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1. Reasoning about causal models with infinitely many variables,

   S. Peters; J. Y. Halpern (February 2022, Proceedings of the Thirty-Sixth AAAI Conference on Artificial Intelligence)

   Generalized structural equations models (GSEMs) are, as the name suggests, a generalization of structural equations models (SEMs). They can deal with (among other things) infinitely many variables with infinite ranges, which is critical for capturing dynamical systems. We provide a sound and complete axiomatization of causal reasoning in GSEMs that is an extension of the sound and complete axiomatization provided by Halpern for SEMs. Considering GSEMs helps clarify what properties Halpern's axioms capture. 

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2. Learning Linear Polytree Structural Equation Model

   Lou, Xingmei; Hu, Yu; Li, Xiaodong (March 2025, Transactions on Machine Learning Research (TMLR))

   We study learning the directed acyclic graph (DAG) for linear structural equation models (SEMs) when the causal structure is a polytree. Under Gaussian polytree models, we derive sufficient sample-size conditions under which the Chow–Liu algorithm exactly recovers both the skeleton and the equivalence class (CPDAG). Matching information-theoretic lower bounds provide necessary conditions, yielding sharp characterizations of problem difficulty. We further analyze inverse correlation matrix estimation with error bounds depending on dimension and the number of v-structures, and extend to group linear polytrees. Comprehensive simulations and benchmark experiments demonstrate robustness when true graphs are only approximately polytrees. 

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3. A linear noise approximation for stochastic epidemic models fit to partially observed incidence counts

   https://doi.org/10.1111/biom.13538  

   Fintzi, Jonathan; Wakefield, Jon; Minin, Vladimir N. (September 2021, Biometrics)

   Abstract Stochastic epidemic models (SEMs) fit to incidence data are critical to elucidating outbreak dynamics, shaping response strategies, and preparing for future epidemics. SEMs typically represent counts of individuals in discrete infection states using Markov jump processes (MJPs), but are computationally challenging as imperfect surveillance, lack of subject‐level information, and temporal coarseness of the data obscure the true epidemic. Analytic integration over the latent epidemic process is impossible, and integration via Markov chain Monte Carlo (MCMC) is cumbersome due to the dimensionality and discreteness of the latent state space. Simulation‐based computational approaches can address the intractability of the MJP likelihood, but are numerically fragile and prohibitively expensive for complex models. A linear noise approximation (LNA) that approximates the MJP transition density with a Gaussian density has been explored for analyzing prevalence data in large‐population settings, but requires modification for analyzing incidence counts without assuming that the data are normally distributed. We demonstrate how to reparameterize SEMs to appropriately analyze incidence data, and fold the LNA into a data augmentation MCMC framework that outperforms deterministic methods, statistically, and simulation‐based methods, computationally. Our framework is computationally robust when the model dynamics are complex and applies to a broad class of SEMs. We evaluate our method in simulations that reflect Ebola, influenza, and SARS‐CoV‐2 dynamics, and apply our method to national surveillance counts from the 2013–2015 West Africa Ebola outbreak. 

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4. Learning Tensor Representations to Improve Quality of Wavefield Data

   https://doi.org/10.1115/QNDE2023-108620  

   Tetali, Harsha Vardhan; Harley, Joel B. (July 2023, Proc. of the Review of Quantitative Nondestructive Evaluation)

   Recent advancements in physics-informed machine learning have contributed to solving partial differential equations through means of a neural network. Following this, several physics-informed neural network works have followed to solve inverse problems arising in structural health monitoring. Other works involving physics-informed neural networks solve the wave equation with partial data and modeling wavefield data generator for efficient sound data generation. While a lot of work has been done to show that partial differential equations can be solved and identified using a neural network, little work has been done the same with more basic machine learning (ML) models. The advantage with basic ML models is that the parameters learned in a simpler model are both more interpretable and extensible. For applications such as ultrasonic nondestructive evaluation, this interpretability is essential for trustworthiness of the methods and characterization of the material system under test. In this work, we show an interpretable, physics-informed representation learning framework that can analyze data across multiple dimensions (e.g., two dimensions of space and one dimension of time). The algorithm comes with convergence guarantees. In addition, our algorithm provides interpretability of the learned model as the parameters correspond to the individual solutions extracted from data. We demonstrate how this algorithm functions with wavefield videos. 

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5. Learning Relational Causal Models with Cycles through Relational Acyclification

   https://doi.org/10.1609/aaai.v37i10.26434  

   Ahsan, Ragib; Arbour, David; Zheleva, Elena (June 2023, Proceedings of the AAAI Conference on Artificial Intelligence)

   In real-world phenomena which involve mutual influence or causal effects between interconnected units, equilibrium states are typically represented with cycles in graphical models. An expressive class of graphical models, relational causal models, can represent and reason about complex dynamic systems exhibiting such cycles or feedback loops. Existing cyclic causal discovery algorithms for learning causal models from observational data assume that the data instances are independent and identically distributed which makes them unsuitable for relational causal models. At the same time, causal discovery algorithms for relational causal models assume acyclicity. In this work, we examine the necessary and sufficient conditions under which a constraint-based relational causal discovery algorithm is sound and complete for cyclic relational causal models. We introduce relational acyclification, an operation specifically designed for relational models that enables reasoning about the identifiability of cyclic relational causal models. We show that under the assumptions of relational acyclification and sigma-faithfulness, the relational causal discovery algorithm RCD is sound and complete for cyclic relational models. We present experimental results to support our claim. 

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