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Matrix decompositions are ubiquitous in machine learning, including applications in dimensionality reduction, data compression and deep learning algorithms. Typical solutions for matrix decompositions have polynomial complexity which significantly increases their computational cost and time. In this work, we leverage efficient processing operations that can be run in parallel on modern Graphical Processing Units (GPUs), predominant computing architecture used e.g. in deep learning, to reduce the computational burden of computing matrix decompositions. More specifically, we reformulate the randomized decomposition problem to incorporate fast matrix multiplication operations (BLAS-3) as building blocks. We show that this formulation, combined with fast random number generators, allows to fully exploit the potential of parallel processing implemented in GPUs. Our extensive evaluation confirms the superiority of this approach over the competing methods and we release the results of this research as a part of the official CUDA implementation (//docs.nvidia.com/cuda/cusolver/index.html).

We propose an alternative approach to neural network training using the monotone vector field, an idea inspired by the seminal work of Juditsky and Nemirovski [Juditsky & Nemirovsky, 2019] developed originally to solve parameter estimation problems for generalized linear models (GLM) by reducing the original non-convex problem to a convex problem of solving a monotone variational inequality (VI). Our approach leads to computationally efficient procedures that converge fast and offer guarantee in some special cases, such as training a single-layer neural network or fine-tuning the last layer of the pre-trained model. Our approach can be used for more efficient fine-tuning of a pre-trained model while freezing the bottom layers, an essential step for deploying many machine learning models such as large language models (LLM). We demonstrate its applicability in training fully-connected (FC) neural networks, graph neural networks (GNN), and convolutional neural networks (CNN) and show the competitive or better performance of our approach compared to stochastic gradient descent methods on both synthetic and real network data prediction tasks regarding various performance metrics.

Partial Label Learning (PLL) grapples with learning from ambiguously labelled data, and it has been successfully applied in fields such as image recognition. Nevertheless, traditional PLL methods rely on the closed-world assumption, which can be limiting in open-world scenarios and negatively impact model performance and generalization. To tackle these challenges, our study introduces a novel method called PLL-OOD, which is the first to incorporate Out-of-Distribution (OOD) detection into the PLL framework. PLL-OOD significantly enhances model adaptability and accuracy by merging self-supervised learning with partial label loss and pioneering the Partial-Energy (PE) score for OOD detection. This approach improves data feature representation and effectively disambiguates candidate labels, using a dynamic label confidence matrix to refine predictions. The PE score, adjusted by label confidence, precisely identifies OOD instances, optimizing model training towards in-distribution data. This innovative method markedly boosts PLL model robustness and performance in open-world settings. To validate our approach, we conducted a comprehensive comparative experiment combining the existing state-of-the-art PLL model with multiple OOD scores on the CIFAR-10 and CIFAR-100 datasets with various OOD datasets. The results demonstrate that the proposed PLL-OOD framework is highly effective and effectiveness outperforms existing models, showcasing its superiority and effectiveness.

Active learning can improve the efficiency of training prediction models by identifying the most informative new labels to acquire. However, non-response to label requests can impact active learning's effectiveness in real-world contexts. We conceptualise this degradation by considering the type of non-response present in the data, demonstrating that biased non-response is particularly detrimental to model performance. We argue that biased non-response is likely in contexts where the labelling process, by nature, relies on user interactions. To mitigate the impact of biased non-response, we propose a cost-based correction to the sampling strategy--the Upper Confidence Bound of the Expected Utility (UCB-EU)--that can, plausibly, be applied to any active learning algorithm. Through experiments, we demonstrate that our method successfully reduces the harm from labelling non-response in many settings. However, we also characterise settings where the non-response bias in the annotations remains detrimental under UCB-EU for specific sampling methods and data generating processes. Finally, we evaluate our method on a real-world dataset from an e-commerce platform. We show that UCB-EU yields substantial performance improvements to conversion models that are trained on clicked impressions. Most generally, this research serves to both better conceptualise the interplay between types of non-response and model improvements via active learning, and to provide a practical, easy-to-implement correction that mitigates model degradation.

