On Learning Latent Models with Multi-Instance Weak Supervision

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 multi-instance Partial Label Learning (multi-instance PLL). Our problem is an extension to the standard PLL problem and 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.