Temporal and Relational Models for Causality: Representation and Learning

Discovering causal dependence is central to understanding the behavior of complex systems and to selecting actions that will achieve particular outcomes. The majority of work in this area has focused on propositional domains, where data instances are assumed to be independent and identically distributed (i.i.d.). However, many real-world domains are inherently relational, i.e., they consist of multiple types of entities that interact with each other, and temporal, i.e., they change over time. This thesis focuses on causal modeling for these more complex relational and temporal domains. This thesis provides an in-depth investigation of the properties of relational models and is extending their expressivity to include a temporal dimension. Specifically, we first investigate alternative ways to ground relational models, and we provide an in-depth analysis of the impact of alternative grounding semantics for feature construction, causal effect estimation, and model selection. Then, we extend relational models to represent discrete time. We generalize the theory of d-separation for this class of temporal and relational models. Finally, we provide a constraint-based algorithm, TRCD, to learn the structure of temporal relational models from data

Method for Enabling Causal Inference in Relational Domains

The analysis of data from complex systems is quickly becoming a fundamental aspect of modern business, government, and science. The field of causal learning is concerned with developing a set of statistical methods that allow practitioners make inferences about unseen interventions. This field has seen significant advances in recent years. However, the vast majority of this work assumes that data instances are independent, whereas many systems are best described in terms of interconnected instances, i.e. relational systems. This discrepancy prevents causal inference techniques from being reliably applied in many real-world settings. In this thesis, I will present three contributions to the field of causal inference that seek to enable the analysis of relational systems. First, I will present theory for consistently testing statistical dependence in relational domains. I then show how the significance of this test can be measured in practice using a novel bootstrap method for structured domains. Second, I show that statistical dependence in relational domains is inherently asymmetric, implying a simple test of causal direction from observational data. This test requires no assumptions on either the marginal distributions of variables or the functional form of dependence. Third, I describe relational causal adjustment, a procedure to identify the effects of arbitrary interventions from observational relational data via an extension of Pearl\u27s backdoor criterion. A series of evaluations on synthetic domains shows the estimates obtained by relational causal adjustment are close to those obtained from explicit experimentation

A Survey on Causal Discovery Methods for Temporal and Non-Temporal Data

Causal Discovery (CD) is the process of identifying the cause-effect relationships among the variables from data. Over the years, several methods have been developed primarily based on the statistical properties of data to uncover the underlying causal mechanism. In this study we introduce the common terminologies in causal discovery, and provide a comprehensive discussion of the approaches designed to identify the causal edges in different settings. We further discuss some of the benchmark datasets available for evaluating the performance of the causal discovery algorithms, available tools to perform causal discovery readily, and the common metrics used to evaluate these methods. Finally, we conclude by presenting the common challenges involved in CD and also, discuss the applications of CD in multiple areas of interest

Reasoning about Independence in Probabilistic Models of Relational Data

We extend the theory of d-separation to cases in which data instances are not independent and identically distributed. We show that applying the rules of d-separation directly to the structure of probabilistic models of relational data inaccurately infers conditional independence. We introduce relational d-separation, a theory for deriving conditional independence facts from relational models. We provide a new representation, the abstract ground graph, that enables a sound, complete, and computationally efficient method for answering d-separation queries about relational models, and we present empirical results that demonstrate effectiveness.Comment: 61 pages, substantial revisions to formalisms, theory, and related wor

D'ya like DAGs? A Survey on Structure Learning and Causal Discovery

Causal reasoning is a crucial part of science and human intelligence. In order to discover causal relationships from data, we need structure discovery methods. We provide a review of background theory and a survey of methods for structure discovery. We primarily focus on modern, continuous optimization methods, and provide reference to further resources such as benchmark datasets and software packages. Finally, we discuss the assumptive leap required to take us from structure to causality.Comment: 35 page

Inferring Causality from Time Series data based on Structural Causal Model and its application to Neural Connectomics

Inferring causation from time series data is of scientific interest in different disciplines, particularly in neural connectomics. While different approaches exist in the literature with parametric modeling assumptions, we focus on a non-parametric model for time series satisfying a Markovian structural causal model with stationary distribution and without concurrent effects. We show that the model structure can be used to its advantage to obtain an elegant algorithm for causal inference from time series based on conditional dependence tests, coined Causal Inference in Time Series (CITS) algorithm. We describe Pearson's partial correlation and Hilbert-Schmidt criterion as candidates for such conditional dependence tests that can be used in CITS for the Gaussian and non-Gaussian settings, respectively. We prove the mathematical guarantee of the CITS algorithm in recovering the true causal graph, under standard mixing conditions on the underlying time series. We also conduct a comparative evaluation of performance of CITS with other existing methodologies in simulated datasets. We then describe the utlity of the methodology in neural connectomics -- in inferring causal functional connectivity from time series of neural activity, and demonstrate its application to a real neurobiological dataset of electro-physiological recordings from the mouse visual cortex recorded by Neuropixel probes

Causal Discovery from Temporal Data: An Overview and New Perspectives

Temporal data, representing chronological observations of complex systems, has always been a typical data structure that can be widely generated by many domains, such as industry, medicine and finance. Analyzing this type of data is extremely valuable for various applications. Thus, different temporal data analysis tasks, eg, classification, clustering and prediction, have been proposed in the past decades. Among them, causal discovery, learning the causal relations from temporal data, is considered an interesting yet critical task and has attracted much research attention. Existing casual discovery works can be divided into two highly correlated categories according to whether the temporal data is calibrated, ie, multivariate time series casual discovery, and event sequence casual discovery. However, most previous surveys are only focused on the time series casual discovery and ignore the second category. In this paper, we specify the correlation between the two categories and provide a systematical overview of existing solutions. Furthermore, we provide public datasets, evaluation metrics and new perspectives for temporal data casual discovery.Comment: 52 pages, 6 figure