Approaches for Recognizing Disease Genes Based on Network

Algorithm 1

CATAPULT algorithm description.

Initialize  𝜃=0,𝑠(𝑥)=0,∀𝑥∈𝑈, and 𝑛(𝑥)=1,∀𝑥∈𝑈

For 𝐭=𝟏,𝟐,𝟑,…,𝐓 :

Step 1. Draw a bootstrap sample 𝑈_𝑡⊆𝑈 of size  𝑛+

Step 2. Train a linear classifier 𝜃_𝑡 using the positive training examples 𝐴 and 𝑈_𝑡 as negative examples by solving:

  min_{𝜃′∈𝑅𝑑}12𝜃^′2+𝐶₋∑_{𝑖∈𝑈𝑡}𝜉_𝑖+𝐶₊∑_𝑖∈𝐴𝜉_𝑖

  Subject to 𝜉_𝑖≥0, ∀𝑖∈𝐴∪𝑈_𝑡

  Φ(𝑥_𝑖),𝜃^′≥1−𝜉_𝑖, ∀𝑖∈𝐴

  −Φ(𝑥_𝑖),𝜃^′≥1−𝜉_𝑖, ∀𝑖∈𝑈_𝑡

Step 3. For any 𝑥∈𝑈⧵𝑈_𝑡 update:

(i)  𝑛(𝑥)←𝑛(𝑥)+1

(ii)  𝑠(𝑥)←𝑠(𝑥)+𝜃_𝑡,Φ(𝑥)

Return 𝑠(𝑥)←𝑠(𝑥)/𝑛(𝑥), ∀𝑥∈𝑈.