The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data that is inherently nonEuclidean. This data can exhibit intricate geometric, topological and algebraic structure: from the geometry of the curvature of space-time, to topologically complex interactions between neurons in the brain, to the algebraic transformations describing symmetries of physical systems. Extracting knowledge from such non-Euclidean data necessitates a broader mathematical perspective. Echoing the 19th-century revolutions that gave rise to non-Euclidean geometry, an emerging line of research is redefining modern machine learning with non-Euclidean structures. Its goal: generalizing classical methods to unconventional data types with geometry, topology, and algebra. In this review, we provide an accessible gateway to this fast-growing field and propose a graphical taxonomy that integrates recent advances into an intuitive unified framework. We subsequently extract insights into current challenges and highlight exciting opportunities for future development in this field.

The objective of change point detection is to identify abrupt changes at potentially multiple points within a data sequence. This task is particularly challenging in the online setting where various types of changes can occur, including shifts in both the marginal and joint distributions of the data. This paper tackles these challenges by sequentially tracking correlation matrices on the Riemannian geometry, where the geodesic distances accurately capture the development of correlations. We propose Rio-CPD, a non-parametric correlation-aware online change point detection framework that combines the Riemannian geometry of the manifold of symmetric positive definite matrices and the cumulative sum statistic (CUSUM) for detecting change points. Rio-CPD enhances CUSUM by computing the geodesic distance from present observations to the Fr\'echet mean of previous observations. With careful choice of metrics equipped to the Riemannian geometry, Rio-CPD is simple and computationally efficient. Experimental results on both synthetic and real-world datasets demonstrate that Rio-CPD outperforms existing methods in detection accuracy and efficiency.

Massive social media data can reflect people's authentic thoughts, emotions, communication, etc., and therefore can be analyzed for early detection of mental health problems such as depression. Existing works about early depression detection on social media lacked interpretability and neglected the heterogeneity of social media data. Furthermore, they overlooked the global interaction among users. To address these issues, we develop a novel method that leverages a Heterogeneous Subgraph Network with Prompt Learning(HSNPL) and contrastive learning mechanisms. Specifically, prompt learning is employed to map users' implicit psychological symbols with excellent interpretability while deep semantic and diverse behavioral features are incorporated by a heterogeneous information network. Then, the heterogeneous graph network with a dual attention mechanism is constructed to model the relationships among heterogeneous social information at the feature level. Furthermore, the heterogeneous subgraph network integrating subgraph attention and self-supervised contrastive learning is developed to explore complicated interactions among users and groups at the user level. Extensive experimental results demonstrate that our proposed method significantly outperforms state-of-the-art methods for depression detection on social media.

This paper investigates neuron dropout as a post-processing bias mitigation for deep neural networks (DNNs). Neural-driven software solutions are increasingly applied in socially critical domains with significant fairness implications. While neural networks are exceptionally good at finding statistical patterns from data, they may encode and amplify existing biases from the historical data. Existing bias mitigation algorithms often require modifying the input dataset or the learning algorithms. We posit that the prevalent dropout methods that prevent over-fitting during training by randomly dropping neurons may be an effective and less intrusive approach to improve the fairness of pre-trained DNNs. However, finding the ideal set of neurons to drop is a combinatorial problem. We propose NeuFair, a family of post-processing randomized algorithms that mitigate unfairness in pre-trained DNNs via dropouts during inference after training. Our randomized search is guided by an objective to minimize discrimination while maintaining the model's utility. We show that our design of randomized algorithms is effective and efficient in improving fairness (up to 69%) with minimal or no model performance degradation. We provide intuitive explanations of these phenomena and carefully examine the influence of various hyperparameters of search algorithms on the results. Finally, we empirically and conceptually compare NeuFair to different state-of-the-art bias mitigators.

This paper proposes LCFL, a novel clustering metric for evaluating clients' data distributions in federated learning. LCFL aligns with federated learning requirements, accurately assessing client-to-client variations in data distribution. It offers advantages over existing clustered federated learning methods, addressing privacy concerns, improving applicability to non-convex models, and providing more accurate classification results. LCFL does not require prior knowledge of clients' data distributions. We provide a rigorous mathematical analysis, demonstrating the correctness and feasibility of our framework. Numerical experiments with neural network instances highlight the superior performance of LCFL over baselines on several clustered federated learning benchmarks.

