Bayesian learning from sequential data using Gaussian processes with signature covariances
We develop a Bayesian approach to learning from sequential data by using Gaussian processes (GPs) with so-called signature kernels as covariance functions. This allows to make sequences of different length comparable and to rely on strong theoretical results from stochastic analysis. Signatures capt...
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| Format: | Conference item |
| Language: | English |
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Proceedings of Machine Learning Research
2020
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| _version_ | 1797083807866683392 |
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| author | Oberhauser, H Toth, C |
| author_facet | Oberhauser, H Toth, C |
| author_sort | Oberhauser, H |
| collection | OXFORD |
| description | We develop a Bayesian approach to learning from sequential data by using Gaussian processes (GPs) with so-called signature kernels as covariance functions. This allows to make sequences of different length comparable and to rely on strong theoretical results from stochastic analysis. Signatures capture sequential structure with tensors that can scale unfavourably in sequence length and state space dimension. To deal with this, we introduce a sparse variational approach with inducing tensors. We then combine the resulting GP with LSTMs and GRUs to build larger models that leverage the strengths of each of these approaches and benchmark the resulting GPs on multivariate time series (TS) classification datasets. |
| first_indexed | 2024-03-07T01:46:40Z |
| format | Conference item |
| id | oxford-uuid:98a6af02-a448-4d06-8919-f187e1351584 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:46:40Z |
| publishDate | 2020 |
| publisher | Proceedings of Machine Learning Research |
| record_format | dspace |
| spelling | oxford-uuid:98a6af02-a448-4d06-8919-f187e13515842022-03-27T00:08:29ZBayesian learning from sequential data using Gaussian processes with signature covariancesConference itemhttp://purl.org/coar/resource_type/c_5794uuid:98a6af02-a448-4d06-8919-f187e1351584EnglishSymplectic ElementsProceedings of Machine Learning Research2020Oberhauser, HToth, CWe develop a Bayesian approach to learning from sequential data by using Gaussian processes (GPs) with so-called signature kernels as covariance functions. This allows to make sequences of different length comparable and to rely on strong theoretical results from stochastic analysis. Signatures capture sequential structure with tensors that can scale unfavourably in sequence length and state space dimension. To deal with this, we introduce a sparse variational approach with inducing tensors. We then combine the resulting GP with LSTMs and GRUs to build larger models that leverage the strengths of each of these approaches and benchmark the resulting GPs on multivariate time series (TS) classification datasets. |
| spellingShingle | Oberhauser, H Toth, C Bayesian learning from sequential data using Gaussian processes with signature covariances |
| title | Bayesian learning from sequential data using Gaussian processes with signature covariances |
| title_full | Bayesian learning from sequential data using Gaussian processes with signature covariances |
| title_fullStr | Bayesian learning from sequential data using Gaussian processes with signature covariances |
| title_full_unstemmed | Bayesian learning from sequential data using Gaussian processes with signature covariances |
| title_short | Bayesian learning from sequential data using Gaussian processes with signature covariances |
| title_sort | bayesian learning from sequential data using gaussian processes with signature covariances |
| work_keys_str_mv | AT oberhauserh bayesianlearningfromsequentialdatausinggaussianprocesseswithsignaturecovariances AT tothc bayesianlearningfromsequentialdatausinggaussianprocesseswithsignaturecovariances |