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Experiment Design for Causal Discovery Based on the Observational/Interventional Data

Safaeian, Ramin | 2024

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 57934 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Tabandeh, Mahmoud; Saleh Kalibar, Saber
  7. Abstract:
  8. In numerous scientific disciplines, analyzing a system often fails to reveal significant relationships between its various variables. However, in certain instances, changes in one variable can influence the behavior of one or more other variables. Systems where such underlying causal relationships exist are referred to as causal systems. The process of inferring the structure of these systems is known as causal learning. In causal learning, given observed samples from a system and under certain assumptions, the joint distribution of the variables can determine the equivalence class of their corresponding graphical model. Once the equivalence class is identified, interventions are employed to gain further edge direction recovery. Intervention involves altering the operation of a causal system to reveal the cause-and-effect relationships between a variable and its neighboring variables. Understanding the direction of edges connected to these neighbors can recover direction of more edges in graph. For instance, if the underlying causal model is represented as a directed acyclic graph, the edges can be oriented to prevent the formation of cycles. This thesis investigates various methods for learning causal systems. Initially, a set of functions for edge orientation is introduced. Subsequently, a set of properties for these functions is stated, which facilitates the acceleration of the edge orientation procedure in experimental design problems. Additionally, an efficient method is proposed for calculating the lower bound on the number of directed edges resulting from an intervention on a node. This lower bound serves as a suitable criterion for selecting variables for intervention based on the minimax criterion. The experimental results demonstrate that the proposed lower bound closely approximates the actual value. Finally, a method is presented for identifying the minimal set of interventions necessary to fully orient all undirected edges in a chordal graph. Moreover, an algorithm is proposed that computes the optimal set of interventions in polynomial time. Through these contributions, this thesis introduces novel methodologies for addressing various related challenges
  9. Keywords:
  10. Intervention ; Experimental Design ; optimal Intervention Set ; Causal Edge Learning

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