Structural equation models (SEMs) are widely used in sciences, ranging from economics topsychology,touncovercausal relationships underlying acomplex system under consideration and estimate structural parameters of interest. We study estimation in a class of generalized SEMs where the object of interest is defined as the solution to a linear operator equation.

To represent the causal relationships between variables, a directed acyclic graph (DAG) is widely utilized in many areas, such as social sciences, epidemics, and genetics. Many causal structure learning approaches are developed to learn the hidden causal structure utilizing deep-learning approaches. However, these approaches have a hidden assumption that the causal relationship remains unchanged over time, which may not hold in real life. In this paper, we develop a new framework to model the dynamic causal graph where the causal relations are allowed to be time-varying. We incorporate the basis approximation method into the score-based causal discovery approach to capture the dynamic pattern of the causal graphs. Utilizing the autoregressive model structure, we could capture both contemporaneous and time-lagged causal relationships while allowing them to vary with time. We propose an algorithm that could provide both past-time estimates and future-time predictions on the causal graphs, and conduct simulations to demonstrate the usefulness of the proposed method. We also apply the proposed method for the covid-data analysis, and provide causal estimates on how policy restriction's effect changes.

In recent years a lot of research has been conducted within the area of causal inference and causal learning. Many methods have been developed to identify the cause-effect pairs in models and have been successfully applied to observational real-world data in order to determine the direction of causal relationships. Many of these methods require simplifying assumptions, such as absence of confounding, cycles, and selection bias. Yet in bivariate situations causal discovery problems remain challenging. One class of such methods, that also allows tackling the bivariate case, is based on Additive Noise Models (ANMs). Unfortunately, one aspect of these methods has not received much attention until now: what is the impact of different noise levels on the ability of these methods to identify the direction of the causal relationship. This work aims to bridge this gap with the help of an empirical study. For this work, we considered bivariate cases, which is the most elementary form of a causal discovery problem where one needs to decide whether X causes Y or Y causes X, given joint distributions of two variables X, Y. Furthermore, two specific methods have been selected, \textit{Regression with Subsequent Independence Test} and \textit{Identification using Conditional Variances}, which have been tested with an exhaustive range of ANMs where the additive noises' levels gradually change from 1% to 10000% of the causes' noise level (the latter remains fixed). Additionally, the experiments in this work consider several different types of distributions as well as linear and non-linear ANMs. The results of the experiments show that these methods can fail to capture the true causal direction for some levels of noise.

We extend the empirical results from the structural equation model (SEM) published in the paper Assortment Planning for Retail Buying, Retail Store Operations, and Firm Performance [1] by implementing the directed acyclic graph as a causal Bayesian neural network. Neural network convergence is shown to improve with the removal of the node with the weakest SEM path when variational inference is provided by perturbing weights with Flipout layers, while results from perturbing weights at the output with the Vadam optimizer are inconclusive.

Scientific documents rely on both mathematics and text to communicate ideas. Inspired by the topical correspondence between mathematical equations and word contexts observed in scientific texts, we propose a novel topic model that jointly generates mathematical equations and their surrounding text (TopicEq). Using an extension of the correlated topic model, the context is generated from a mixture of latent topics, and the equation is generated by an RNN that depends on the latent topic activations. To experiment with this model, we create a corpus of 400K equation-context pairs extracted from a range of scientific articles from arXiv, and fit the model using a variational autoencoder approach. Experimental results show that this joint model significantly outperforms existing topic models and equation models for scientific texts. Moreover, we qualitatively show that the model effectively captures the relationship between topics and mathematics, enabling novel applications such as topic-aware equation generation, equation topic inference, and topic-aware alignment of mathematical symbols and words.

We address the problem of causal interpretation of the graphical structure of Bayesian belief networks (BBNs). We review the concept of causality explicated in the domain of structural equations models and show that it is applicable to BBNs. In this view, which we call mechanism-based, causality is defined within models and causal asymmetries arise when mechanisms are placed in the context of a system. We lay the link between structural equations models and BBNs models and formulate the conditions under which the latter can be given causal interpretation.

When observational data is available from practical studies and a directed cyclic graph for how various variables affect each other is known based on substantive understanding of the process, we consider a problem in which a control plan of a treatment variable is conducted in order to bring a response variable close to a target value with variation reduction. We formulate an optimal control plan concerning a certain treatment variable through path coefficients in the framework of linear nonrecursive structural equation models. Based on the formulation, we clarify the properties of causal effects when conducting a control plan. The results enable us to evaluate the effect of a control plan on the variance from observational data.

Structural equation models can be seen as an extension of Gaussian belief networks to cyclic graphs, and we show they can be understood generatively as the model for the joint distribution of long term average equilibrium activity of Gaussian dynamic belief networks. Most use of structural equation models in fMRI involves postulating a particular structure and comparing learnt parameters across different groups. In this paper it is argued that there are situations where priors about structure are not firm or exhaustive, and given sufficient data, it is worth investigating learning network structure as part of the approach to connectivity analysis. First we demonstrate structure learning on a toy problem. We then show that for particular fMRI data the simple models usually assumed are not supported. We show that is is possible to learn sensible structural equation models that can provide modelling benefits, but that are not necessarily going to be the same as a true causal model, and suggest the combination of prior models and learning or the use of temporal information from dynamic models may provide more benefits than learning structural equations alone.

First we demonstrate stiucture learning on a toy problem.