The paradigm of linear structural equation modeling readily allows one to incorporate causal feedback loops in the model specification. These appear as directed cycles in the common graphical representation of the models. However, the presence of cycles entails difficulties such as the fact that models need no longer be characterized by conditional independence relations. As a result, learning cyclic causal structures remains a challenging problem. In this paper, we offer new insights on this problem in the context of linear non-Gaussian models. First, we precisely characterize when two directed graphs determine the same linear non-Gaussian model. Next, we take up a setting of cycle-disjoint graphs, for which we are able to show that simple quadratic and cubic polynomial relations among low-order moments of a non-Gaussian distribution allow one to locate source cycles. Complementing this with a strategy of decorrelating cycles and multivariate regression allows one to infer a block-topological order among the directed cycles, which leads to a {consistent and computationally efficient algorithm} for learning causal structures with disjoint cycles.

It is important to identify the discriminative features for high dimensional clustering. However, due to the lack of cluster labels, the regularization methods developed for supervised feature selection can not be directly applied. To learn the pseudo labels and select the discriminative features simultaneously, we propose a new unsupervised feature selection method, named GlObal and Local information combined Feature Selection (GOLFS), for high dimensional clustering problems. The GOLFS algorithm combines both local geometric structure via manifold learning and global correlation structure of samples via regularized self-representation to select the discriminative features. The combination improves the accuracy of both feature selection and clustering by exploiting more comprehensive information. In addition, an iterative algorithm is proposed to solve the optimization problem and the convergency is proved. Simulations and two real data applications demonstrate the excellent finite-sample performance of GOLFS on both feature selection and clustering.

Contrastive learning operates on a simple yet effective principle: Embeddings of positive pairs are pulled together, while those of negative pairs are pushed apart. In this paper, we propose a unified framework for understanding contrastive learning through the lens of cosine similarity, and present two key theoretical insights derived from this framework. First, in full-batch settings, we show that perfect alignment of positive pairs is unattainable when negative-pair similarities fall below a threshold, and this misalignment can be mitigated by incorporating within-view negative pairs into the objective. Second, in mini-batch settings, smaller batch sizes induce stronger separation among negative pairs in the embedding space, i.e., higher variance in their similarities, which in turn degrades the quality of learned representations compared to full-batch settings. To address this, we propose an auxiliary loss that reduces the variance of negative-pair similarities in mini-batch settings. Empirical results show that incorporating the proposed loss improves performance in small-batch settings.

We consider the problem of tool-to-tool matching (TTTM), also called, chamber matching in the context of a semiconductor manufacturing equipment. Traditional TTTM approaches utilize static configuration data or depend on a golden reference which are difficult to obtain in a commercial manufacturing line. Further, existing methods do not extend very well to a heterogeneous setting, where equipment are of different make-and-model, sourced from different equipment vendors. We propose novel TTTM analysis pipelines to overcome these issues. We hypothesize that a mismatched equipment would have higher variance and/or higher number of modes in the data. Our best univariate method achieves a correlation coefficient >0.95 and >0.5 with the variance and number of modes, respectively showing that the proposed methods are effective. Also, the best multivariate method achieves a correlation coefficient >0.75 with the top-performing univariate methods, showing its effectiveness. Finally, we analyze the sensitivity of the multivariate algorithms to the algorithm hyper-parameters.

This article introduces a novel, geometric approach for multi-manifold clustering (MMC), i.e. for clustering a collection of potentially intersecting, d-dimensional manifolds into the individual manifold components. We first compute a locality graph on d-simplices, using the dihedral angle in between adjacent simplices as the graph weights, and then compute infinity path distances in this simplex graph. This procedure gives a metric on simplices which we refer to as the largest angle path distance (LAPD). We analyze the properties of LAPD under random sampling, and prove that with an appropriate denoising procedure, this metric separates the manifold components with high probability. We validate the proposed methodology with extensive numerical experiments on both synthetic and real-world data sets. These experiments demonstrate that the method is robust to noise, curvature, and small intersection angle, and generally out-performs other MMC algorithms. In addition, we provide a highly scalable implementation of the proposed algorithm, which leverages approximation schemes for infinity path distance to achieve quasi-linear computational complexity.

