In today's digital age, social media platforms playa crucial role in shaping public opinion. This study explores how discussions led by influencers on Twitter, now known as ‘X’, affect public sentiment and contribute to online polarization. We developed a counterfactual framework to analyze the polarization scores of conversations in scenarios both with and without the presence of an influential figure. Two case studies, centered on the polarizing issues of climate change and gun control, were examined. Our research highlights the significant impact these figures have on public discourse, providing valuable insights into how online discussions can influence societal divisions.

The proliferation of high-dimensional data in the era of big data has presented significant challenges for machine learning models. Feature selection methods have emerged as essential preprocessing techniques to address these challenges. However, most existing feature selection techniques primarily rely on correlations or associations between features and the target variable, overlooking the consideration of causal relationships. This study introduces a novel causal feature selection (CFS) algorithm that leverages causal structure learning to identify a subset of causal features. Our approach involves employing a causal graph discovery method to represent the causal relationships among variables and the causal effects of features on the target variable. To evaluate the effectiveness of our proposed CFS algorithm, we introduce a new evaluation criterion based on causal metrics, offering a principled and rigorous approach to assess the performance of causal feature selection methods. We empirically evaluate our algorithm using synthetic and real-world datasets, demonstrating that the truncated subsets of features selected by the CFS algorithm exhibit comparable or improved performance compared to baseline methods while utilizing fewer causal features.

Causal discovery has become increasingly popular in recent years, with the emergence of various methods for inferring causal relationships from observational data. While NOTEARS is a widely-used structure learning method known for its effectiveness in handling scalar-valued continuous data, it is not well-posed for conceptual data. In this study, we present a novel extension of the NOTEARS method, called Concept-Driven NOTEARS (CD-NOTEARS), that leverages concept-level prior knowledge to impose DAGness on concepts instead of the raw high-dimensional data. Our proposed approach preserves the non-parametric nature of the original NOTEARS method and is evaluated on synthetic, benchmark, and real-world datasets. The results demonstrate that CD-NOTEARS outperforms the original implementation and offers a promising tool for causal discovery in scenarios where causality should be imposed on the concept level. Our study provides insights into how incorporating concept-level knowledge improves the performance of causal discovery and paves the way for further research in this direction.

Causal structure learning from observational data remains a non-trivial task due to various factors such as finite sampling, unobserved confounding factors, and measurement errors. Constraint-based and score-based methods tend to suffer from high computational complexity due to the combinatorial nature of estimating the directed acyclic graph (DAG). Motivated by the ‘Cause-Effect Pair’ NIPS 2013 Workshop on Causality Challenge, in this paper, we take a different approach and generate a probability distribution over all possible graphs informed by the cause-effect pair features proposed in response to the workshop challenge. The goal of the paper is to propose new methods based on this probabilistic information and compare their performance with traditional and state-of-the-art approaches. Our experiments, on both synthetic and real datasets, show that our proposed methods not only have statistically similar or better performances than some traditional approaches but also are computationally faster.

Real-time nonlinear Bayesian filtering algorithms are overwhelmed by data volume, velocity and increasing complexity of computational models. In this paper, we propose a novel ensemble based nonlinear Bayesian filtering approach which only requires a small number of simulations and can be applied to high-dimensional systems in the presence of intractable likelihood functions. The proposed approach uses linear latent projections to estimate the joint probability distribution between states, parameters, and observables using a mixture of Gaussian components generated by the reconstruction error for each ensemble member. Since it leverages the computational machinery behind linear latent variable models, it can achieve fast implementations without the need to compute high-dimensional sample covariance matrices. The performance of the proposed approach is compared with the performance of ensemble Kalman filter on a high-dimensional Lorenz nonlinear dynamical system.

Neural networks have achieved significant success in many areas. Nevertheless, conventional neural networks lack uncertainty information, which plays an important role especially in critical-safety applications such as self-driving cars. When uncertainty is characterized using probability the main modeling approach is the construction of Bayesian neural networks. Obtaining the posterior distribution for these models is computationally intensive and analytical solutions are intractable. In this work, we propose a novel algorithm to infer the weights for Bayesian neural networks based on the ensemble Kalman filter. To evaluate the performance of the algorithm, we use ten regression datasets from University of California at Irvine machine learning repository, and a natural language dataset. The results suggest that EnKF can be used as a gradient-free alternative to training deep neural networks to capture prediction uncertainty.

Long Short-Term Memory networks trained with gradient descent and back-propagation have received great success in various applications. However, point estimation of the weights of the networks is prone to over-fitting problems and lacks important uncertainty information associated with the estimation. However, exact Bayesian neural network methods are intractable and non-applicable for real-world applications. In this study, we propose an approximate estimation of the weights uncertainty using Ensemble Kalman Filter, which is easily scalable to a large number of weights. Furthermore, we optimize the covariance of the noise distribution in the ensemble update step using maximum likelihood estimation. To assess the proposed algorithm, we apply it to outlier detection in five realworld events retrieved from the Twitter platform.

The objective of this paper is to develop a methodology for generating probabilistic risk maps for unobserved quantities of interests such as aflatoxin. Aflatoxin is a naturally occurring carcinogenic and it is a serious global issue and an emerging risk for crop producers. The production of aflatoxin is highly dependent on environmental conditions such temperature and water activity, and it can contaminate grains before harvest or during storage. The focus of this paper is to develop a procedure to account for spatial dependencies and uncertainties in risk calculations, to provide various stakeholders with situational awareness to better understand, communicate, and mitigate the aflatoxin risk before harvest. The proposed probabilistic model is obtained in two stages: the production of aflatoxin with quantified uncertainties is modeled under various temperature and water activity conditions within a controlled environment (wet-lab), and then the predictive aflatoxin model is linked with environmental conditions obtained on a regular basis to generate regional probabilistic risk maps. Since both aflatoxin production and environmental data are modeled using Gaussian processes, the resulted probabilistic model is a stacked Gaussian process, where the environmental Gaussian process model governs the input space of the aflatoxin Gaussian process model. The regional prediction of aflatoxin is obtained by marginalizing over the latent space provided by the environmental variables. The methodology is applied to calculate the aflatoxin levels of corn lands in South Carolina in the drought year 2012, where few field measurements are available for an initial comparison with our aflatoxin predictions.

Fixed interval smoothing for systems with nonlinear process and measurement models is studied and applied to the assimilation of sensor data in a Chemical, Biological, Radiological or Nuclear (CBRN) incident scenario. A two-filter smoother that uses a Backward Sigma-Point Information Filter, and also a forward-backward Rauch-Tung-Striebel (RTS) smoothing form are re-derived using the weighted statistical linearization concept. Both methods are derived in the context of the Unscented Kalman Filter. The square root version of the resulting RTS Unscented Kalman Filter / Smoother is applied to a CBRN dispersion puff-based model with variable state dimension, and the data assimilation performance of the method is compared with a Particle Filter implementation.