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A method to improve protein function prediction for sparsely annotated PPI networks is introduced. The method extends the DSD majority vote algorithm introduced by Cao et al. to give confidence scores on predicted labels and to use predictions of high confidence to predict the labels of other nodes in subsequent rounds. We call this a majority vote cascade. Several cascade variants are tested in a stringent cross-validation experiment on PPI networks from S. cerevisiae and D. melanogaster, and we show that for many different settings with several alternative confidence functions, cascading improves the accuracy of the predictions. A list of the most confident new label predictions in the two networks is also reported. Code and networks for the cross-validation experiments appear at http://bcb.cs.tufts.edu/cascade. 

Third-state dynamics (Angluin et al. 2008; Perron et al. 2009) is a well-known process for quickly and robustly computing approximate majority through interactions between randomly-chosen pairs of agents. In this paper, we consider this process in a new model with persistent-state catalytic inputs, as well as in the presence of transient leak faults. Based on models considered in recent protocols for populations with persistent-state agents (Dudek et al. 2017; Alistarh et al. 2017; Alistarh et al. 2020), we formalize a Catalytic Input (CI) model comprising n input agents and m worker agents. For m = Θ(n), we show that computing the parity of the input population with high probability requires at least Ω(n2) total interactions, demonstrating a strong separation between the CI and standard population protocol models. On the other hand, we show that the third-state dynamics can be naturally adapted to this new model to solve approximate majority in O(n log n) total steps with high probability when the input margin is Ω(√(n log n)), which preserves the time and space efficiency of the corresponding protocol in the original model. We then show the robustness of third-state dynamics protocols to the transient leak faults considered by (Alistarh et al. 2017; Alistarh et al 2020). In both the original and CI models, these protocols successfully compute approximate majority with high probability in the presence of leaks occurring at each time step with probability β ≤ O(√(n log n}/n). The resilience of these dynamics to adversarial leaks exhibits a subtle connection to previous results involving Byzantine agents. 

A method to improve protein function prediction for sparsely annotated PPI networks is introduced. The method extends the DSD majority vote algorithm introduced by Cao et al. to give confidence scores on predicted labels and to use predictions of high confidence to predict the labels of other nodes in subsequent rounds. We call this a majority vote cascade. Several cascade variants are tested in a stringent cross-validation experiment on PPI networks from S. cerevisiae and D. melanogaster, and we show that for many different settings with several alternative confidence functions, cascading improves the accuracy of the predictions. A list of the most confident new label predictions in the two networks is also reported. Code, networks for the cross-validation experiments, and supplementary figures and tables appear at http://bcb.cs.tufts.edu/cascade.