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The consistency of the maximum likelihood estimator for mixtures of elliptically-symmetric distributions for estimating its population version is shown, where the underlying distribution $P$ is nonparametric and does not necessarily belong to the class of mixtures on which the estimator is based. In a situation where $P$ is a mixture of well enough separated but nonparametric distributions it is shown that the components of the population version of the estimator correspond to the well separated components of $P$. This provides some theoretical justification for the use of such estimators for cluster analysis in case that $P$ has well separated subpopulations even if these subpopulations differ from what the mixture model assumes.

Mathematical models for excitable tissue with explicit representation of individual cells are highly detailed and can, unlike classical homogenized models, represent complex cellular geometries and local membrane variations. However, these cell-based models are challenging to approximate numerically, partly due to their mixed-dimensional nature with unknowns both in the bulk and at the lower-dimensional cellular membranes. We here develop and evaluate a novel solution strategy for the cell-based KNP-EMI model describing ionic electrodiffusion in and between intra- and extracellular compartments with explicit representation of individual cells. The strategy is based on operator splitting, a multiplier-free formulation of the coupled dynamics across sub-regions, and a discontinuous Galerkin discretization. In addition to desirable theoretical properties, such as local mass conservation, the scheme is practical as it requires no specialized functionality in the finite element assembly and order optimal solvers for the resulting linear systems can be realized with black-box algebraic multigrid preconditioners. Numerical investigations show that the proposed solution strategy is accurate, robust with respect to discretization parameters, and that the parallel scalability of the solver is close to optimal - both for idealized and realistic two and three dimensional geometries.

Recent advances unveiled physical neural networks as promising machine learning platforms, offering faster and more energy-efficient information processing. Compared with extensively-studied optical neural networks, the development of mechanical neural networks (MNNs) remains nascent and faces significant challenges, including heavy computational demands and learning with approximate gradients. Here, we introduce the mechanical analogue of in situ backpropagation to enable highly efficient training of MNNs. We demonstrate that the exact gradient can be obtained locally in MNNs, enabling learning through their immediate vicinity. With the gradient information, we showcase the successful training of MNNs for behavior learning and machine learning tasks, achieving high accuracy in regression and classification. Furthermore, we present the retrainability of MNNs involving task-switching and damage, demonstrating the resilience. Our findings, which integrate the theory for training MNNs and experimental and numerical validations, pave the way for mechanical machine learning hardware and autonomous self-learning material systems.

Image reconstruction is an essential step of every medical imaging method, including Photoacoustic Tomography (PAT), which is a promising modality of imaging, that unites the benefits of both ultrasound and optical imaging methods. Reconstruction of PAT images using conventional methods results in rough artifacts, especially when applied directly to sparse PAT data. In recent years, generative adversarial networks (GANs) have shown a powerful performance in image generation as well as translation, rendering them a smart choice to be applied to reconstruction tasks. In this study, we proposed an end-to-end method called DensePANet to solve the problem of PAT image reconstruction from sparse data. The proposed model employs a novel modification of UNet in its generator, called FD-UNet++, which considerably improves the reconstruction performance. We evaluated the method on various in-vivo and simulated datasets. Quantitative and qualitative results show the better performance of our model over other prevalent deep learning techniques.

We hypothesize that due to the greedy nature of learning in multi-modal deep neural networks, these models tend to rely on just one modality while under-fitting the other modalities. Such behavior is counter-intuitive and hurts the models' generalization, as we observe empirically. To estimate the model's dependence on each modality, we compute the gain on the accuracy when the model has access to it in addition to another modality. We refer to this gain as the conditional utilization rate. In the experiments, we consistently observe an imbalance in conditional utilization rates between modalities, across multiple tasks and architectures. Since conditional utilization rate cannot be computed efficiently during training, we introduce a proxy for it based on the pace at which the model learns from each modality, which we refer to as the conditional learning speed. We propose an algorithm to balance the conditional learning speeds between modalities during training and demonstrate that it indeed addresses the issue of greedy learning. The proposed algorithm improves the model's generalization on three datasets: Colored MNIST, Princeton ModelNet40, and NVIDIA Dynamic Hand Gesture.

