Learning immune-defectives graph through group tests

This paper abstracts the unified problem of drug discovery and pathogen identification as an inhibitor-defective classification problem and learning of 'association pattern' between the inhibitors and defectives. We refer to the 'association graph' between the inhibitors and defectives as the Immune-Defectives Graph (IDG). Here, the expression of a defective might be inhibited by a subset of the inhibitors rather than all the inhibitors as in the well-known 1-inhibitor model. A test containing a defective is positive iff it does not contain its associated inhibitor. The goal of this paper is to identify the defectives, inhibitors, and their 'associations' with high probability, or in other words, learn the IDG using group tests. We propose a probabilistic non-adaptive pooling design, a probabilistic two-stage adaptive pooling design and decoding algorithms for learning the IDG. The sample complexity of the number of tests required for the proposed two-stage adaptive pooling design is shown to be close to the lower bound, while that for the proposed non-adaptive pooling design is close to the lower bound in the large inhibitor regime.