Nonlinear causal discovery from observational data imposes strict identifiability assumptions on the formulation of structural equations utilized in the data generating process. The evaluation of structure learning methods under assumption violations requires a rigorous and interpretable approach, which quantifies both the structural similarity of the estimation with the ground truth and the capacity of the discovered graphs to be used for causal inference. Motivated by the lack of unified performance assessment framework, we introduce an interpretable, six-dimensional evaluation metric, i.e., distance to optimal solution (DOS), which is specifically tailored to the field of causal discovery. Furthermore, this is the first research to assess the performance of structure learning algorithms from seven different families on increasing percentage of non-identifiable, nonlinear causal patterns, inspired by real-world processes. Our large-scale simulation study, which incorporates seven experimental factors, shows that besides causal order-based methods, amortized causal discovery delivers results with comparatively high proximity to the optimal solution.

Heterogeneity is a fundamental and challenging issue in federated learning, especially for the graph data due to the complex relationships among the graph nodes. To deal with the heterogeneity, lots of existing methods perform the weighted federation based on their calculated similarities between pairwise clients (i.e., subgraphs). However, their inter-subgraph similarities estimated with the outputs of local models are less reliable, because the final outputs of local models may not comprehensively represent the real distribution of subgraph data. In addition, they ignore the critical intra-heterogeneity which usually exists within each subgraph itself. To address these issues, we propose a novel Federated learning method by integrally modeling the Inter-Intra Heterogeneity (FedIIH). For the inter-subgraph relationship, we propose a novel hierarchical variational model to infer the whole distribution of subgraph data in a multi-level form, so that we can accurately characterize the inter-subgraph similarities with the global perspective. For the intra-heterogeneity, we disentangle the subgraph into multiple latent factors and partition the model parameters into multiple parts, where each part corresponds to a single latent factor. Our FedIIH not only properly computes the distribution similarities between subgraphs, but also learns disentangled representations that are robust to irrelevant factors within subgraphs, so that it successfully considers the inter- and intra- heterogeneity simultaneously. Extensive experiments on six homophilic and five heterophilic graph datasets in both non-overlapping and overlapping settings demonstrate the effectiveness of our method when compared with nine state-of-the-art methods. Specifically, FedIIH averagely outperforms the second-best method by a large margin of 5.79% on all heterophilic datasets.

Following the universal availability of generative AI systems with the release of ChatGPT, automatic detection of deceptive text created by Large Language Models has focused on domains such as academic plagiarism and "fake news". However, generative AI also poses a threat to the livelihood of creative writers, and perhaps to literary culture in general, through reduction in quality of published material. Training a Large Language Model on writers' output to generate "sham books" in a particular style seems to constitute a new form of plagiarism. This problem has been little researched. In this study, we trained Machine Learning classifier models to distinguish short samples of human-written from machine-generated creative fiction, focusing on classic detective novels. Our results show that a Naive Bayes and a Multi-Layer Perceptron classifier achieved a high degree of success (accuracy > 95%), significantly outperforming human judges (accuracy < 55%). This approach worked well with short text samples (around 100 words), which previous research has shown to be difficult to classify. We have deployed an online proof-of-concept classifier tool, AI Detective, as a first step towards developing lightweight and reliable applications for use by editors and publishers, with the aim of protecting the economic and cultural contribution of human authors.

The Poisson Multi-Bernoulli Mixture (PMBM) density is a conjugate multi-target density for the standard point target model with Poisson point process birth. This means that both the filtering and predicted densities for the set of targets are PMBM. In this paper, we first show that the PMBM density is also conjugate for sets of trajectories with the standard point target measurement model. Second, based on this theoretical foundation, we develop two trajectory PMBM filters that provide recursions to calculate the posterior density for the set of all trajectories that have ever been present in the surveillance area, and the posterior density of the set of trajectories present at the current time step in the surveillance area. These two filters therefore provide complete probabilistic information on the considered trajectories enabling optimal trajectory estimation. Third, we establish that the density of the set of trajectories in any time window, given the measurements in a possibly different time window, is also a PMBM. Finally, the trajectory PMBM filters are evaluated via simulations, and are shown to yield state-of-the-art performance compared to other multi-target tracking algorithms based on random finite sets and multiple hypothesis tracking.

This paper tackles the challenge of one-bit off-grid direction of arrival (DOA) estimation in a single snapshot scenario based on a learning-based Bayesian approach. Firstly, we formulate the off-grid DOA estimation model, utilizing the first-order off-grid approximation, incorporating one-bit data quantization. Subsequently, we address this problem using the Sparse Bayesian based framework and solve iteratively. However, traditional Sparse Bayesian methods often face challenges such as high computational complexity and the need for extensive hyperparameter tuning. To balance estimation accuracy and computational efficiency, we propose a novel Learning-based Sparse Bayesian framework, which leverages an unrolled neural network architecture. This framework autonomously learns hyperparameters through supervised learning, offering more accurate off-grid DOA estimates and improved computational efficiency compared to some state-of-the-art methods. Furthermore, the proposed approach is applicable to both uniform linear arrays and non-uniform sparse arrays. Simulation results validate the effectiveness of the proposed framework.

