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In this article, we propose two kinds of neural networks inspired by power method and inverse power method to solve linear eigenvalue problems. These neural networks share similar ideas with traditional methods, in which the differential operator is realized by automatic differentiation. The eigenfunction of the eigenvalue problem is learned by the neural network and the iterative algorithms are implemented by optimizing the specially defined loss function. The largest positive eigenvalue, smallest eigenvalue and interior eigenvalues with the given prior knowledge can be solved efficiently. We examine the applicability and accuracy of our methods in the numerical experiments in one dimension, two dimensions and higher dimensions. Numerical results show that accurate eigenvalue and eigenfunction approximations can be obtained by our methods.

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The provision of social care applications is crucial for elderly people to improve their quality of life and enables operators to provide early interventions. Accurate predictions of user dropouts in healthy ageing applications are essential since they are directly related to individual health statuses. Machine Learning (ML) algorithms have enabled highly accurate predictions, outperforming traditional statistical methods that struggle to cope with individual patterns. However, ML requires a substantial amount of data for training, which is challenging due to the presence of personal identifiable information (PII) and the fragmentation posed by regulations. In this paper, we present a federated machine learning (FML) approach that minimizes privacy concerns and enables distributed training, without transferring individual data. We employ collaborative training by considering individuals and organizations under FML, which models both cross-device and cross-silo learning scenarios. Our approach is evaluated on a real-world dataset with non-independent and identically distributed (non-iid) data among clients, class imbalance and label ambiguity. Our results show that data selection and class imbalance handling techniques significantly improve the predictive accuracy of models trained under FML, demonstrating comparable or superior predictive performance than traditional ML models.

In this article, we propose using network-based sampling strategies to estimate the number of unsheltered people experiencing homelessness within a given administrative service unit, known as a Continuum of Care. Further, we specifically advocate for the network sampling method known as Respondent Driven Sampling (RDS), which has been shown to provide unbiased or low-biased estimates of totals and proportions for hard-to-reach populations in contexts where a sampling frame (e.g., housing addresses) not available. To make the RDS estimator work for estimating the total number of unsheltered people, we introduce a new method that leverages administrative data from the HUD-mandated Homeless Management Information System (HMIS). The HMIS provides high-quality counts and demographics for people experiencing homelessness who sleep in emergency shelters. We then demonstrate this method using network data collected in Nashville, TN, combined with simulation methods to illustrate the efficacy of this approach. Finally, we end with discussing how this could be used in practice.

Bayesian inference for neural networks, or Bayesian deep learning, has the potential to provide well-calibrated predictions with quantified uncertainty and robustness. However, the main hurdle for Bayesian deep learning is its computational complexity due to the high dimensionality of the parameter space. In this work, we propose a novel scheme that addresses this limitation by constructing a low-dimensional subspace of the neural network parameters-referred to as an active subspace-by identifying the parameter directions that have the most significant influence on the output of the neural network. We demonstrate that the significantly reduced active subspace enables effective and scalable Bayesian inference via either Monte Carlo (MC) sampling methods, otherwise computationally intractable, or variational inference. Empirically, our approach provides reliable predictions with robust uncertainty estimates for various regression tasks.

In this study, we investigated whether self-supervised pretraining could produce a neural network feature extractor applicable to multiple classification tasks in B-mode lung ultrasound analysis. When fine-tuning on three lung ultrasound tasks, pretrained models resulted in an improvement of the average across-task area under the receiver operating curve (AUC) by 0.032 and 0.061 on local and external test sets respectively. Compact nonlinear classifiers trained on features outputted by a single pretrained model did not improve performance across all tasks; however, they did reduce inference time by 49% compared to serial execution of separate fine-tuned models. When training using 1% of the available labels, pretrained models consistently outperformed fully supervised models, with a maximum observed test AUC increase of 0.396 for the task of view classification. Overall, the results indicate that self-supervised pretraining is useful for producing initial weights for lung ultrasound classifiers.

Graph neural networks (GNNs) have achieved tremendous success in the task of graph classification and its diverse downstream real-world applications. Despite the huge success in learning graph representations, current GNN models have demonstrated their vulnerability to potentially existent adversarial examples on graph-structured data. Existing approaches are either limited to structure attacks or restricted to local information, urging for the design of a more general attack framework on graph classification, which faces significant challenges due to the complexity of generating local-node-level adversarial examples using the global-graph-level information. To address this "global-to-local" attack challenge, we present a novel and general framework to generate adversarial examples via manipulating graph structure and node features. Specifically, we make use of Graph Class Activation Mapping and its variant to produce node-level importance corresponding to the graph classification task. Then through a heuristic design of algorithms, we can perform both feature and structure attacks under unnoticeable perturbation budgets with the help of both node-level and subgraph-level importance. Experiments towards attacking four state-of-the-art graph classification models on six real-world benchmarks verify the flexibility and effectiveness of our framework.

