Hierarchical Generative Models: Theory and Inference
Abstract
Many types of data are generated in a top-down fashion. When we speak we refine a high-level concept repeatedly, obtaining along the way sentences, words, syllables, and sounds. When we draw a picture, we begin with a high-level concept which is repeatedly refined as we draw at finer quality with more localized attention. Biological data is often also generated in a top-down fashion. The current day genetic composition was obtained from previous generations by well-defined processes of recombination and mutation.We propose to study Hierarchical Generative Models (abbreviated HGMs). This family f models allows defining in mathematically precise terms such top-down data generating processes. The main goal of studying such processes is to develop methods to perform inference to inform decisions regarding data coming from such models. For example, we may want to answer questions such as: Is this an image of a dog? Is it agitated? What language is being spoken? How is this unknown genetic entity related to ones we know?Our approach for studying HGMs, their properties and inference is based on the mathematical theory of the underlying models. This theory builds on insights from statistical physics, in particular from the theory of spin-glasses, as well as on modern tools from probability, combinatorics, analysis, and algorithms.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- May 08, 2020
- Source ID
- N000142012487
Entities
People
- Elchanan Mossel
Organizations
- Massachusetts Institute of Technology
- Office of Naval Research
- United States Navy