The graph coloring problem is an optimization problem involving the assignment of one of q colors to each vertex of a graph such that no two adjacent vertices share the same color. This problem is NP-hard and arises in various practical applications. In this work, we present a novel algorithm that leverages graph neural networks to tackle the problem efficiently, particularly for large graphs. We propose a physics-inspired approach that leverages tools used in statistical mechanics to improve the training and performance of the algorithm. The scaling of our method is evaluated for different connectivities and graph sizes. Finally, we demonstrate the effectiveness of our method on a dataset of Erdos-Renyi graphs, showing its applicability also in hard-to-solve connectivity regions where traditional methods struggle.

This paper presents a novel coordinate descent algorithm leveraging a combination of one-directional line search and gradient information for parameter updates for a squared error loss function. Each parameter undergoes updates determined by either the line search or gradient method, contingent upon whether the modulus of the gradient of the loss with respect to that parameter surpasses a predefined threshold. Notably, a larger threshold value enhances algorithmic efficiency. Despite the potentially slower nature of the line search method relative to gradient descent, its parallelizability facilitates computational time reduction. Experimental validation conducted on a 2-layer Rectified Linear Unit network with synthetic data elucidates the impact of hyperparameters on convergence rates and computational efficiency.

Multivariate decision trees are powerful machine learning tools for classification and regression that attract many researchers and industry professionals. An optimal binary tree has two types of vertices, (i) branching vertices which have exactly two children and where datapoints are assessed on a set of discrete features and (ii) leaf vertices at which datapoints are given a prediction, and can be obtained by solving a biobjective optimization problem that seeks to (i) maximize the number of correctly classified datapoints and (ii) minimize the number of branching vertices. Branching vertices are linear combinations of training features and therefore can be thought of as hyperplanes. In this paper, we propose two cut-based mixed integer linear optimization (MILO) formulations for designing optimal binary classification trees (leaf vertices assign discrete classes). Our models leverage on-the-fly identification of minimal infeasible subsystems (MISs) from which we derive cutting planes that hold the form of packing constraints. We show theoretical improvements on the strongest flow-based MILO formulation currently in the literature and conduct experiments on publicly available datasets to show our models' ability to scale, strength against traditional branch and bound approaches, and robustness in out-of-sample test performance. Our code and data are available on GitHub.

This paper presents a comparative study on the automated classification of seven different varieties of dry beans using machine learning models. Leveraging a dataset of 12,909 dry bean samples, reduced from an initial 13,611 through outlier removal and feature extraction, we applied Principal Component Analysis (PCA) for dimensionality reduction and trained two multiclass classifiers: XGBoost and Support Vector Machine (SVM). The models were evaluated using nested cross-validation to ensure robust performance assessment and hyperparameter tuning. The XGBoost and SVM models achieved overall correct classification rates of 94.00% and 94.39%, respectively. The results underscore the efficacy of these machine learning approaches in agricultural applications, particularly in enhancing the uniformity and efficiency of seed classification. This study contributes to the growing body of work on precision agriculture, demonstrating that automated systems can significantly support seed quality control and crop yield optimization. Future work will explore incorporating more diverse datasets and advanced algorithms to further improve classification accuracy.

Counterfactual explanations (CEs) aim to enhance the interpretability of machine learning models by illustrating how alterations in input features would affect the resulting predictions. Common CE approaches require an additional model and are typically constrained to binary counterfactuals. In contrast, we propose a novel method that operates directly on the latent space of a generative model, specifically a Diffusion Autoencoder (DAE). This approach offers inherent interpretability by enabling the generation of CEs and the continuous visualization of the model's internal representation across decision boundaries. Our method leverages the DAE's ability to encode images into a semantically rich latent space in an unsupervised manner, eliminating the need for labeled data or separate feature extraction models. We show that these latent representations are helpful for medical condition classification and the ordinal regression of severity pathologies, such as vertebral compression fractures (VCF) and diabetic retinopathy (DR). Beyond binary CEs, our method supports the visualization of ordinal CEs using a linear model, providing deeper insights into the model's decision-making process and enhancing interpretability. Experiments across various medical imaging datasets demonstrate the method's advantages in interpretability and versatility. The linear manifold of the DAE's latent space allows for meaningful interpolation and manipulation, making it a powerful tool for exploring medical image properties. Our code is available at https://github.com/matanat/dae_counterfactual.

