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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. Joint latent space models for network data with high-dimensional node variables

   https://doi.org/10.1093/biomet/asab063  

   Zhang, Xuefei; Xu, Gongjun; Zhu, Ji (December 2021, Biometrika)

   Summary Network latent space models assume that each node is associated with an unobserved latent position in a Euclidean space, and such latent variables determine the probability of two nodes connecting with each other. In many applications, nodes in the network are often observed along with high-dimensional node variables, and these node variables provide important information for understanding the network structure. However, classical network latent space models have several limitations in incorporating node variables. In this paper, we propose a joint latent space model where we assume that the latent variables not only explain the network structure, but are also informative for the multivariate node variables. We develop a projected gradient descent algorithm that estimates the latent positions using a criterion incorporating both network structure and node variables. We establish theoretical properties of the estimators and provide insights into how incorporating high-dimensional node variables could improve the estimation accuracy of the latent positions. We demonstrate the improvement in latent variable estimation and the improvements in associated downstream tasks, such as missing value imputation for node variables, by simulation studies and an application to a Facebook data example. 

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3. Do-calculus enables estimation of causal effects in partially observed biomolecular pathways

   https://doi.org/10.1093/bioinformatics/btac251  

   Mohammad-Taheri, Sara; Zucker, Jeremy; Hoyt, Charles Tapley; Sachs, Karen; Tewari, Vartika; Ness, Robert; Vitek, Olga (June 2022, Bioinformatics)

   Abstract Motivation Estimating causal queries, such as changes in protein abundance in response to a perturbation, is a fundamental task in the analysis of biomolecular pathways. The estimation requires experimental measurements on the pathway components. However, in practice many pathway components are left unobserved (latent) because they are either unknown, or difficult to measure. Latent variable models (LVMs) are well-suited for such estimation. Unfortunately, LVM-based estimation of causal queries can be inaccurate when parameters of the latent variables are not uniquely identified, or when the number of latent variables is misspecified. This has limited the use of LVMs for causal inference in biomolecular pathways. Results In this article, we propose a general and practical approach for LVM-based estimation of causal queries. We prove that, despite the challenges above, LVM-based estimators of causal queries are accurate if the queries are identifiable according to Pearl’s do-calculus and describe an algorithm for its estimation. We illustrate the breadth and the practical utility of this approach for estimating causal queries in four synthetic and two experimental case studies, where structures of biomolecular pathways challenge the existing methods for causal query estimation. Availability and implementation The code and the data documenting all the case studies are available at https://github.com/srtaheri/LVMwithDoCalculus. Supplementary information Supplementary data are available at Bioinformatics online. 

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4. An exploratory analysis of the latent structure of process data via action sequence autoencoders

   https://doi.org/10.1111/bmsp.12203  

   Tang, Xueying; Wang, Zhi; Liu, Jingchen; Ying, Zhiliang (May 2020, British Journal of Mathematical and Statistical Psychology)

   Computer simulations have become a popular tool for assessing complex skills such as problem‐solving. Log files of computer‐based items record the human–computer interactive processes for each respondent in full. The response processes are very diverse, noisy, and of non‐standard formats. Few generic methods have been developed to exploit the information contained in process data. In this paper we propose a method to extract latent variables from process data. The method utilizes a sequence‐to‐sequence autoencoder to compress response processes into standard numerical vectors. It does not require prior knowledge of the specific items and human–computer interaction patterns. The proposed method is applied to both simulated and real process data to demonstrate that the resulting latent variables extract useful information from the response processes. 

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5. Towards Characterizing Domain Counterfactuals for Invertible Latent Causal Models

   Zhou, Zeyu; Bai, Ruqi; Kulinski, Sean; Kocaoglu, Murat; Inouye, David I (May 2024, International Conference on Learning Representations)

   Answering counterfactual queries has important applications such as explainability, robustness, and fairness but is challenging when the causal variables are unobserved and the observations are non-linear mixtures of these latent variables, such as pixels in images. One approach is to recover the latent Structural Causal Model (SCM), which may be infeasible in practice due to requiring strong assumptions, e.g., linearity of the causal mechanisms or perfect atomic interventions. Meanwhile, more practical ML-based approaches using naive domain translation models to generate counterfactual samples lack theoretical grounding and may construct invalid counterfactuals. In this work, we strive to strike a balance between practicality and theoretical guarantees by analyzing a specific type of causal query called domain counterfactuals, which hypothesizes what a sample would have looked like if it had been generated in a different domain (or environment). We show that recovering the latent SCM is unnecessary for estimating domain counterfactuals, thereby sidestepping some of the theoretic challenges. By assuming invertibility and sparsity of intervention, we prove domain counterfactual estimation error can be bounded by a data fit term and intervention sparsity term. Building upon our theoretical results, we develop a theoretically grounded practical algorithm that simplifies the modeling process to generative model estimation under autoregressive and shared parameter constraints that enforce intervention sparsity. Finally, we show an improvement in counterfactual estimation over baseline methods through extensive simulated and image-based experiments. 

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