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1. Discovery and inference of a causal network with hidden confounding*

   https://doi.org/10.1080/01621459.2023.2261658  

   Chen, Li; Li, Chunlin; Shen, Xiaotong; Pan, Wei (October 2023, Journal of the American Statistical Association)

   This article proposes a novel causal discovery and inference method called GrIVET for a Gaussian directed acyclic graph with unmeasured confounders. GrIVET consists of an order-based causal discovery method and a likelihood-based inferential procedure. For causal discovery, we generalize the existing peeling algorithm to estimate the ancestral relations and candidate instruments in the presence of hidden confounders. Based on this, we propose a new procedure for instrumental variable estimation of each direct effect by separating it from any mediation effects. For inference, we develop a new likelihood ratio test of multiple causal effects that is able to account for the unmeasured confounders. Theoretically, we prove that the proposed method has desirable guarantees, including robustness to invalid instruments and uncertain interventions, estimation consistency, low-order polynomial time complexity, and validity of asymptotic inference. Numerically, GrIVET performs well and compares favorably against state-of-the-art competitors. Furthermore, we demonstrate the utility and effectiveness of the proposed method through an application inferring regulatory pathways from Alzheimer’s disease gene expression data. 

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2. Experimental Design for Learning Causal Graphs with Latent Variables

   Kocaoglu, Murat; Shanmugam, Karthikeyan; Bareinboim, Elias (January 2017, Nips)

   We consider the problem of learning causal structures with latent variables using interventions. Our objective is not only to learn the causal graph between the observed variables, but to locate unobserved variables that could confound the relationship between observables. Our approach is stage-wise: We first learn the observable graph, i.e., the induced graph between observable variables. Next, we learn the existence and location of the latent variables given the observable graph. We propose an efficient randomized algorithm that can learn the observable graph using O(d log2n) interventions where d is the degree of the graph. We further propose an efficient deterministic variant which uses O(log n + l) interventions, where l is the longest directed path in the graph. Next, we propose an algorithm that uses only O(d2 log n) interventions that can learn the latents between both nonadjacent and adjacent variables. While a naive baseline approach would require O(n2) interventions, our combined algorithm can learn the causal graph with latents using O(d log2n + d2 log (n)) interventions. 

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3. Entropic Inequality Constraints from e-separation Relations in Directed Acyclic Graphs with Hidden Variables

   Noam Finkelstein; Beata Zjawin; Elie Wolfe; Ilya Shpitser; Robert W. Spekkens (July 2021, Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence)

   de Campos, Cassio and (Ed.)

   Directed acyclic graphs (DAGs) with hidden variables are often used to characterize causal relations between variables in a system. When some variables are unobserved, DAGs imply a notoriously complicated set of constraints on the distribution of observed variables. In this work, we present entropic inequality constraints that are implied by e- separation relations in hidden variable DAGs with discrete observed variables. The constraints can intuitively be understood to follow from the fact that the capacity of variables along a causal path- way to convey information is restricted by their entropy; e.g. at the extreme case, a variable with entropy 0 can convey no information. We show how these constraints can be used to learn about the true causal model from an observed data distribution. In addition, we propose a measure of causal influence called the minimal mediary entropy, and demonstrate that it can augment traditional measures such as the average causal effect. 

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4. Learning joint latent space EBM prior model for multi-layer generator

   https://doi.org/10.1109/CVPR52729.2023.00351  

   Cui, J; Wu, Y N; Han, T (June 2023, Conference on Computer Vision and Pattern Recognition (CVPR 2023))

   This paper studies the fundamental problem of learning multi-layer generator models. The multi-layer generator model builds multiple layers of latent variables as a prior model on top of the generator, which benefits learning complex data distribution and hierarchical representations. However, such a prior model usually focuses on modeling inter-layer relations between latent variables by assuming non-informative (conditional) Gaussian distributions, which can be limited in model expressivity. To tackle this issue and learn more expressive prior models, we propose an energy-based model (EBM) on the joint latent space over all layers of latent variables with the multi-layer generator as its backbone. Such joint latent space EBM prior model captures the intra-layer contextual relations at each layer through layer-wise energy terms, and latent variables across different layers are jointly corrected. We develop a joint training scheme via maximum likelihood estimation (MLE), which involves Markov Chain Monte Carlo (MCMC) sampling for both prior and posterior distributions of the latent variables from different layers. To ensure efficient inference and learning, we further propose a variational training scheme where an inference model is used to amortize the costly posterior MCMC sampling. Our experiments demonstrate that the learned model can be expressive in generating high-quality images and capturing hierarchical features for better outlier detection. 

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5. Causal Inference Despite Limited Global Confounding via Mixture Models

   Gordon, S.; Mazaheri, B.; Rabani, Y.; Schulman, L. (April 2023, Proceedings of Machine Learning Research)

   van der Schaar, M.; Zhang, C.; Janzing, D. (Ed.)

   A Bayesian Network is a directed acyclic graph (DAG) on a set of n random variables (the vertices); a Bayesian Network Distribution (BND) is a probability distribution on the random variables that is Markovian on the graph. A finite k-mixture of such models is graphically represented by a larger graph which has an additional “hidden” (or “latent”) random variable U, ranging in {1,...,k}, and a directed edge from U to every other vertex. Models of this type are fundamental to causal inference, where U models an unobserved confounding effect of multiple populations, obscuring the causal relationships in the observable DAG. By solving the mixture problem and recovering the joint probability distribution with U, traditionally unidentifiable causal relationships become identifiable. Using a reduction to the more well-studied “product” case on empty graphs, we give the first algorithm to learn mixtures of non-empty DAGs. 

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