We develop a model the dynamics of human mesenchymal stem cells (hMSCs) and chondrocytes evolving in a nonwoven polyethylene terephtalate (PET) scaffold impregnated with hyaluron and supplied with a differentiation medium. The scaffold and the cells are assumed to be contained in a bioreactor with fluid perfusion. The differentiation of hMSCs into chondrocytes favors the production of extracellular matrix (ECM) and is influenced by fluid stress. The model takes deformations of ECM and PET scaffold into account. The scaffold structure is explicitly included by statistical assessment of the fibre distribution from CT images. The effective macroscopic equations are obtained by appropriate upscaling from dynamics on lower (microscopic and mesoscopic) scales and feature in the motility terms an explicit cell diffusion tensor encoding the assessed anisotropic scaffold structure. Numerical simulations show its influence on the overall cell and tissue dynamics.

This article is concerned with the multilevel Monte Carlo (MLMC) methods for approximating expectations of some functions of the solution to the Heston 3/2-model from mathematical finance, which takes values in $(0, \infty)$ and possesses superlinearly growing drift and diffusion coefficients. To discretize the SDE model, a new Milstein-type scheme is proposed to produce independent sample paths. The proposed scheme can be explicitly solved and is positivity-preserving unconditionally, i.e., for any time step-size $h>0$. This positivity-preserving property for large discretization time steps is particularly desirable in the MLMC setting. Furthermore, a mean-square convergence rate of order one is proved in the non-globally Lipschitz regime, which is not trivial, as the diffusion coefficient grows super-linearly. The obtained order-one convergence in turn promises the desired relevant variance of the multilevel estimator and justifies the optimal complexity $\mathcal{O}(\epsilon^{-2})$ for the MLMC approach, where $\epsilon > 0$ is the required target accuracy. Numerical experiments are finally reported to confirm the theoretical findings.

Trustworthy AI is crucial to the widespread adoption of AI in high-stakes applications with fairness, robustness, and accuracy being some of the key trustworthiness metrics. In this work, we propose a controllable framework for data-centric trustworthy AI (DCTAI)- VTruST, that allows users to control the trade-offs between the different trustworthiness metrics of the constructed training datasets. A key challenge in implementing an efficient DCTAI framework is to design an online value-function-based training data subset selection algorithm. We pose the training data valuation and subset selection problem as an online sparse approximation formulation. We propose a novel online version of the Orthogonal Matching Pursuit (OMP) algorithm for solving this problem. Experimental results show that VTruST outperforms the state-of-the-art baselines on social, image, and scientific datasets. We also show that the data values generated by VTruST can provide effective data-centric explanations for different trustworthiness metrics.

Objective: To analyze the current scientific knowledge and research lines focused on environmentally sustainable health systems, including the role of nurses. Background: There seem to be differences between creating interventions focused on environmentally sustainable health systems, including nurses, and the scarcity of research on this topic, framed on the Sustainable Development Goals. Methods: A bibliometric analysis was carried out, via three databases (Web of Science, Scopus, and Pubmed), and the guideline recommendations were followed to select bibliometric data. Results: The search resulted in 159 publications, significantly increasing the trends from 2017 to 2021 (p=0.028). The most relevant countries in this area were the United States of America, the United Kingdom, and Sweden. Also, the top articles were from relevant journals, indexed in Journal Citation Report, and the first and the second quartile linked to the nursing field and citations (p<0.001). Conclusion: Education is key to achieving environmentally sustainable health systems via institutions and policies. Implications for nursing management: There is a lack of experimental data and policies on achieving or maintaining environmentally sustainable health care systems, indicating that nurses have an important role and should be consulted and included in decision-making policies regarding sustainability in the healthcare systems.

The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite giving a near-perfect fit to training data without any explicit effort to control model complexity, these methods exhibit excellent predictive accuracy. We conjecture that specific principles underlie these phenomena: that overparametrization allows gradient methods to find interpolating solutions, that these methods implicitly impose regularization, and that overparametrization leads to benign overfitting. We survey recent theoretical progress that provides examples illustrating these principles in simpler settings. We first review classical uniform convergence results and why they fall short of explaining aspects of the behavior of deep learning methods. We give examples of implicit regularization in simple settings, where gradient methods lead to minimal norm functions that perfectly fit the training data. Then we review prediction methods that exhibit benign overfitting, focusing on regression problems with quadratic loss. For these methods, we can decompose the prediction rule into a simple component that is useful for prediction and a spiky component that is useful for overfitting but, in a favorable setting, does not harm prediction accuracy. We focus specifically on the linear regime for neural networks, where the network can be approximated by a linear model. In this regime, we demonstrate the success of gradient flow, and we consider benign overfitting with two-layer networks, giving an exact asymptotic analysis that precisely demonstrates the impact of overparametrization. We conclude by highlighting the key challenges that arise in extending these insights to realistic deep learning settings.

Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.