## Causal learning via interventions: estimation and design

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##### Authors

Varıcı, Burak

##### Issue Date

2024-05

##### Type

Electronic thesis

Thesis

Thesis

##### Language

en_US

##### Keywords

Electrical engineering

##### Alternative Title

##### Abstract

The focus of this dissertation is leveraging the interventions in causal learning. Directed acyclic graphs (DAGs) have been used to compactly represent cause-effect relationships among random variables. Interventions refer to the changes in the causal mechanisms that govern the causal model and they are essential to causality in many aspects, such as causal structure learning, causal representation learning, and predicting the effects of an action in causal models. This dissertation broadly investigates the estimation and design of interventions in these aspects. We first consider the problem of estimating unknown intervention targets in causal models. We are motivated by two significant challenges. First, most of the interventional structure learning algorithms require the knowledge of the intervention targets. Secondly, there exist application domains in which the goal is to learn only the differences between two related networks. We take a direct approach and decouple the estimation of intervention targets from learning the causal structure in its entirety, which is the key to developing scalable algorithms. We focus on linear structural equation models (SEMs) with soft interventions and propose a framework that consists of a sequence of precision difference estimation steps. We study both causally sufficient and insufficient models, and design efficient algorithms with consistency guarantees. Our method can also be used in conjunction with existing observational learning algorithms to refine their results when interventional data becomes available. Finally, we establish sample complexity guarantees of our algorithms. Next, we consider using interventions to learn latent causal models and representations. Causal variables are not always observed directly but can be latent, only observed through an unknown transformation function. Causal representation learning (CRL) aims to invert the data generation process of high-dimensional observations and recover the underlying causal variables and their relationships. We proposed a novel framework (Score-based CRL) that leverages interventional data and properties of the score functions (gradient of log-likelihood) to identify latent causal variables and their relationships. Our key idea is that true inverse transform can be recovered by minimizing the number of changes in the score functions of latent variables across interventional environments. Our work establishes the first identifiability results for nonparametric causal models under a linear transform, and the first provably correct algorithm for the setting of general nonparametric transformations while also removing faithfulness assumptions on causal models. The third focus of this dissertation is designing an optimal sequence of interventions in a given causal graph to maximize the expected value of a reward node. This is, naturally, posed as a causal bandit problem. The majority of the previous works on causal bandits assume that interventional distributions are at least partially known. Acquiring such knowledge becomes prohibitive even in moderate-sized graphs when the set of possible interventions grows exponentially with the number of nodes. We address this issue on linear SEMs as follows: We avoid directly estimating exponentially many reward distributions and instead estimate the parameters that fully specify the SEMs to compute the rewards. Under boundedness assumptions on noise and the parameter space, we establish upper bounds on the regrets of proposed algorithms and a minimax lower bound for the problem. Remarkably, the achievable and lower bounds conform in their scaling behavior with respect to the horizon and graph parameters and are not affected by the cardinality of the intervention space. Finally, this dissertation investigates causal discovery of a mixture of DAGs. In some complex systems, such as time-varying causal systems, specifying all causal relationships with a single DAG is not viable. We aim to address this problem and formalize a framework for recovering the causal graph representing a mixture of DAGs. Specifically, we introduce the notion of emergent edges, which are the causal variables that are nonadjacent in individual models but become connected in the mixture. We establish the necessary and sufficient conditions for emergence of these spurious connections for a mixture of DAGs and propose an algorithm to infer the learnable causal relations. Furthermore, we analyze the necessary and sufficient interventions on a mixture of DAGs to identify these spurious connections.

##### Description

May2024

School of Engineering

School of Engineering

##### Full Citation

##### Publisher

Rensselaer Polytechnic Institute, Troy, NY