We conducted three experiments to investigate how large language models (LLMs) evaluate posterior probabilities. Our results reveal the coexistence of two modes in posterior judgment among state-of-the-art models: a normative mode, which adheres to Bayes' rule, and a representative-based mode, which relies on similarity -- paralleling human System 1 and System 2 thinking. Additionally, we observed that LLMs struggle to recall base rate information from their memory, and developing prompt engineering strategies to mitigate representative-based judgment may be challenging. We further conjecture that the dual modes of judgment may be a result of the contrastive loss function employed in reinforcement learning from human feedback. Our findings underscore the potential direction for reducing cognitive biases in LLMs and the necessity for cautious deployment of LLMs in critical areas. The remarkable advancements in large language models (LLMs) have ushered in a new era where these models rival human expertise across domains like academia, law, medicine, and finance [4, 12, 13, 22-24]. In this study, we explore how LLMs judge this posterior probability. A higher similarity corresponds to a higher assessed posterior probability. This study comprises three experiments with progressively stricter conditions, reducing the information available for posterior likelihood assessment. The structured test provides all information needed for normative judgment, the semi-structured test omits the diagnosticity of evidence, and the unstructured test requires LLMs to recall all components of Bayes' rule. Results reveal that LLMs' judgments shift from f Representativeness can be constructed through typicality or prototypicality. Typicality describes the common or average case of the class, whereas prototypicality embodies the most idealized and iconic version of the class. For instance, a typical example of a physicist is a smart man who likes math and physics, while a prototypical example of a physicist is Stephen Hawking. This study moves beyond bias detection to investigate the basis upon which LLMs assess probabilities. This has important practical implications for the integration of LLMs into various critical fields.

Time-to-event analysis provides insights into clinical prognosis and treatment recommendations. However, this task is more challenging than standard regression problems due to the presence of censored observations. Additionally, the lack of confidence assessment, model robustness, and prediction calibration raises concerns about the reliability of predictions. To address these challenges, we propose an evidential regression model specifically designed for time-to-event prediction. The proposed model quantifies both epistemic and aleatory uncertainties using Gaussian Random Fuzzy Numbers and belief functions, providing clinicians with uncertainty-aware survival time predictions. The model is trained by minimizing a generalized negative log-likelihood function accounting for data censoring. Experimental evaluations using simulated datasets with different data distributions and censoring conditions, as well as real-world datasets across diverse clinical applications, demonstrate that our model delivers both accurate and reliable performance, outperforming state-of-the-art methods. These results highlight the potential of our approach for enhancing clinical decision-making in survival analysis.

The construction of loss functions presents a major challenge in data-driven modeling involving weak-form operators in PDEs and gradient flows, particularly due to the need to select test functions appropriately. We address this challenge by introducing self-test loss functions, which employ test functions that depend on the unknown parameters, specifically for cases where the operator depends linearly on the unknowns. The proposed self-test loss function conserves energy for gradient flows and coincides with the expected log-likelihood ratio for stochastic differential equations. Importantly, it is quadratic, facilitating theoretical analysis of identifiability and well-posedness of the inverse problem, while also leading to efficient parametric or nonparametric regression algorithms. It is computationally simple, requiring only low-order derivatives or even being entirely derivative-free, and numerical experiments demonstrate its robustness against noisy and discrete data.

This research presents preliminary work to address the challenge of identifying at-risk students using supervised machine learning and three unique data categories: engagement, demographics, and performance data collected from Fall 2023 using Canvas and the California State University, Fullerton dashboard. We aim to tackle the persistent challenges of higher education retention and student dropout rates by screening for at-risk students and building a high-risk identification system. By focusing on previously overlooked behavioral factors alongside traditional metrics, this work aims to address educational gaps, enhance student outcomes, and significantly boost student success across disciplines at the University. Pre-processing steps take place to establish a target variable, anonymize student information, manage missing data, and identify the most significant features. Given the mixed data types in the datasets and the binary classification nature of this study, this work considers several machine learning models, including Support Vector Machines (SVM), Naive Bayes, K-nearest neighbors (KNN), Decision Trees, Logistic Regression, and Random Forest. These models predict at-risk students and identify critical periods of the semester when student performance is most vulnerable. We will use validation techniques such as train test split and k-fold cross-validation to ensure the reliability of the models. Our analysis indicates that all algorithms generate an acceptable outcome for at-risk student predictions, while Naive Bayes performs best overall.

The MAP problem in Bayesian networks is notoriously intractable, even when approximated. In an earlier paper we introduced the Most Frugal Explanation heuristic approach to solving MAP, by partitioning the set of intermediate variables (neither observed nor part of the MAP variables) into a set of relevant variables, which are marginalized out, and irrelevant variables, which will be assigned a sampled value from their domain. In this study we explore whether knowledge about which variables are relevant for a particular query (i.e., domain knowledge) speeds up computation sufficiently to beat both exact MAP as well as approximate MAP while giving reasonably accurate results. Our results are inconclusive, but also show that this probably depends on the specifics of the MAP query, most prominently the number of MAP variables.