The Challenge of Generating Causal Hypotheses Using Network Models

Statistical network models based on Pairwise Markov Random Fields (PMRFs) are popular tools for analyzing multivariate psychological data, in large part due to their perceived role in generating insights into causal relationships: a practice known as causal discovery in the causal modeling literature. However, since network models are not presented as causal discovery tools, the role they play in generating causal insights is poorly understood among empirical researchers. In this paper, we provide a treatment of how PMRFs such as the Gaussian Graphical Model (GGM) work as causal discovery tools, using Directed Acyclic Graphs (DAGs) and Structural Equation Models (SEMs) as causal models. We describe the key assumptions needed for causal discovery and show the equivalence class of causal models that networks identify from data. We clarify four common misconceptions found in the empirical literature relating to networks as causal skeletons; chains of relationships; collider bias; and cyclic causal models

Causal Discovery for Relational Domains: Representation, Reasoning, and Learning

Many domains are currently experiencing the growing trend to record and analyze massive, observational data sets with increasing complexity. A commonly made claim is that these data sets hold potential to transform their corresponding domains by providing previously unknown or unexpected explanations and enabling informed decision-making. However, only knowledge of the underlying causal generative process, as opposed to knowledge of associational patterns, can support such tasks. Most methods for traditional causal discovery—the development of algorithms that learn causal structure from observational data—are restricted to representations that require limiting assumptions on the form of the data. Causal discovery has almost exclusively been applied to directed graphical models of propositional data that assume a single type of entity with independence among instances. However, most real-world domains are characterized by systems that involve complex interactions among multiple types of entities. Many state-of-the-art methods in statistics and machine learning that address such complex systems focus on learning associational models, and they are oftentimes mistakenly interpreted as causal. The intersection between causal discovery and machine learning in complex systems is small. The primary objective of this thesis is to extend causal discovery to such complex systems. Specifically, I formalize a relational representation and model that can express the causal and probabilistic dependencies among the attributes of interacting, heterogeneous entities. I show that the traditional method for reasoning about statistical independence from model structure fails to accurately derive conditional independence facts from relational models. I introduce a new theory—relational d-separation—and a novel, lifted representation—the abstract ground graph—that supports a sound, complete, and computationally efficient method for algorithmically deriving conditional independencies from probabilistic models of relational data. The abstract ground graph representation also presents causal implications that enable the detection of causal direction for bivariate relational dependencies without parametric assumptions. I leverage these implications and the theoretical framework of relational d-separation to develop a sound and complete algorithm—the relational causal discovery (RCD) algorithm—that learns causal structure from relational data

The Challenge of Generating Causal Hypotheses Using Network Models

Statistical network models based on Pairwise Markov Random Fields (PMRFs) are popular tools for analyzing multivariate psychological data, in large part due to their perceived role in generating insights into causal relationships: a practice known as causal discovery in the causal modeling literature. However, since network models are not presented as causal discovery tools, the role they play in generating causal insights is poorly understood among empirical researchers. In this paper, we provide a treatment of how PMRFs such as the Gaussian Graphical Model (GGM) work as causal discovery tools, using Directed Acyclic Graphs (DAGs) and Structural Equation Models (SEMs) as causal models. We describe the key assumptions needed for causal discovery and show the equivalence class of causal models that networks identify from data. We clarify four common misconceptions found in the empirical literature relating to networks as causal skeletons; chains of relationships; collider bias; and cyclic causal models

Causal Mapping of Emotion Networks in the Human Brain: Framework and Initial Findings

Emotions involve many cortical and subcortical regions, prominently including the amygdala. It remains unknown how these multiple network components interact, and it remains unknown how they cause the behavioral, autonomic, and experiential effects of emotions. Here we describe a framework for combining a novel technique, concurrent electrical stimulation with fMRI (es-fMRI), together with a novel analysis, inferring causal structure from fMRI data (causal discovery). We outline a research program for investigating human emotion with these new tools, and provide initial findings from two large resting-state datasets as well as case studies in neurosurgical patients with electrical stimulation of the amygdala. The overarching goal is to use causal discovery methods on fMRI data to infer causal graphical models of how brain regions interact, and then to further constrain these models with direct stimulation of specific brain regions and concurrent fMRI. We conclude by discussing limitations and future extensions. The approach could yield anatomical hypotheses about brain connectivity, motivate rational strategies for treating mood disorders with deep brain stimulation, and could be extended to animal studies that use combined optogenetic fMRI

Pragmatic Causal Inference

Data-driven causal inference from real-world multivariate systems can be biased for a number of reasons. These include unmeasured confounding, systematic censoring of observations, data dependence induced by a network of unit interactions, and misspecification of parametric models. This dissertation proposes statistical methods spanning three major steps of the causal inference workflow -- discovery of a suitable causal model, which in our case, can be visualized via one of several classes of causal graphical models, identification of target causal parameters as functions of the observed data distribution, and estimation of these parameters from finite samples. The overarching goal of these methods is to augment the data scientist's toolkit to tackle the aforementioned challenges in real-world systems in theoretically sound yet practical ways. We provide a continuous optimization procedure for causal discovery in the presence of latent confounders, and a computationally efficient discrete search procedure for discovery and downstream estimation of causal effects in causal graphs encoding interactions between units in a network. For identification, we provide an algorithm that generalizes the state-of-the-art for recovery of target parameters in missing not at random distributions that can be represented graphically via directed acyclic graphs. Finally for estimation, we provide results on the tangent space of causal graphical models with latent variables which may be used to improve the efficiency of semiparametric estimators for any target parameter of interest. We also provide novel estimators, including influence-function based estimators, for the average causal effect of a point exposure on an outcome when there are latent variables in the system

Learning Instrumental Variables with Structural and Non-Gaussianity Assumptions

Learning a causal effect from observational data requires strong assumptions. One possible method is to use instrumental variables, which are typically justified by background knowledge. It is possible, under further assumptions, to discover whether a variable is structurally instrumental to a target causal effect X→YX→Y. However, the few existing approaches are lacking on how general these assumptions can be, and how to express possible equivalence classes of solutions. We present instrumental variable discovery methods that systematically characterize which set of causal effects can and cannot be discovered under local graphical criteria that define instrumental variables, without reconstructing full causal graphs. We also introduce the first methods to exploit non-Gaussianity assumptions, highlighting identifiability problems and solutions. Due to the difficulty of estimating such models from finite data, we investigate how to strengthen assumptions in order to make the statistical problem more manageable