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| Natura: | Preprint |
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2023
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| Accesso online: | https://arxiv.org/abs/2306.13796 |
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| _version_ | 1866916321179992064 |
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| author | Wang, Kaifu Tsamoura, Efthymia Roth, Dan |
| author_facet | Wang, Kaifu Tsamoura, Efthymia Roth, Dan |
| contents | We consider a weakly supervised learning scenario where the supervision signal is generated by a transition function $σ$ of labels associated with multiple input instances. We formulate this problem as \emph{multi-instance Partial Label Learning (multi-instance PLL)}, which is an extension to the standard PLL problem. Our problem is met in different fields, including latent structural learning and neuro-symbolic integration. Despite the existence of many learning techniques, limited theoretical analysis has been dedicated to this problem. In this paper, we provide the first theoretical study of multi-instance PLL with possibly an unknown transition $σ$. Our main contributions are as follows. Firstly, we propose a necessary and sufficient condition for the learnability of the problem. This condition non-trivially generalizes and relaxes the existing small ambiguity degree in the PLL literature, since we allow the transition to be deterministic. Secondly, we derive Rademacher-style error bounds based on a top-$k$ surrogate loss that is widely used in the neuro-symbolic literature. Furthermore, we conclude with empirical experiments for learning under unknown transitions. The empirical results align with our theoretical findings; however, they also expose the issue of scalability in the weak supervision literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_13796 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Learning Latent Models with Multi-Instance Weak Supervision Wang, Kaifu Tsamoura, Efthymia Roth, Dan Machine Learning We consider a weakly supervised learning scenario where the supervision signal is generated by a transition function $σ$ of labels associated with multiple input instances. We formulate this problem as \emph{multi-instance Partial Label Learning (multi-instance PLL)}, which is an extension to the standard PLL problem. Our problem is met in different fields, including latent structural learning and neuro-symbolic integration. Despite the existence of many learning techniques, limited theoretical analysis has been dedicated to this problem. In this paper, we provide the first theoretical study of multi-instance PLL with possibly an unknown transition $σ$. Our main contributions are as follows. Firstly, we propose a necessary and sufficient condition for the learnability of the problem. This condition non-trivially generalizes and relaxes the existing small ambiguity degree in the PLL literature, since we allow the transition to be deterministic. Secondly, we derive Rademacher-style error bounds based on a top-$k$ surrogate loss that is widely used in the neuro-symbolic literature. Furthermore, we conclude with empirical experiments for learning under unknown transitions. The empirical results align with our theoretical findings; however, they also expose the issue of scalability in the weak supervision literature. |
| title | On Learning Latent Models with Multi-Instance Weak Supervision |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2306.13796 |