Information Flow on Networks
Abstract
Many types of data are generated via processes that are only partially observed. When we speak, we refine a high-level concept repeatedly, obtaining along the way sentences, words, syllables, and sounds that are finally communicated. When we draw a picture, we begin with a high-level concept that is repeatedly refined as we draw at a finer quality and with more localized attention. Biological data is often generated in a top-down fashion. The current-day genetic composition was obtained from previous generations by mathematically well-defined processes of recombination and mutation. Similarly, the evolution of social networks are is influenced both by the observed parts of the network and by sources of influences that are unobserved. We propose to study hierarchical generating models (HGMs), which model such datageneration processes in mathematically precise terms. Our aim is to develop a mathematical theory of HGMs which has the following properties: Realism. The HGMs are good models for the data they represent. Reconstruction. There are provably efficient algorithms for the reconstruction of an underlying HGM given the observed data. Depth. There is a mathematical proof that the hidden layers of the process are necessary for inference. Our approach for studying HGMs, their properties and inference is based on the mathematical theory of the underlying models. This theory builds on modern tools from probability, combinatorics, analysis, and algorithms.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Sep 11, 2020
- Source ID
- N000142012826
Entities
People
- Elchanan Mossel
Organizations
- Massachusetts Institute of Technology
- Office of Naval Research
- United States Navy