE) called the prior encoding variational autoencoder ($$\pi $$VAE). $$\pi $$VAE is a new continuous stochastic process. We use $$\pi $$VAE to learn low dimensional embeddings of function classes by combining a trainable feature mapping with generative model using a VAE. We show that our framework can accurately learn expressive function classes such as Gaussian processes, but also properties of functions such as their integrals. For popular tasks, such as spatial interpolation, $$\pi $$VAE achieves state-of-the-art performance both in terms of accuracy and computational efficiency. Perhaps most usefully, we demonstrate an elegant and scalable means of performing fully Bayesian inference for stochastic processes within probabilistic programming languages such as Stan. Bayesian inference MCMC VAE Spatio-temporal Flaxman, Seth aut Berah, Tresnia aut Zhu, Harrison aut Pakkanen, Mikko aut Bhatt, Samir aut Enthalten in Statistics and computing Springer US, 1991 32(2022), 6 vom: 17. Okt. (DE-627)131007963 (DE-600)1087487-2 (DE-576)052732894 0960-3174 nnns volume:32 year:2022 number:6 day:17 month:10 https://doi.org/10.1007/s11222-022-10151-w lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT AR 32 2022 6 17 10 |
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$$\pi $$vae: a stochastic process prior for bayesian deep learning with mcmc |
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$$\pi $$VAE: a stochastic process prior for Bayesian deep learning with MCMC |
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Abstract Stochastic processes provide a mathematically elegant way to model complex data. In theory, they provide flexible priors over function classes that can encode a wide range of interesting assumptions. However, in practice efficient inference by optimisation or marginalisation is difficult, a problem further exacerbated with big data and high dimensional input spaces. We propose a novel variational autoencoder (VAE) called the prior encoding variational autoencoder ($$\pi $$VAE). $$\pi $$VAE is a new continuous stochastic process. We use $$\pi $$VAE to learn low dimensional embeddings of function classes by combining a trainable feature mapping with generative model using a VAE. We show that our framework can accurately learn expressive function classes such as Gaussian processes, but also properties of functions such as their integrals. For popular tasks, such as spatial interpolation, $$\pi $$VAE achieves state-of-the-art performance both in terms of accuracy and computational efficiency. Perhaps most usefully, we demonstrate an elegant and scalable means of performing fully Bayesian inference for stochastic processes within probabilistic programming languages such as Stan. © The Author(s) 2022 |
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Abstract Stochastic processes provide a mathematically elegant way to model complex data. In theory, they provide flexible priors over function classes that can encode a wide range of interesting assumptions. However, in practice efficient inference by optimisation or marginalisation is difficult, a problem further exacerbated with big data and high dimensional input spaces. We propose a novel variational autoencoder (VAE) called the prior encoding variational autoencoder ($$\pi $$VAE). $$\pi $$VAE is a new continuous stochastic process. We use $$\pi $$VAE to learn low dimensional embeddings of function classes by combining a trainable feature mapping with generative model using a VAE. We show that our framework can accurately learn expressive function classes such as Gaussian processes, but also properties of functions such as their integrals. For popular tasks, such as spatial interpolation, $$\pi $$VAE achieves state-of-the-art performance both in terms of accuracy and computational efficiency. Perhaps most usefully, we demonstrate an elegant and scalable means of performing fully Bayesian inference for stochastic processes within probabilistic programming languages such as Stan. © The Author(s) 2022 |
| abstract_unstemmed |
Abstract Stochastic processes provide a mathematically elegant way to model complex data. In theory, they provide flexible priors over function classes that can encode a wide range of interesting assumptions. However, in practice efficient inference by optimisation or marginalisation is difficult, a problem further exacerbated with big data and high dimensional input spaces. We propose a novel variational autoencoder (VAE) called the prior encoding variational autoencoder ($$\pi $$VAE). $$\pi $$VAE is a new continuous stochastic process. We use $$\pi $$VAE to learn low dimensional embeddings of function classes by combining a trainable feature mapping with generative model using a VAE. We show that our framework can accurately learn expressive function classes such as Gaussian processes, but also properties of functions such as their integrals. For popular tasks, such as spatial interpolation, $$\pi $$VAE achieves state-of-the-art performance both in terms of accuracy and computational efficiency. Perhaps most usefully, we demonstrate an elegant and scalable means of performing fully Bayesian inference for stochastic processes within probabilistic programming languages such as Stan. © The Author(s) 2022 |
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$$\pi $$VAE: a stochastic process prior for Bayesian deep learning with MCMC |
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https://doi.org/10.1007/s11222-022-10151-w |
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| author2 |
Flaxman, Seth Berah, Tresnia Zhu, Harrison Pakkanen, Mikko Bhatt, Samir |
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Flaxman, Seth Berah, Tresnia Zhu, Harrison Pakkanen, Mikko Bhatt, Samir |
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131007963 |
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| doi_str |
10.1007/s11222-022-10151-w |
| up_date |
2024-07-04T01:58:48.915Z |
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