Weakly supervised machine learning algorithms are able to learn from ambiguous samples or labels,e.g.,multi-instance learning or partial-label learning.However,in some real-world tasks,each training sample is associated with not only multiple instances but also a candidate label set that contains one ground-truth label and some false positive labels.Specifically,at least one instance pertains to the ground-truth label while no instance belongs to the false positive labels.In this paper,we formalize such problems as multi-instance partial-label learning(MIPL).Existing multi-instance learning algorithms and partial-label learning algorithms are suboptimal for solving MIPL problems since the former fails to disambiguate a candidate label set,and the latter cannot handle a multi-instance bag.To address these issues,a tailored algorithm named MIPLGP,i.e.,multi-instance partial-label learning with Gaussian processes,is proposed.MIPLGP first assigns each instance with a candidate label set in an augmented label space,then transforms the candidate label set into a logarithmic space to yield the disambiguated and continuous labels via an exclusive disambiguation strategy,and last induces a model based on the Gaussian processes.Experimental results on various datasets validate that MIPLGP is superior to well-established multi-instance learning and partial-label learning algorithms for solving MIPL problems.