Inferring Functional and Statistical Dependencies: an Interventional Approach
Abstract
Research in many disciplines, including biology, economics, social sciences, computer science, and physics, involves studying networks of interacting, stochastic processes. The human brain, stock market, and Internet are some examples. For numerous research problems, it is important to characterize the structure of these large networks of interacting processes that elucidates the extent to which the past of some processes affects the future of others. In particular, it can be useful to have a succinct representation of the structure, such as a simple graphical model of the network. For instance, each node could represent a process, with directed edges between the nodes representing directions of influence.There is a large body of research on developing well defined graphical representations of networks of random variables. Markov networks, Bayesian networks, dynamic Bayesian networks, and chain graph models are some well-known examples. In these, random variables are represented as nodes in the graph. Edges represent conditional dependence relationships between the variables. These graphical models can be used for arbitrary sets of random variables, but the relationships they show are mutual. These graphs have been successfully used to represent the structure of networks of static stochastic systems. Some applications include object recognition, error-correcting codes, cellular networks, and medical diagnostics. Markov networks and Bayesian networks in particular represent two different perspectives on the structure of networks of random variables. Markov networks directly represent the dependence between each pair of variables, conditioned on all other variables. Bayesian networks represent factorizations of the joint distribution, so each variable potentially depends on preceding variables, and then the conditional terms are reduced. Networks of random variables do not lend themselves to concise representation of interacting stochastic processes, which are sets of random variables indexed over time. Representing each random variable as a node results in large, cumbersome graphs growing with time. Moreover, such a representation will not aid with visualization of the structure of inter-dynamics of coupled time series. For instance, it could be difficult to see how the past of some processes affects the future of others. The problem of learning directional influences has been approached predominantly from two angles: 1) understanding functional dependencies and 2) learning statistical dependencies. While much progress has been made, still fundamental questions remain unanswered for both aforementioned directions. More importantly, very little is known about how the two types of casual influence, functional and statistical, are in general related. The goal of this proposal is to introduce and investigate a framework that not only allows resolving questions of causal influence in a broader class of models than the state of art, but also provides a unifying theory to relate functional and statistical causality beyond linear models and restrictive assumptions on the distribution of noise in the system. Our proposed framework is interventional in nature. Discovering directional influence structure by intervention is based on measuring the influence of a variable (potential cause) on another variable (target) in a network through the following processes. The behavior of the target variable is observed when different values are assigned to the potential cause, while other variables~ effects are removed.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jun 13, 2019
- Source ID
- N000141912333
Entities
People
- Negar Kiyavash
Organizations
- Georgia Tech Research Corporation
- Office of Naval Research
- United States Navy