Protein function prediction is to assign biological or biochemical functions to proteins, and it is a challenging computational problem characterized by several factors: (1) the number of function labels (annotations) is large, (2) a protein may be associated with multiple labels, (3) the function labels are structured in a hierarchy, and (4) the labels are incomplete. Current predictive models often assume that the labels of the labeled proteins are complete, i.e. no label is missing. But in real scenarios, we may be aware of only some hierarchical labels of a protein, and we may not know whether additional ones are actually present. The scenario of incomplete hierarchical labels, a challenging and practical problem, is seldom studied in protein function prediction.