Survival regression with proper scoring rules and monotonic neural networks
We consider frequently used scoring rules for right-censored survival regression models such as time-dependent concordance, survival-CRPS, integrated Brier score and integrated binomial log-likelihood, and prove that neither of them is a proper scoring rule. This means that the true survival distrib...
| Main Authors: | , , , |
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| Format: | Conference item |
| Language: | English |
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Journal of Machine Learning Research
2022
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| _version_ | 1826307753983868928 |
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| author | Rindt, D Hu, R Steinsaltz, D Sejdinovic, D |
| author_facet | Rindt, D Hu, R Steinsaltz, D Sejdinovic, D |
| author_sort | Rindt, D |
| collection | OXFORD |
| description | We consider frequently used scoring rules for right-censored survival regression models such as time-dependent concordance, survival-CRPS, integrated Brier score and integrated binomial log-likelihood, and prove that neither of them is a proper scoring rule. This means that the true survival distribution may be scored worse than incorrect distributions, leading to inaccurate estimation. We prove, in contrast to these scores, that the right-censored log-likelihood is a proper scoring rule, i.e. the highest expected score is achieved by the true distribution. Despite this, modern feed-forward neural-network-based survival regression models are unable to train and validate directly on right-censored log-likelihood, due to its intractability, and resort to the aforementioned alternatives, i.e. non-proper scoring rules. We therefore propose a simple novel survival regression method capable of directly optimizing log-likelihood using a monotonic restriction on the time-dependent weights, coined SurvivalMonotonic-net (SuMo-net). SuMo-net achieves state-of-the-art log-likelihood scores across several datasets with 20–100x computational speedup on inference over existing state-of-the-art neural methods and is readily applicable to datasets with several million observations. |
| first_indexed | 2024-03-07T07:09:20Z |
| format | Conference item |
| id | oxford-uuid:80de77f9-c708-4a92-8a2a-1eb00d447a0a |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:09:20Z |
| publishDate | 2022 |
| publisher | Journal of Machine Learning Research |
| record_format | dspace |
| spelling | oxford-uuid:80de77f9-c708-4a92-8a2a-1eb00d447a0a2022-05-31T10:56:21ZSurvival regression with proper scoring rules and monotonic neural networksConference itemhttp://purl.org/coar/resource_type/c_5794uuid:80de77f9-c708-4a92-8a2a-1eb00d447a0aEnglishSymplectic ElementsJournal of Machine Learning Research2022Rindt, DHu, RSteinsaltz, DSejdinovic, DWe consider frequently used scoring rules for right-censored survival regression models such as time-dependent concordance, survival-CRPS, integrated Brier score and integrated binomial log-likelihood, and prove that neither of them is a proper scoring rule. This means that the true survival distribution may be scored worse than incorrect distributions, leading to inaccurate estimation. We prove, in contrast to these scores, that the right-censored log-likelihood is a proper scoring rule, i.e. the highest expected score is achieved by the true distribution. Despite this, modern feed-forward neural-network-based survival regression models are unable to train and validate directly on right-censored log-likelihood, due to its intractability, and resort to the aforementioned alternatives, i.e. non-proper scoring rules. We therefore propose a simple novel survival regression method capable of directly optimizing log-likelihood using a monotonic restriction on the time-dependent weights, coined SurvivalMonotonic-net (SuMo-net). SuMo-net achieves state-of-the-art log-likelihood scores across several datasets with 20–100x computational speedup on inference over existing state-of-the-art neural methods and is readily applicable to datasets with several million observations. |
| spellingShingle | Rindt, D Hu, R Steinsaltz, D Sejdinovic, D Survival regression with proper scoring rules and monotonic neural networks |
| title | Survival regression with proper scoring rules and monotonic neural networks |
| title_full | Survival regression with proper scoring rules and monotonic neural networks |
| title_fullStr | Survival regression with proper scoring rules and monotonic neural networks |
| title_full_unstemmed | Survival regression with proper scoring rules and monotonic neural networks |
| title_short | Survival regression with proper scoring rules and monotonic neural networks |
| title_sort | survival regression with proper scoring rules and monotonic neural networks |
| work_keys_str_mv | AT rindtd survivalregressionwithproperscoringrulesandmonotonicneuralnetworks AT hur survivalregressionwithproperscoringrulesandmonotonicneuralnetworks AT steinsaltzd survivalregressionwithproperscoringrulesandmonotonicneuralnetworks AT sejdinovicd survivalregressionwithproperscoringrulesandmonotonicneuralnetworks |