Learning minimal representations of stochastic processes with variational autoencoders
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912835958734848 |
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| author | Fernández-Fernández, Gabriel Manzo, Carlo Lewenstein, Maciej Dauphin, Alexandre Muñoz-Gil, Gorka |
| author_facet | Fernández-Fernández, Gabriel Manzo, Carlo Lewenstein, Maciej Dauphin, Alexandre Muñoz-Gil, Gorka |
| contents | Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we introduce an unsupervised machine learning approach to determine the minimal set of parameters required to effectively describe the dynamics of a stochastic process. Our method builds upon an extended $β$-variational autoencoder architecture. By means of simulated datasets corresponding to paradigmatic diffusion models, we showcase its effectiveness in extracting the minimal relevant parameters that accurately describe these dynamics. Furthermore, the method enables the generation of new trajectories that faithfully replicate the expected stochastic behavior. Overall, our approach enables the autonomous discovery of unknown parameters describing stochastic processes, hence enhancing our comprehension of complex phenomena across various fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_11608 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Learning minimal representations of stochastic processes with variational autoencoders Fernández-Fernández, Gabriel Manzo, Carlo Lewenstein, Maciej Dauphin, Alexandre Muñoz-Gil, Gorka Soft Condensed Matter Machine Learning Biological Physics Data Analysis, Statistics and Probability Quantitative Methods Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we introduce an unsupervised machine learning approach to determine the minimal set of parameters required to effectively describe the dynamics of a stochastic process. Our method builds upon an extended $β$-variational autoencoder architecture. By means of simulated datasets corresponding to paradigmatic diffusion models, we showcase its effectiveness in extracting the minimal relevant parameters that accurately describe these dynamics. Furthermore, the method enables the generation of new trajectories that faithfully replicate the expected stochastic behavior. Overall, our approach enables the autonomous discovery of unknown parameters describing stochastic processes, hence enhancing our comprehension of complex phenomena across various fields. |
| title | Learning minimal representations of stochastic processes with variational autoencoders |
| topic | Soft Condensed Matter Machine Learning Biological Physics Data Analysis, Statistics and Probability Quantitative Methods |
| url | https://arxiv.org/abs/2307.11608 |