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1. Quantifying Individuals' Theory-based Knowledge using Probabilistic Causal Graphs: A Bayesian Hierarchical Approach

   Hans, Atharva; Chaudhari, Ashish M.; Bilionis, Ilias; Panchal, Jitesh H. (January 2020, ASME 2020 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE 2020))

   Extracting an individual’s knowledge structure is a challenging task as it requires formalization of many concepts and their interrelationships. While there has been significant research on how to represent knowledge to support computational design tasks, there is limited understanding of the knowledge structures of human designers. This understanding is necessary for comprehension of cognitive tasks such as decision making and reasoning, and for improving educational programs. In this paper, we focus on quantifying theory-based causal knowledge, which is a specific type of knowledge held by human designers. We develop a probabilistic graph-based model for representing individuals’ concept-specific causal knowledge for a given theory. We propose a methodology based on probabilistic directed acyclic graphs (DAGs) that uses logistic likelihood function for calculating the probability of a correct response. The approach involves a set of questions for gathering responses from 205 engineering students, and a hierarchical Bayesian approach for inferring individuals’ DAGs from the observed responses. We compare the proposed model to a baseline three-parameter logistic (3PL) model from the item response theory. The results suggest that the graph-based logistic model can estimate individual students’ knowledge graphs. Comparisons with the 3PL model indicate that knowledge assessment is more accurate when quantifying knowledge at the level of causal relations than quantifying it using a scalar ability parameter. The proposed model allows identification of parts of the curriculum that a student struggles with and parts they have already mastered which is essential for remediation. 

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2. A Bayesian Hierarchical Model for Extracting Individuals' Theory-based Causal Knowledge

   https://doi.org/10.1115/1.4055596  

   Hans, Atharva; Chaudhari, Ashish M.; Bilionis, Ilias; Panchal, Jitesh H. (September 2022, Journal of Computing and Information Science in Engineering)

   Abstract Extracting an individual's scientific knowledge is essential for improving educational assessment and understanding cognitive tasks in engineering activities such as reasoning and decision making. However, knowledge extraction is an almost impossible endeavor if the domain of knowledge and the available observational data are unrestricted. The objective of this paper is to quantify individuals' theory-based causal knowledge from their responses to given questions. Our approach uses directed acyclic graphs (DAGs) to represent causal knowledge for a given theory and a graph-based logistic model that maps individuals' question-specific subgraphs to question responses. We follow a hierarchical Bayesian approach to estimate individuals' DAGs from observations.The method is illustrated using 205 engineering students' responses to questions on fatigue analysis in mechanical parts. In our results, we demonstrate how the developed methodology provides estimates of population-level DAG and DAGs for individual students. This dual representation is essential for remediation since it allows us to identify parts of a theory that a population or individual struggles with and parts they have already mastered. An addendum of the method is that it enables predictions about individuals' responses to new questions based on the inferred individual-specific DAGs. The latter has implications for the descriptive modeling of human problem-solving, a critical ingredient in sociotechnical systems modeling. 

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3. Semiparametric Inference For Causal Effects In Graphical Models With Hidden Variables

   Bhattacharya, Rohit; Nabi, Razieh; Shpitser, Ilya (October 2022, Journal of machine learning research)

   Identification theory for causal effects in causal models associated with hidden variable directed acyclic graphs (DAGs) is well studied. However, the corresponding algorithms are underused due to the complexity of estimating the identifying functionals they output. In this work, we bridge the gap between identification and estimation of population-level causal effects involving a single treatment and a single outcome. We derive influence function based estimators that exhibit double robustness for the identified effects in a large class of hidden variable DAGs where the treatment satisfies a simple graphical criterion; this class includes models yielding the adjustment and front-door functionals as special cases. We also provide necessary and sufficient conditions under which the statistical model of a hidden variable DAG is nonparametrically saturated and implies no equality constraints on the observed data distribution. Further, we derive an important class of hidden variable DAGs that imply observed data distributions observationally equivalent (up to equality constraints) to fully observed DAGs. In these classes of DAGs, we derive estimators that achieve the semiparametric efficiency bounds for the target of interest where the treatment satisfies our graphical criterion. Finally, we provide a sound and complete identification algorithm that directly yields a weight based estimation strategy for any identifiable effect in hidden variable causal models. 

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4. A biologist's guide to model selection and causal inference

   https://doi.org/10.1098/rspb.2020.2815  

   Laubach, Zachary M.; Murray, Eleanor J.; Hoke, Kim L.; Safran, Rebecca J.; Perng, Wei (January 2021, Proceedings of the Royal Society B: Biological Sciences)

   A goal of many research programmes in biology is to extract meaningful insights from large, complex datasets. Researchers in ecology, evolution and behavior (EEB) often grapple with long-term, observational datasets from which they construct models to test causal hypotheses about biological processes. Similarly, epidemiologists analyse large, complex observational datasets to understand the distribution and determinants of human health. A key difference in the analytical workflows for these two distinct areas of biology is the delineation of data analysis tasks and explicit use of causal directed acyclic graphs (DAGs), widely adopted by epidemiologists. Here, we review the most recent causal inference literature and describe an analytical workflow that has direct applications for EEB. We start this commentary by defining four distinct analytical tasks (description, prediction, association, causal inference). The remainder of the text is dedicated to causal inference, specifically focusing on the use of DAGs to inform the modelling strategy. Given the increasing interest in causal inference and misperceptions regarding this task, we seek to facilitate an exchange of ideas between disciplinary silos and provide an analytical framework that is particularly relevant for making causal inference from observational data. 

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5. D-VAE: A Variational Autoencoder for Directed Acyclic Graphs

   Zhang, Muhan; Jiang, Shali; Cui, Zhicheng; Garnett, Roman; Chen, Yixin (January 2019, Advances in neural information processing systems)

   Graph structured data are abundant in the real world. Among different graph types, directed acyclic graphs (DAGs) are of particular interest to machine learning researchers, as many machine learning models are realized as computations on DAGs, including neural networks and Bayesian networks. In this paper, we study deep generative models for DAGs, and propose a novel DAG variational autoencoder (D-VAE). To encode DAGs into the latent space, we leverage graph neural networks. We propose an asynchronous message passing scheme that allows encoding the computations on DAGs, rather than using existing simultaneous message passing schemes to encode local graph structures. We demonstrate the effectiveness of our proposed DVAE through two tasks: neural architecture search and Bayesian network structure learning. Experiments show that our model not only generates novel and valid DAGs, but also produces a smooth latent space that facilitates searching for DAGs with better performance through Bayesian optimization. 

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