This work investigates the structural properties, cycloid trajectories, and non-asymptotic convergence guarantees of the Expectation-Maximization (EM) algorithm for two-component Mixed Linear Regression (2MLR) with unknown mixing weights and regression parameters. Recent studies have established global convergence for 2MLR with known balanced weights and super-linear convergence in noiseless and high signal-to-noise ratio (SNR) regimes. However, the theoretical behavior of EM in the fully unknown setting remains unclear, with its trajectory and convergence order not yet fully characterized. We derive explicit EM update expressions for 2MLR with unknown mixing weights and regression parameters across all SNR regimes and analyze their structural properties and cycloid trajectories. In the noiseless case, we prove that the trajectory of the regression parameters in EM iterations traces a cycloid by establishing a recurrence relation for the sub-optimality angle, while in high SNR regimes we quantify its discrepancy from the cycloid trajectory. The trajectory-based analysis reveals the order of convergence: linear when the EM estimate is nearly orthogonal to the ground truth, and quadratic when the angle between the estimate and ground truth is small at the population level. Our analysis establishes non-asymptotic guarantees by sharpening bounds on statistical errors between finite-sample and population EM updates, relating EM's statistical accuracy to the sub-optimality angle, and proving convergence with arbitrary initialization at the finite-sample level. This work provides a novel trajectory-based framework for analyzing EM in Mixed Linear Regression.

ABSTRACT It involves the completely novel ways of integrating ML algorithms with traditional statistical modelling that has changed the way we analyze data, do predictive analytics or make decisions in the fields of the data. In this paper, we study some ML and statistical model connections to understand ways in which some modern ML algorithms help'enrich' conventional models; we demonstrate how new algorithms improve performance, scale, flexibility and robustness of the tradi tional models. It shows that the hybrid models are of great improvement in predictive accuracy, robustness, and interpretability. Keyword: Machine Learning, Statistical Modelling, Regression, Classification, Predictive Analytics, Hybrid Models, Dimensiona lity Reduction, Algorithmic Bias, Interpretability, Cross - Disciplinary Applications 1. INTRODUCTION Statistical modelling has very historically been the theoretical framework to understand relationships between variables and make inferences and test hypothes es. Its strength is that it is able to offer interpretations in terms of interpretable parameters and probabilistic assumptions [15].

Many real-world decisions are made under uncertainty by solving optimization problems using predicted quantities. This predict-then-optimize paradigm has motivated decision-focused learning, which trains models with awareness of how the optimizer uses predictions, improving the performance of downstream decisions. Despite its promise, scaling is challenging: state-of-the-art methods either differentiate through a solver or rely on task-specific surrogates, both of which require frequent and expensive calls to an optimizer, often a combinatorial one. In this paper, we leverage dual variables from the downstream problem to shape learning and introduce Dual-Guided Loss (DGL), a simple, scalable objective that preserves decision alignment while reducing solver dependence. We construct DGL specifically for combinatorial selection problems with natural one-of-many constraints, such as matching, knapsack, and shortest path. Our approach (a) decouples optimization from gradient updates by solving the downstream problem only periodically; (b) between refreshes, trains on dual-adjusted targets using simple differentiable surrogate losses; and (c) as refreshes become less frequent, drives training cost toward standard supervised learning while retaining strong decision alignment. We prove that DGL has asymptotically diminishing decision regret, analyze runtime complexity, and show on two problem classes that DGL matches or exceeds state-of-the-art DFL methods while using far fewer solver calls and substantially less training time. Code is available at https://github.com/

Food banks are crucial for alleviating food insecurity, but their effectiveness hinges on accurately forecasting highly volatile in-kind donations to ensure equitable and efficient resource distribution. Traditional forecasting models often fail to maintain consistent accuracy due to unpredictable fluctuations and concept drift driven by seasonal variations and natural disasters such as hurricanes in the Southeastern U.S. and wildfires in the West Coast. To address these challenges, we propose FoodRL, a novel reinforcement learning (RL) based metalearning framework that clusters and dynamically weights diverse forecasting models based on recent performance and contextual information. Evaluated on multi-year data from two structurally distinct U.S. food banks-one large regional West Coast food bank affected by wildfires and another state-level East Coast food bank consistently impacted by hurricanes, FoodRL consistently outperforms baseline methods, particularly during periods of disruption or decline. By delivering more reliable and adaptive forecasts, FoodRL can facilitate the redistribution of food equivalent to 1.7 million additional meals annually, demonstrating its significant potential for social impact as well as adaptive ensemble learning for humanitarian supply chains.

We explore the recently introduced persistent reachability homology (PRH) of digraph data, i.e. data in the form of directed graphs. In particular, we study the effectiveness of PRH in network classification task in a key neuroscience problem: epilepsy detection. PRH is a variation of the persistent homology of digraphs, more traditionally based on the directed flag complex (DPH). A main advantage of PRH is that it considers the condensations of the digraphs appearing in the persistent filtration and thus is computed from smaller digraphs. We compare the effectiveness of PRH to that of DPH and we show that PRH outperforms DPH in the classification task. We use the Betti curves and their integrals as topological features and implement our pipeline on support vector machine.