The growing energy and performance costs of deep learning have driven the community to reduce the size of neural networks by selectively pruning components. Similarly to their biological counterparts, sparse networks generalize just as well, if not better than, the original dense networks. Sparsity can reduce the memory footprint of regular networks to fit mobile devices, as well as shorten training time for ever growing networks. In this paper, we survey prior work on sparsity in deep learning and provide an extensive tutorial of sparsification for both inference and training. We describe approaches to remove and add elements of neural networks, different training strategies to achieve model sparsity, and mechanisms to exploit sparsity in practice. Our work distills ideas from more than 300 research papers and provides guidance to practitioners who wish to utilize sparsity today, as well as to researchers whose goal is to push the frontier forward. We include the necessary background on mathematical methods in sparsification, describe phenomena such as early structure adaptation, the intricate relations between sparsity and the training process, and show techniques for achieving acceleration on real hardware. We also define a metric of pruned parameter efficiency that could serve as a baseline for comparison of different sparse networks. We close by speculating on how sparsity can improve future workloads and outline major open problems in the field.

A key requirement for the success of supervised deep learning is a large labeled dataset - a condition that is difficult to meet in medical image analysis. Self-supervised learning (SSL) can help in this regard by providing a strategy to pre-train a neural network with unlabeled data, followed by fine-tuning for a downstream task with limited annotations. Contrastive learning, a particular variant of SSL, is a powerful technique for learning image-level representations. In this work, we propose strategies for extending the contrastive learning framework for segmentation of volumetric medical images in the semi-supervised setting with limited annotations, by leveraging domain-specific and problem-specific cues. Specifically, we propose (1) novel contrasting strategies that leverage structural similarity across volumetric medical images (domain-specific cue) and (2) a local version of the contrastive loss to learn distinctive representations of local regions that are useful for per-pixel segmentation (problem-specific cue). We carry out an extensive evaluation on three Magnetic Resonance Imaging (MRI) datasets. In the limited annotation setting, the proposed method yields substantial improvements compared to other self-supervision and semi-supervised learning techniques. When combined with a simple data augmentation technique, the proposed method reaches within 8% of benchmark performance using only two labeled MRI volumes for training, corresponding to only 4% (for ACDC) of the training data used to train the benchmark.

Breast cancer remains a global challenge, causing over 1 million deaths globally in 2018. To achieve earlier breast cancer detection, screening x-ray mammography is recommended by health organizations worldwide and has been estimated to decrease breast cancer mortality by 20-40%. Nevertheless, significant false positive and false negative rates, as well as high interpretation costs, leave opportunities for improving quality and access. To address these limitations, there has been much recent interest in applying deep learning to mammography; however, obtaining large amounts of annotated data poses a challenge for training deep learning models for this purpose, as does ensuring generalization beyond the populations represented in the training dataset. Here, we present an annotation-efficient deep learning approach that 1) achieves state-of-the-art performance in mammogram classification, 2) successfully extends to digital breast tomosynthesis (DBT; "3D mammography"), 3) detects cancers in clinically-negative prior mammograms of cancer patients, 4) generalizes well to a population with low screening rates, and 5) outperforms five-out-of-five full-time breast imaging specialists by improving absolute sensitivity by an average of 14%. Our results demonstrate promise towards software that can improve the accuracy of and access to screening mammography worldwide.

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.

Radiologist is "doctor's doctor", biomedical image segmentation plays a central role in quantitative analysis, clinical diagnosis, and medical intervention. In the light of the fully convolutional networks (FCN) and U-Net, deep convolutional networks (DNNs) have made significant contributions in biomedical image segmentation applications. In this paper, based on U-Net, we propose MDUnet, a multi-scale densely connected U-net for biomedical image segmentation. we propose three different multi-scale dense connections for U shaped architectures encoder, decoder and across them. The highlights of our architecture is directly fuses the neighboring different scale feature maps from both higher layers and lower layers to strengthen feature propagation in current layer. Which can largely improves the information flow encoder, decoder and across them. Multi-scale dense connections, which means containing shorter connections between layers close to the input and output, also makes much deeper U-net possible. We adopt the optimal model based on the experiment and propose a novel Multi-scale Dense U-Net (MDU-Net) architecture with quantization. Which reduce overfitting in MDU-Net for better accuracy. We evaluate our purpose model on the MICCAI 2015 Gland Segmentation dataset (GlaS). The three multi-scale dense connections improve U-net performance by up to 1.8% on test A and 3.5% on test B in the MICCAI Gland dataset. Meanwhile the MDU-net with quantization achieves the superiority over U-Net performance by up to 3% on test A and 4.1% on test B.