One principal approach for illuminating a black-box neural network is feature attribution, i.e. identifying the importance of input features for the network's prediction. The predictive information of features is recently proposed as a proxy for the measure of their importance. So far, the predictive information is only identified for latent features by placing an information bottleneck within the network. We propose a method to identify features with predictive information in the input domain. The method results in fine-grained identification of input features' information and is agnostic to network architecture. The core idea of our method is leveraging a bottleneck on the input that only lets input features associated with predictive latent features pass through. We compare our method with several feature attribution methods using mainstream feature attribution evaluation experiments. The code is publicly available.

Due to their increasing spread, confidence in neural network predictions became more and more important. However, basic neural networks do not deliver certainty estimates or suffer from over or under confidence. Many researchers have been working on understanding and quantifying uncertainty in a neural network's prediction. As a result, different types and sources of uncertainty have been identified and a variety of approaches to measure and quantify uncertainty in neural networks have been proposed. This work gives a comprehensive overview of uncertainty estimation in neural networks, reviews recent advances in the field, highlights current challenges, and identifies potential research opportunities. It is intended to give anyone interested in uncertainty estimation in neural networks a broad overview and introduction, without presupposing prior knowledge in this field. A comprehensive introduction to the most crucial sources of uncertainty is given and their separation into reducible model uncertainty and not reducible data uncertainty is presented. The modeling of these uncertainties based on deterministic neural networks, Bayesian neural networks, ensemble of neural networks, and test-time data augmentation approaches is introduced and different branches of these fields as well as the latest developments are discussed. For a practical application, we discuss different measures of uncertainty, approaches for the calibration of neural networks and give an overview of existing baselines and implementations. Different examples from the wide spectrum of challenges in different fields give an idea of the needs and challenges regarding uncertainties in practical applications. Additionally, the practical limitations of current methods for mission- and safety-critical real world applications are discussed and an outlook on the next steps towards a broader usage of such methods is given.

Deep neural networks have revolutionized many machine learning tasks in power systems, ranging from pattern recognition to signal processing. The data in these tasks is typically represented in Euclidean domains. Nevertheless, there is an increasing number of applications in power systems, where data are collected from non-Euclidean domains and represented as the graph-structured data with high dimensional features and interdependency among nodes. The complexity of graph-structured data has brought significant challenges to the existing deep neural networks defined in Euclidean domains. Recently, many studies on extending deep neural networks for graph-structured data in power systems have emerged. In this paper, a comprehensive overview of graph neural networks (GNNs) in power systems is proposed. Specifically, several classical paradigms of GNNs structures (e.g., graph convolutional networks, graph recurrent neural networks, graph attention networks, graph generative networks, spatial-temporal graph convolutional networks, and hybrid forms of GNNs) are summarized, and key applications in power systems such as fault diagnosis, power prediction, power flow calculation, and data generation are reviewed in detail. Furthermore, main issues and some research trends about the applications of GNNs in power systems are discussed.

Ensembles over neural network weights trained from different random initialization, known as deep ensembles, achieve state-of-the-art accuracy and calibration. The recently introduced batch ensembles provide a drop-in replacement that is more parameter efficient. In this paper, we design ensembles not only over weights, but over hyperparameters to improve the state of the art in both settings. For best performance independent of budget, we propose hyper-deep ensembles, a simple procedure that involves a random search over different hyperparameters, themselves stratified across multiple random initializations. Its strong performance highlights the benefit of combining models with both weight and hyperparameter diversity. We further propose a parameter efficient version, hyper-batch ensembles, which builds on the layer structure of batch ensembles and self-tuning networks. The computational and memory costs of our method are notably lower than typical ensembles. On image classification tasks, with MLP, LeNet, and Wide ResNet 28-10 architectures, our methodology improves upon both deep and batch ensembles.

In this paper, we propose the joint learning attention and recurrent neural network (RNN) models for multi-label classification. While approaches based on the use of either model exist (e.g., for the task of image captioning), training such existing network architectures typically require pre-defined label sequences. For multi-label classification, it would be desirable to have a robust inference process, so that the prediction error would not propagate and thus affect the performance. Our proposed model uniquely integrates attention and Long Short Term Memory (LSTM) models, which not only addresses the above problem but also allows one to identify visual objects of interests with varying sizes without the prior knowledge of particular label ordering. More importantly, label co-occurrence information can be jointly exploited by our LSTM model. Finally, by advancing the technique of beam search, prediction of multiple labels can be efficiently achieved by our proposed network model.

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