Upcoming measurements of the kinetic Sunyaev-Zel'dovich (kSZ) effect, which results from Cosmic Microwave Background (CMB) photons scattering off moving electrons, offer a powerful probe of the Epoch of Reionization (EoR). The kSZ signal contains key information about the timing, duration, and spatial structure of the EoR. A precise measurement of the CMB optical depth $τ$, a key parameter that characterizes the universe's integrated electron density, would significantly constrain models of early structure formation. However, the weak kSZ signal is difficult to extract from CMB observations due to significant contamination from astrophysical foregrounds. We present a machine learning approach to extract $τ$ from simulated kSZ maps. We train advanced machine learning models, including swin transformers, on high-resolution seminumeric simulations of the kSZ signal. To robustly quantify prediction uncertainties of $τ$, we employ the Laplace Approximation (LA). This approach provides an efficient and principled Gaussian approximation to the posterior distribution over the model's weights, allowing for reliable error estimation. We investigate and compare two distinct application modes: a post-hoc LA applied to a pre-trained model, and an online LA where model weights and hyperparameters are optimized jointly by maximizing the marginal likelihood. This approach provides a framework for robustly constraining $τ$ and its associated uncertainty, which can enhance the analysis of upcoming CMB surveys like the Simons Observatory and CMB-S4.

Cognitive diagnosis models (CDMs) are pivotal for creating fine-grained learner profiles in modern intelligent education platforms. However, these models are trained on sensitive student data, raising significant privacy concerns. While membership inference attacks (MIA) have been studied in various domains, their application to CDMs remains a critical research gap, leaving their privacy risks unquantified. This paper is the first to systematically investigate MIA against CDMs. We introduce a novel and realistic grey-box threat model that exploits the explainability features of these platforms, where a model's internal knowledge state vectors are exposed to users through visualizations such as radar charts. We demonstrate that these vectors can be accurately reverse-engineered from such visualizations, creating a potent attack surface. Based on this threat model, we propose a profile-based MIA (P-MIA) framework that leverages both the model's final prediction probabilities and the exposed internal knowledge state vectors as features. Extensive experiments on three real-world datasets against mainstream CDMs show that our grey-box attack significantly outperforms standard black-box baselines.

Fake news detection has been a long-standing research focus in social networks. Recent studies suggest that incorporating sentiment information from both news content and user comments can enhance detection performance. However, existing approaches typically treat sentiment features as auxiliary signals, overlooking role differentiation, that is, the same sentiment polarity may originate from users with distinct roles, thereby limiting their ability to capture nuanced patterns for effective detection. To address this issue, we propose SARC, a Sentiment-Augmented Role Clustering framework which utilizes sentiment-enhanced deep clustering to identify user roles for improved fake news detection. The framework first generates user features through joint comment text representation (with BiGRU and Attention mechanism) and sentiment encoding. It then constructs a differentiable deep clustering module to automatically categorize user roles. Finally, unlike existing approaches which take fake news label as the unique supervision signal, we propose a joint optimization objective integrating role clustering and fake news detection to further improve the model performance. Experimental results on two benchmark datasets, RumourEval-19 and Weibo-comp, demonstrate that SARC achieves superior performance across all metrics compared to baseline models. The code is available at: https://github.com/jxshang/SARC.

Transportation remains a major contributor to greenhouse gas emissions, highlighting the urgency of transitioning toward sustainable alternatives such as Electric Vehicles (EVs). Yet, uneven spatial distribution and irregular utilization of charging infrastructure create challenges for both power grid stability and investment planning. This study introduces Traffic-Weather Graph Convolutional Network (TW-GCN), a spatio-temporal forecasting framework that combines Graph Convolutional Networks with temporal architectures to predict EV charging demand in Tennessee, United States. We utilize real-world traffic flows, weather conditions, and proprietary data provided by one of the largest U.S.-based EV infrastructure companies to capture both spatial dependencies and temporal dynamics. Extensive experiments across varying forecasting horizons, clustering strategies, and sequence lengths reveal that mid-horizon (3-hour) forecasts achieve the best balance between responsiveness and stability, with One-dimensional convo-lutional neural networks consistently outperforming other temporal models. Regional analysis shows disparities in predictive accuracy across East, Middle, and West Tennessee, reflecting how station density, Points of Interest and local demand variability shape model capabilities. The proposed TW-GCN framework advances the integration of data-driven intelligence into EV infrastructure planning while supporting sustainable mobility transitions.

Machine learning (ML) models are susceptible to various risks to security, privacy, and fairness. Most defenses are designed to protect against each risk individually (intended interactions) but can inadvertently affect susceptibility to other unrelated risks (unintended interactions). We introduce Amulet, the first Python library for evaluating both intended and unintended interactions among ML defenses and risks. Amulet is comprehensive by including representative attacks, defenses, and metrics; extensible to new modules due to its modular design; consistent with a user-friendly API template for inputs and outputs; and applicable for evaluating novel interactions. By satisfying all four properties, Amulet offers a unified foundation for studying how defenses interact, enabling the first systematic evaluation of unintended interactions across multiple risks.