Coordination is a fundamental aspect of life. The advent of social media has made it integral also to online human interactions, such as those that characterize thriving online communities and social movements. At the same time, coordination is also core to effective disinformation, manipulation, and hate campaigns. This survey collects, categorizes, and critically discusses the body of work produced as a result of the growing interest on coordinated online behavior. We reconcile industry and academic definitions, propose a comprehensive framework to study coordinated online behavior, and review and critically discuss the existing detection and characterization methods. Our analysis identifies open challenges and promising directions of research, serving as a guide for scholars, practitioners, and policymakers in understanding and addressing the complexities inherent to online coordination.

Background: Sepsis is a severe condition responsible for many deaths worldwide. Accurate prediction of sepsis outcomes is crucial for timely and effective treatment. Although previous studies have used ML to forecast outcomes, they faced limitations in feature selection and model comprehensibility, resulting in less effective predictions. Thus, this research aims to develop an interpretable and accurate ML model to help clinical professionals predict in-hospital mortality. Methods: We analyzed ICU patient records from the MIMIC-III database based on specific criteria and extracted relevant data. Our feature selection process included a literature review, clinical input refinement, and using Random Forest to select the top 35 features. We performed data preprocessing, including cleaning, imputation, standardization, and applied SMOTE for oversampling to address imbalance, resulting in 4,683 patients, with admission counts of 17,429. We compared the performance of Random Forest, Gradient Boosting, Logistic Regression, SVM, and KNN models. Results: The Random Forest model was the most effective in predicting sepsis-related in-hospital mortality. It outperformed other models, achieving an accuracy of 0.90 and an AUROC of 0.97, significantly better than the existing literature. Our meticulous feature selection contributed to the model's precision and identified critical determinants of sepsis mortality. These results underscore the pivotal role of data-driven ML in healthcare, especially for predicting in-hospital mortality due to sepsis. Conclusion: This study represents a significant advancement in predicting in-hospital sepsis mortality, highlighting the potential of ML in healthcare. The implications are profound, offering a data-driven approach that enhances decision-making in patient care and reduces in-hospital mortality.

Positive and negative dependence are fundamental concepts that characterize the attractive and repulsive behavior of random subsets. Although some probabilistic models are known to exhibit positive or negative dependence, it is challenging to seamlessly bridge them with a practicable probabilistic model. In this study, we introduce a new family of distributions, named the discrete kernel point process (DKPP), which includes determinantal point processes and parts of Boltzmann machines. We also develop some computational methods for probabilistic operations and inference with DKPPs, such as calculating marginal and conditional probabilities and learning the parameters. Our numerical experiments demonstrate the controllability of positive and negative dependence and the effectiveness of the computational methods for DKPPs.

Providing an arbitrage-free valuation formula and specifying risk-neutral dynamics are essentially two sides of the same coin in option pricing. Yet, the modeling methodology has been leaning towards the latter for decades. That is, the invention of an option pricing model typically starts with proposing a stochastic process that is a martingale for the underlying asset, so that the corresponding risk-neural measure is constructed, and henceforth the arbitrage-free option valuation can be determined either analytically or numerically. Such a methodology was established through the pioneering work of Bachelier [4] and Black and Scholes [9], and since then, almost all of the prevailing models have been invented along this paradigm. The list includes but is not limited to local volatility models by Dupire [17], Cox [14], stochastic volatility models by Heston [20], Hagan et al. [18], Bates [8], jump-diffusion models by Merton [28], Kou [24], and other models built upon Lévy processes by Madan et al. [26], Barndorff-Nielsen [7]. Nonetheless, the reverse approach, which first provides an arbitrage-free valuation formula as in Carr and Madan [11], Davis and Hobson [15] and then finds the underlying martingale supporting the formula, is still possible, as noted in [21, 27]. In recent work, Carr and Torricelli [12] starts with one particular pricing formula that yields logistically distributed marginals. Although there is no underlying Lévy process that produces such marginals, by allowing the increment to be nonstationary, an additive logistic process can be constructed to support that pricing formula.

We introduce algorithms for robustly computing intrinsic coordinates on point clouds. Our approach relies on generating many candidate coordinates by subsampling the data and varying hyperparameters of the embedding algorithm (e.g., manifold learning). We then identify a subset of representative embeddings by clustering the collection of candidate coordinates and using shape descriptors from topological data analysis. The final output is the embedding obtained as an average of the representative embeddings using generalized Procrustes analysis.