Linear Predictive Clustering (LPC) partitions samples based on shared linear relationships between feature and target variables, with numerous applications including marketing, medicine, and education. Greedy optimization methods, commonly used for LPC, alternate between clustering and linear regression but lack global optimality. While effective for separable clusters, they struggle in non-separable settings where clusters overlap in feature space. In an alternative constrained optimization paradigm, Bertsimas and Shioda (2007) formulated LPC as a Mixed-Integer Program (MIP), ensuring global optimality regardless of separability but suffering from poor scalability. This work builds on the constrained optimization paradigm to introduce two novel approaches that improve the efficiency of global optimization for LPC. By leveraging key theoretical properties of separability, we derive near-optimal approximations with provable error bounds, significantly reducing the MIP formulation's complexity and improving scalability. Additionally, we can further approximate LPC as a Quadratic Pseudo-Boolean Optimization (QPBO) problem, achieving substantial computational improvements in some settings. Comparative analyses on synthetic and real-world datasets demonstrate that our methods consistently achieve near-optimal solutions with substantially lower regression errors than greedy optimization while exhibiting superior scalability over existing MIP formulations.

One of the central aspects of model explainability in machine learning is the identification and interpretation of feature importance [1]. Understanding which features drive the predictions, on both local and global levels, not only enhances the user's trust in the automated decision process but also provides valuable insights into the underlying data structure and feature interactions within the prediction process. As a consequence, numerous methods have been proposed for assessing feature contributions in a model-agnostic setting, ranging from simple error-based permutation importance tests [2] and basic information-theoretic approaches [3], to more sophisticated techniques such as SHAP, which relies on the weighted average contribution of features across possible subsets [4]. Despite their success, these methods often fail to isolate true marginal contributions of individual features, particularly in the presence of high-order interactions, cases where the importance of a feature depends not only on its contribution but also on its combined influence with other features. Such interactions can make it difficult to determine whether a feature provides unique information alone or in conjunction with specific feature subsets, leading to synergistic or redundant effects. To address this, König et al. [5] propose a model-agnostic approach to disentangle standalone, interaction, and dependency effects by decomposing the explained variance of a pretrained model's prediction.

Generation planning approaches face challenges in managing the incompatible mathematical structures between stochastic production simulations for reliability assessment and optimization models for generation planning, which hinders the integration of reliability constraints. This study proposes an approach to embedding reliability verification constraints into generation expansion planning by leveraging a weighted oblique decision tree (WODT) technique. For each planning year, a generation mix dataset, labeled with reliability assessment simulations, is generated. An WODT model is trained using this dataset. Reliability-feasible regions are extracted via depth-first search technique and formulated as disjunctive constraints. These constraints are then transformed into mixed-integer linear form using a convex hull modeling technique and embedded into a unit commitment-integrated generation expansion planning model. The proposed approach is validated through a long-term generation planning case study for the Electric Reliability Council of Texas (ERCOT) region, demonstrating its effectiveness in achieving reliable and optimal planning solutions.

We review the recent development of machine-learning (ML) force-field frameworks for Landau-Lifshitz-Gilbert (LLG) dynamics simulations of itinerant electron magnets, focusing on the general theory and implementations of symmetry-invariant representations of spin configurations. The crucial properties that such magnetic descriptors must satisfy are differentiability with respect to spin rotations and invariance to both lattice point-group symmetry and internal spin rotation symmetry. We propose an efficient implementation based on the concept of reference irreducible representations, modified from the group-theoretical power-spectrum and bispectrum methods. The ML framework is demonstrated using the s-d models, which are widely applied in spintronics research. We show that LLG simulations based on local fields predicted by the trained ML models successfully reproduce representative non-collinear spin structures, including 120$^\circ$, tetrahedral, and skyrmion crystal orders of the triangular-lattice s-d models. Large-scale thermal quench simulations enabled by ML models further reveal intriguing freezing dynamics and glassy stripe states consisting of skyrmions and bi-merons. Our work highlights the utility of ML force-field approach to dynamical modeling of complex spin orders in itinerant electron magnets.

This study investigates crash severity risk modeling strategies for work zones involving large vehicles (i.e., trucks, buses, and vans) when there are crash data imbalance between low-severity (LS) and high-severity (HS) crashes. We utilized crash data, involving large vehicles in South Carolina work zones for the period between 2014 and 2018, which included 4 times more LS crashes compared to HS crashes. The objective of this study is to explore crash severity prediction performance of various models under different feature selection and data balancing techniques. The findings of this study highlight a disparity between LS and HS predictions, with less-accurate prediction of HS crashes compared to LS crashes due to class imbalance and feature overlaps between LS and HS crashes. Combining features from multiple feature selection techniques: statistical correlation, feature importance, recursive elimination, statistical tests, and mutual information, slightly improves HS crash prediction performance. Data balancing techniques such as NearMiss-1 and RandomUnderSampler, maximize HS recall when paired with certain prediction models, such as Bayesian Mixed Logit (BML), NeuralNet, and RandomForest, making them suitable for HS crash prediction. Conversely, RandomOverSampler, HS Class Weighting, and Kernel-based Synthetic Minority Oversampling (K-SMOTE), used with certain prediction models such as BML, CatBoost, and LightGBM, achieve a balanced performance, defined as achieving an equitable trade-off between LS and HS prediction performance metrics. These insights provide safety analysts with guidance to select models, feature selection techniques, and data balancing techniques that align with their specific safety objectives, offering a robust foundation for enhancing work-zone crash severity prediction.