Genotype imputation enhances genetic data by predicting missing SNPs using reference haplotype information. Traditional methods leverage linkage disequilibrium (LD) to infer untyped SNP genotypes, relying on the similarity of LD structures between genotyped target sets and fully sequenced reference panels. Recently, reference-free deep learning-based methods have emerged, offering a promising alternative by predicting missing genotypes without external databases, thereby enhancing privacy and accessibility. However, these methods often produce models with tens of millions of parameters, leading to challenges such as the need for substantial computational resources to train and inefficiency for client-sided deployment. Our study addresses these limitations by introducing a baseline for a novel genotype imputation pipeline that supports client-sided imputation models generalizable across any genotyping chip and genomic region. This approach enhances patient privacy by performing imputation directly on edge devices. As a case study, we focus on PRS313, a polygenic risk score comprising 313 SNPs used for breast cancer risk prediction. Utilizing consumer genetic panels such as 23andMe, our model democratizes access to personalized genetic insights by allowing 23andMe users to obtain their PRS313 score. We demonstrate that simple linear regression can significantly improve the accuracy of PRS313 scores when calculated using SNPs imputed from consumer gene panels, such as 23andMe. Our linear regression model achieved an R^2 of 0.86, compared to 0.33 without imputation and 0.28 with simple imputation (substituting missing SNPs with the minor allele frequency). These findings suggest that popular SNP analysis libraries could benefit from integrating linear regression models for genotype imputation, providing a viable and light-weight alternative to reference based imputation.

Quantifying a patient's health status provides clinicians with insight into patient risk, and the ability to better triage and manage resources. Early Warning Scores (EWS) are widely deployed to measure overall health status, and risk of adverse outcomes, in hospital patients. However, current EWS are limited both by their lack of personalisation and use of static observations. We propose a pipeline that groups intensive care unit patients by the trajectories of observations data throughout their stay as a basis for the development of personalised risk predictions. Feature importance is considered to provide model explainability. Using the MIMIC-IV dataset, six clusters were identified, capturing differences in disease codes, observations, lengths of admissions and outcomes. Applying the pipeline to data from just the first four hours of each ICU stay assigns the majority of patients to the same cluster as when the entire stay duration is considered. In-hospital mortality prediction models trained on individual clusters had higher F1 score performance in five of the six clusters when compared against the unclustered patient cohort. The pipeline could form the basis of a clinical decision support tool, working to improve the clinical characterisation of risk groups and the early detection of patient deterioration.

This paper presents a novel and comprehensive solution to enhance both the robustness and efficiency of question answering (QA) systems through supervised contrastive learning (SCL). Training a high-performance QA system has become straightforward with pre-trained language models, requiring only a small amount of data and simple fine-tuning. However, despite recent advances, existing QA systems still exhibit significant deficiencies in functionality and training efficiency. We address the functionality issue by defining four key tasks: user input intent classification, out-of-domain input detection, new intent discovery, and continual learning. We then leverage a unified SCL-based representation learning method to efficiently build an intra-class compact and inter-class scattered feature space, facilitating both known intent classification and unknown intent detection and discovery. Consequently, with minimal additional tuning on downstream tasks, our approach significantly improves model efficiency and achieves new state-of-the-art performance across all tasks.

We investigate the impact of dataset-specific hyperparameter, feature encoding, and architecture tuning on five recent model families for tabular data generation through an extensive benchmark on 16 datasets. This study addresses the practical need for a unified evaluation of models that fully considers hyperparameter optimization. Additionally, we propose a reduced search space for each model that allows for quick optimization, achieving nearly equivalent performance at a significantly lower cost.Our benchmark demonstrates that, for most models, large-scale dataset-specific tuning substantially improves performance compared to the original configurations. Furthermore, we confirm that diffusion-based models generally outperform other models on tabular data. However, this advantage is not significant when the entire tuning and training process is restricted to the same GPU budget for all models.

We consider the problem of active learning for global sensitivity analysis of expensive black-box functions. Our aim is to efficiently learn the importance of different input variables, e.g., in vehicle safety experimentation, we study the impact of the thickness of various components on safety objectives. Since function evaluations are expensive, we use active learning to prioritize experimental resources where they yield the most value. We propose novel active learning acquisition functions that directly target key quantities of derivative-based global sensitivity measures (DGSMs) under Gaussian process surrogate models. We showcase the first application of active learning directly to DGSMs, and develop tractable uncertainty reduction and information gain acquisition functions for these measures. Through comprehensive evaluation on synthetic and real-world problems, our study demonstrates how these active learning acquisition strategies substantially enhance the sample efficiency of DGSM estimation, particularly with limited evaluation budgets. Our work paves the way for more efficient and accurate sensitivity analysis in various scientific and engineering applications.