Distribution regression for sequential data
Distribution regression refers to the supervised learning problem where labels are only available for groups of inputs instead of individual inputs. In this paper, we develop a rigorous mathematical framework for distribution regression where inputs are complex data streams. Leveraging properties of...
| Հիմնական հեղինակներ: | , , , , |
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| Ձևաչափ: | Internet publication |
| Լեզու: | English |
| Հրապարակվել է: |
2020
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| _version_ | 1826312720285171712 |
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| author | Lemercier, M Salvi, C Damoulas, T Bonilla, EV Lyons, T |
| author_facet | Lemercier, M Salvi, C Damoulas, T Bonilla, EV Lyons, T |
| author_sort | Lemercier, M |
| collection | OXFORD |
| description | Distribution regression refers to the supervised learning problem where labels are only available for groups of inputs instead of individual inputs. In this paper, we develop a rigorous mathematical framework for distribution regression where inputs are complex data streams. Leveraging properties of the expected signature and a recent signature kernel trick for sequential data from stochastic analysis, we introduce two new learning techniques, one feature-based and the other kernel-based. Each is suited to a different data regime in terms of the number of data streams and the dimensionality of the individual streams. We provide theoretical results on the universality of both approaches and demonstrate empirically their robustness to irregularly sampled multivariate time-series, achieving state-of-the-art performance on both synthetic and real-world examples from thermodynamics, mathematical finance and agricultural science. |
| first_indexed | 2024-04-09T03:58:47Z |
| format | Internet publication |
| id | oxford-uuid:ff19fd39-905e-4ae1-a467-2a4098f8c715 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-04-09T03:58:47Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | oxford-uuid:ff19fd39-905e-4ae1-a467-2a4098f8c7152024-03-27T15:30:57ZDistribution regression for sequential dataInternet publicationhttp://purl.org/coar/resource_type/c_7ad9uuid:ff19fd39-905e-4ae1-a467-2a4098f8c715EnglishSymplectic Elements2020Lemercier, MSalvi, CDamoulas, TBonilla, EVLyons, TDistribution regression refers to the supervised learning problem where labels are only available for groups of inputs instead of individual inputs. In this paper, we develop a rigorous mathematical framework for distribution regression where inputs are complex data streams. Leveraging properties of the expected signature and a recent signature kernel trick for sequential data from stochastic analysis, we introduce two new learning techniques, one feature-based and the other kernel-based. Each is suited to a different data regime in terms of the number of data streams and the dimensionality of the individual streams. We provide theoretical results on the universality of both approaches and demonstrate empirically their robustness to irregularly sampled multivariate time-series, achieving state-of-the-art performance on both synthetic and real-world examples from thermodynamics, mathematical finance and agricultural science. |
| spellingShingle | Lemercier, M Salvi, C Damoulas, T Bonilla, EV Lyons, T Distribution regression for sequential data |
| title | Distribution regression for sequential data |
| title_full | Distribution regression for sequential data |
| title_fullStr | Distribution regression for sequential data |
| title_full_unstemmed | Distribution regression for sequential data |
| title_short | Distribution regression for sequential data |
| title_sort | distribution regression for sequential data |
| work_keys_str_mv | AT lemercierm distributionregressionforsequentialdata AT salvic distributionregressionforsequentialdata AT damoulast distributionregressionforsequentialdata AT bonillaev distributionregressionforsequentialdata AT lyonst distributionregressionforsequentialdata |