Causal structure of networks of stochastic processes

Etesami, Seyedjalal

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https://hdl.handle.net/2142/98151 Copy

Description

Title

Causal structure of networks of stochastic processes

Author(s)

Etesami, Seyedjalal

Issue Date

2017-05-31

Director of Research (if dissertation) or Advisor (if thesis)

Kiyavash, Negar

Doctoral Committee Chair(s)

Kiyavash, Negar

Committee Member(s)

• Coleman, Todd P.
• Srikant, Rayadurgam
• Belabbas, Ali
• He, Niao

Department of Study

Industrial&Enterprise Sys Eng

Discipline

Industrial Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Causal learning
• Dynamical systems
• Stochastic systems

Abstract

We propose different approaches to infer causal influences between agents in a network using only observed time series. This includes graphical models to depict causal relationships in the network, algorithms to identify the graphs in different scenarios and when only a subset of agents are observed. We demonstrate the utility of the methods by identifying causal influences between markets and causal flow of information between media sites. We study the statistical and functional dependencies in network of processes. Statistical dependencies can be encoded by directed information graphs (DIGs) and functional relationships using functional dependency graphs (FDGs), both of which are graphical models where nodes represent random processes. DIGs are based on directed information that is an information theoretic quantity. To capture the functional dependencies in a dynamical system, we introduce a new measure in this work and show that the FDGs are a generalization of DIGs. We also establish sufficient conditions under which the FDG defined by our measure is equivalent to the DIG. As an example, we study the relationship between DIGs and linear dynamical graphs (LDGs), that are also a type of graphical models to encode functional dependencies in linear dynamical systems. In this case, we show that any causal LDGs can be reconstructed through learning the corresponding DIGs. Another contribution is to propose an approach for learning causal interaction network of mutually exciting linear Hawkes processes. In such processes, a natural notion of functional causality exists between processes that is encoded in their corresponding excitation matrices. We show that such causal interaction network is equivalent to the DIG of the processes. Furthermore, We present an algorithm for learning the support of excitation matrix (or equivalently the DIG). The performance of the algorithm is evaluated for a synthesized multivariate Hawkes network as well as real world dataset. We also study the problem of causal discovery in presence of latent variables, in which only a subset of processes can be observed. We propose an approach for learning latent directed polytrees as long as there exists an appropriately defined discrepancy measure between the observed nodes. Specifically, we use our approach for learning directed information polytrees. We prove that the approach is consistent for learning minimal latent directed trees. Furthermore, we study the problem of structural learning in vector autoregressive (VAR) models with latent variables. In this case, we extend the identifiability to a broader class of structures. In particular, we show that most of the causal structure of a VAR model can be recovered successfully when only the causal network among the latent variables is a directed tree. Last but not least, we introduce a new statistical metric inspired by Dobrushin’s coefficient [1] to measure the dependency or causal direction between variables from observational or interventional data. Our metric has been developed based on the paradigm that the conditional distribution of the variable of interest given all the direct causes will not change by intervening on other variables in the system. We show the advantageous of our measure over other dependency measures in the literature. We demonstrate the effectiveness of the proposed algorithms through simulations and data analysis.

Graduation Semester

2017-08

Type of Resource

text

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Copyright 2017 Seyedjalal Etesami

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