# Synthesizing New Expertise via Collaboration

Bijan Mazaheri, Siddharth Jain, Jehoshua Bruck

June, 2021

### Abstract

Consider a set of classes and an uncertain input. Suppose, we do not have access to data and only have knowledge of perfect experts between a few classes in the set. What constitutes a consistent set of opinions? How can we use this to predict the opinions of experts on missing sub-domains? In this paper, we define a framework to analyze this problem. In particular, we define an expert graph where vertices represent classes and edges represent binary experts on the topics of their vertices. We derive necessary conditions for an expert graph to be valid. Further, we show that these conditions are also sufficient if the graph is a cycle, which can yield unintuitive results. Using these conditions, we provide an algorithm to obtain upper and lower bounds on the weights of unknown edges in an expert graph.

Publication

In *2021 IEEE International Symposium on Information Theory*

###### Ph.D Candidate in Computing and Mathematical Sciences

I am a Ph.D candidate at Caltech. My interests include mixture models, high level data fusion, and stability to distribution shift - usually through the lense of causality.