The lack of high-quality public cyber incident data limits empirical research and predictive modeling for cyber risk assessment. This challenge persists due to the reluctance of companies to disclose incidents that could damage their reputation or investor confidence. Therefore, from an actuarial perspective, potential resolutions conclude two aspects: the enhancement of existing cyber incident datasets and the implementation of advanced modeling techniques to optimize the use of the available data. A review of existing data-driven methods highlights a significant lack of entity-specific organizational features in publicly available datasets. To address this gap, we propose a novel InsurTech framework that enriches cyber incident data with entity-specific attributes. We develop various machine learning (ML) models: a multilabel classification model to predict the occurrence of cyber incident types (e.g., Privacy Violation, Data Breach, Fraud and Extortion, IT Error, and Others) and a multioutput regression model to estimate their annual frequencies. While classifier and regressor chains are implemented to explore dependencies among cyber incident types as well, no significant correlations are observed in our datasets. Besides, we apply multiple interpretable ML techniques to identify and cross-validate potential risk factors developed by InsurTech across ML models. We find that InsurTech empowered features enhance prediction occurrence and frequency estimation robustness compared to only using conventional risk factors. The framework generates transparent, entity-specific cyber risk profiles, supporting customized underwriting and proactive cyber risk mitigation. It provides insurers and organizations with data-driven insights to support decision-making and compliance planning.

Tensor Network (TN) Kernel Machines speed up model learning by representing parameters as low-rank TNs, reducing computation and memory use. However, most TN-based Kernel methods are deterministic and ignore parameter uncertainty. Further, they require manual tuning of model complexity hyperparameters like tensor rank and feature dimensions, often through trial-and-error or computationally costly methods like cross-validation. We propose Bayesian Tensor Network Kernel Machines, a fully probabilistic framework that uses sparsity-inducing hierarchical priors on TN factors to automatically infer model complexity. This enables automatic inference of tensor rank and feature dimensions, while also identifying the most relevant features for prediction, thereby enhancing model interpretability. All the model parameters and hyperparameters are treated as latent variables with corresponding priors. Given the Bayesian approach and latent variable dependencies, we apply a mean-field variational inference to approximate their posteriors. We show that applying a mean-field approximation to TN factors yields a Bayesian ALS algorithm with the same computational complexity as its deterministic counterpart, enabling uncertainty quantification at no extra computational cost. Experiments on synthetic and real-world datasets demonstrate the superior performance of our model in prediction accuracy, uncertainty quantification, interpretability, and scalability.

Structural assessment of biomolecular complexes is vital for translating molecular models into functional insights, shaping our understanding of biology and aiding drug discovery. However, current structure-based scoring functions often lack generalizability across diverse biomolecular systems. We present BioScore, a foundational scoring function that addresses key challenges -- data sparsity, cross-system representation, and task compatibility -- through a dual-scale geometric graph learning framework with tailored modules for structure assessment and affinity prediction. BioScore supports a wide range of tasks, including affinity prediction, conformation ranking, and structure-based virtual screening. Evaluated on 16 benchmarks spanning proteins, nucleic acids, small molecules, and carbohydrates, BioScore consistently outperforms or matches 70 traditional and deep learning methods. Our newly proposed PPI Benchmark further enables comprehensive evaluation of protein-protein complex scoring. BioScore demonstrates broad applicability: (1) pretraining on mixed-structure data boosts protein-protein affinity prediction by up to 40% and antigen-antibody binding correlation by over 90%; (2) cross-system generalizability enables zero- and few-shot prediction with up to 71% correlation gain; and (3) its unified representation captures chemically challenging systems such as cyclic peptides, improving affinity prediction by over 60%. BioScore establishes a robust and generalizable framework for structural assessment across complex biomolecular landscapes.

--In this paper, we propose RFF-GP-HSMM, a fast unsupervised time-series segmentation method that incorporates random Fourier features (RFF) to address the high computational cost of the Gaussian process hidden semi-Markov model (GP-HSMM). GP-HSMM models time-series data using Gaussian processes, requiring inversion of an N N kernel matrix during training, where N is the number of data points. T o address this, the proposed method approximates the Gaussian process with linear regression using RFF, preserving expressive power while eliminating the need for inversion of the kernel matrix. Experiments on the Carnegie Mellon University (CMU) motion-capture dataset demonstrate that the proposed method achieves segmentation performance comparable to that of conventional methods, with approximately 278 times faster segmentation on time-series data comprising 39,200 frames. Segmentation enables the extraction of frequent events and facilitates analysis of their underlying structure, even in complex time-series data that are difficult to analyze manually.

We propose the Linearly Adaptive Cross Entropy Loss function. This is a novel measure derived from the information theory. In comparison to the standard cross entropy loss function, the proposed one has an additional term that depends on the predicted probability of the true class. This feature serves to enhance the optimization process in classification tasks involving one-hot encoded class labels. The proposed one has been evaluated on a ResNet-based model using the CIFAR-100 dataset. Preliminary results show that the proposed one consistently outperforms the standard cross entropy loss function in terms of classification accuracy. Moreover, the proposed one maintains simplicity, achieving practically the same efficiency to the traditional cross entropy loss. These findings suggest that our approach could broaden the scope for future research into loss function design.