Multi-modal entity alignment (MMEA) aims to identify equivalent entities between multi-modal knowledge graphs (MMKGs), where the entities can be associated with related images. Most existing studies integrate multi-modal information heavily relying on the automatically-learned fusion module, rarely suppressing the redundant information for MMEA explicitly. To this end, we explore variational information bottleneck for multi-modal entity alignment (IBMEA), which emphasizes the alignment-relevant information and suppresses the alignment-irrelevant information in generating entity representations. Specifically, we devise multi-modal variational encoders to generate modal-specific entity representations as probability distributions. Then, we propose four modal-specific information bottleneck regularizers, limiting the misleading clues in refining modal-specific entity representations. Finally, we propose a modal-hybrid information contrastive regularizer to integrate all the refined modal-specific representations, enhancing the entity similarity between MMKGs to achieve MMEA. We conduct extensive experiments on two cross-KG and three bilingual MMEA datasets. Experimental results demonstrate that our model consistently outperforms previous state-of-the-art methods, and also shows promising and robust performance in low-resource and high-noise data scenarios.

Metallic spin glass systems, such as dilute magnetic alloys, are characterized by randomly distributed local moments coupled to each other through a long-range electron-mediated effective interaction. We present a scalable machine learning (ML) framework for dynamical simulations of metallic spin glasses. A Behler-Parrinello type neural-network model, based on the principle of locality, is developed to accurately and efficiently predict electron-induced local magnetic fields that drive the spin dynamics. A crucial component of the ML model is a proper symmetry-invariant representation of local magnetic environment which is direct input to the neural net. We develop such a magnetic descriptor by incorporating the spin degrees of freedom into the atom-centered symmetry function methods which are widely used in ML force-field models for quantum molecular dynamics. We apply our approach to study the relaxation dynamics of an amorphous generalization of the s-d model. Our work highlights the promising potential of ML models for large-scale dynamical modeling of itinerant magnets with quenched disorder.

In this blog, you will discover why machine learning practitioners should study linear algebra to improve their skills and capabilities as practitioners. After reading this blog, you will understand how can linear algebra be applied in machine learning. Linear algebra is the study of vector spaces, lines and planes, and mappings that are used for linear transforms. It was initially formalized in the 1800s to find the unknowns in linear equations systems, and hence it is relatively a young field of study. Linear Algebra is an essential field of mathematics that can also be called the mathematics of data.

Machine learning systems have been extensively used as auxiliary tools in domains that require critical decision-making, such as healthcare and criminal justice. The explainability of decisions is crucial for users to develop trust on these systems. In recent years, the globally-consistent rule-based summary-explanation and its max-support (MS) problem have been proposed, which can provide explanations for particular decisions along with useful statistics of the dataset. However, globally-consistent summary-explanations with limited complexity typically have small supports, if there are any. In this paper, we propose a relaxed version of summary-explanation, i.e., the $q$-consistent summary-explanation, which aims to achieve greater support at the cost of slightly lower consistency. The challenge is that the max-support problem of $q$-consistent summary-explanation (MSqC) is much more complex than the original MS problem, resulting in over-extended solution time using standard branch-and-bound solvers. To improve the solution time efficiency, this paper proposes the weighted column sampling~(WCS) method based on solving smaller problems by sampling variables according to their simplified increase support (SIS) values. Experiments verify that solving MSqC with the proposed SIS-based WCS method is not only more scalable in efficiency, but also yields solutions with greater support and better global extrapolation effectiveness.

Ship roll motion in high sea states has large amplitudes and nonlinear dynamics, and its prediction is significant for operability, safety, and survivability. This paper presents a novel data-driven methodology to provide a multi-step prediction of ship roll motions in high sea states. A hybrid neural network is proposed that combines long short-term memory (LSTM) and convolutional neural network (CNN) in parallel. The motivation is to extract the nonlinear dynamic characteristics and the hydrodynamic memory information through the advantage of CNN and LSTM, respectively. For the feature selection, the time histories of motion states and wave heights are selected to involve sufficient information. Taken a scaled KCS as the study object, the ship motions in sea state 7 irregular long-crested waves are simulated and used for the validation. The results show that at least one period of roll motion can be accurately predicted. Compared with the single LSTM and CNN methods, the proposed method has better performance in predicting the amplitude of roll angles. Besides, the comparison results also demonstrate that selecting motion states and wave heights as feature space improves the prediction accuracy, verifying the effectiveness of the proposed method.