  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 fail 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. Our code and
datasets will be made publicly available.
