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1. GPIRT: A Gaussian Process Model for Item Response Theory

   Duck-Mayr, JBrandon; Garnett, Roman; Montgomery, Jacob (April 2020, Proceedings of Machine Learning Research)

   null (Ed.)

   The goal of item response theoretic (IRT) models is to provide estimates of latent traits from binary observed indicators and at the same time to learn the item response funcitons (IRFs) that map from latent trait to observed response. However, in many cases observed behavior can deviate significantly from the parametric assumptions of traditional IRT models. Nonparametric IRT (NIRT) models overcome these challenges by relaxing assumptions about the form of the IRFs, but standard tools are unable to simultaneously estimate flexible IRFs and recover ability estimates for respondents. We propose a Bayesian nonparametric model that solves this problem by placing Gaussian process priors on the latent functions defining the IRFs. This allows us to simultaneously relax assumptions about the shape of the IRFs while preserving the ability to estimate latent traits. This in turn allows us to easily extend the model to further tasks such as active learning. GPIRT therefore provides a simple and intuitive solution to several longstanding problems in the IRT literature. 

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2. Causal Diffusion Autoencoders: Toward Counterfactual Generation via Diffusion Probabilistic Models

   https://doi.org/10.3233/FAIA240780  

   Komanduri, Aneesh; Zhao, Chen; Chen, Feng; Wu, Xintao (October 2024, IOS Press)

   Diffusion probabilistic models (DPMs) have become the state-of-the-art in high-quality image generation. However, DPMs have an arbitrary noisy latent space with no interpretable or controllable semantics. Although there has been significant research effort to improve image sample quality, there is little work on representation-controlled generation using diffusion models. Specifically, causal modeling and controllable counterfactual generation using DPMs is an underexplored area. In this work, we propose CausalDiffAE, a diffusion-based causal representation learning framework to enable counterfactual generation according to a specified causal model. Our key idea is to use an encoder to extract high-level semantically meaningful causal variables from high-dimensional data and model stochastic variation using reverse diffusion. We propose a causal encoding mechanism that maps high-dimensional data to causally related latent factors and parameterize the causal mechanisms among latent factors using neural networks. To enforce the disentanglement of causal variables, we formulate a variational objective and leverage auxiliary label information in a prior to regularize the latent space. We propose a DDIM-based counterfactual generation procedure subject to do-interventions. Finally, to address the limited label supervision scenario, we also study the application of CausalDiffAE when a part of the training data is unlabeled, which also enables granular control over the strength of interventions in generating counterfactuals during inference. We empirically show that CausalDiffAE learns a disentangled latent space and is capable of generating high-quality counterfactual images. 

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3. Item Response Theory – A Statistical Framework for Educational and Psychological Measurement

   Yunxiao Chen, Xiaoou Li (March 2023, Statistical science)

   Item response theory (IRT) has become one of the most popular statistical models for psychometrics, a field of study concerned with the theory and techniques of psychological measurement. The IRT models are latent factor models tailored to the analysis, interpretation, and prediction of individuals’ behaviors in answering a set of measurement items that typically involve categorical response data. Many important questions of measurement are directly or indirectly answered through the use of IRT models, including scoring individuals’ test performances, validating a test scale, linking two tests, among others. This paper provides a review of item response theory, including its statistical framework and psychometric applications. We establish connections between item response theory and related topics in statistics, including empirical Bayes, nonparametric methods, matrix completion, regularized estimation, and sequential analysis. Possible future directions of IRT are discussed from the perspective of statistical learning. 

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4. Curvilinearity in the Reference Composite and Practical Implications for Measurement

   https://doi.org/10.1111/jedm.12402  

   Liao, Xiangyi; Bolt, Daniel M; Kim, Jee‐Seon (June 2024, Journal of Educational Measurement)

   Abstract Item difficulty and dimensionality often correlate, implying that unidimensional IRT approximations to multidimensional data (i.e., reference composites) can take a curvilinear form in the multidimensional space. Although this issue has been previously discussed in the context of vertical scaling applications, we illustrate how such a phenomenon can also easily occur within individual tests. Measures of reading proficiency, for example, often use different task types within a single assessment, a feature that may not only lead to multidimensionality, but also an association between item difficulty and dimensionality. Using a latent regression strategy, we demonstrate through simulations and empirical analysis how associations between dimensionality and difficulty yield a nonlinear reference composite where the weights of the underlying dimensionschangeacross the scale continuum according to the difficulties of the items associated with the dimensions. We further show how this form of curvilinearity produces systematic forms of misspecification in traditional unidimensional IRT models (e.g., 2PL) and can be better accommodated by models such as monotone‐polynomial or asymmetric IRT models. Simulations and a real‐data example from the Early Childhood Longitudinal Study—Kindergarten are provided for demonstration. Some implications for measurement modeling and for understanding the effects of 2PL misspecification on measurement metrics are discussed. 

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5. Nonparametric Failure Time: Time-to-Event Machine Learning with Heteroskedastic Bayesian Additive Regression Trees and Low Information Omnibus Dirichlet Process Mixtures

   https://doi.org/10.1111/biom.13857  

   Sparapani, Rodney A; Logan, Brent R; Maiers, Martin J; Laud, Purushottam W; McCulloch, Robert E (March 2023, Biometrics)

   Abstract Many popular survival models rely on restrictive parametric, or semiparametric, assumptions that could provide erroneous predictions when the effects of covariates are complex. Modern advances in computational hardware have led to an increasing interest in flexible Bayesian nonparametric methods for time-to-event data such as Bayesian additive regression trees (BART). We propose a novel approach that we call nonparametric failure time (NFT) BART in order to increase the flexibility beyond accelerated failure time (AFT) and proportional hazard models. NFT BART has three key features: (1) a BART prior for the mean function of the event time logarithm; (2) a heteroskedastic BART prior to deduce a covariate-dependent variance function; and (3) a flexible nonparametric error distribution using Dirichlet process mixtures (DPM). Our proposed approach widens the scope of hazard shapes including nonproportional hazards, can be scaled up to large sample sizes, naturally provides estimates of uncertainty via the posterior and can be seamlessly employed for variable selection. We provide convenient, user-friendly, computer software that is freely available as a reference implementation. Simulations demonstrate that NFT BART maintains excellent performance for survival prediction especially when AFT assumptions are violated by heteroskedasticity. We illustrate the proposed approach on a study examining predictors for mortality risk in patients undergoing hematopoietic stem cell transplant (HSCT) for blood-borne cancer, where heteroskedasticity and nonproportional hazards are likely present. 

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