Protein-protein interaction (PPI) networks are naturally viewed as infrastructure to infer signalling pathways. The descriptors of signal events between two interacting proteins such as upstream/downstream signal flow, activation/inhibition relationship and protein modification are indispensable for inferring signalling pathways from PPI networks. However, such descriptors are not available in most cases as most PPI networks are seldom semantically annotated. In this work, we extend ℓ2-regularized logistic regression to the scenario of multi-label learning for predicting the activation/inhibition relationships in human PPI networks. The phenomenon that both activation and inhibition relationships exist between two interacting proteins is computationally modelled by multi-label learning framework. The problem of GO (gene ontology) sparsity is tackled by introducing the homolog knowledge as independent homolog instances. ℓ2-regularized logistic regression is accordingly adopted here to penalize the homolog noise and to reduce the computational complexity of the double-sized training data. Computational results show that the proposed method achieves satisfactory multi-label learning performance and outperforms the existing phenotype correlation method on the experimental data of Drosophila melanogaster. Several predictions have been validated against recent literature. The predicted activation/inhibition relationships in human PPI networks are provided in the supplementary file for further biomedical research.