In this paper, we study the generalization performance of global minima for implementing empirical risk minimization (ERM) on over-parameterized deep ReLU nets. Using a novel deepening scheme for deep ReLU nets, we rigorously prove that there exist perfect global minima achieving almost optimal generalization error bounds for numerous types of data under mild conditions. Since over-parameterization is crucial to guarantee that the global minima of ERM on deep ReLU nets can be realized by the widely used stochastic gradient descent (SGD) algorithm, our results indeed fill a gap between optimization and generalization.

Brain disorders in the early and late life of humans potentially share pathological alterations in brain functions. However, the key evidence from neuroimaging data for pathological commonness remains unrevealed. To explore this hypothesis, we build a deep learning model, using multi-site functional magnetic resonance imaging data (N=4,410, 6 sites), for classifying 5 different brain disorders from healthy controls, with a set of common features. Our model achieves 62.6 1.9% overall classification accuracy on data from the 6 investigated sites and detects a set of commonly affected functional subnetworks at different spatial scales, including default mode, executive control, visual, and limbic networks. In the deep-layer feature representation for individual data, we observe young and aging patients with disorders are continuously distributed, which is in line with the clinical concept of the "spectrum of disorders". The revealed spectrum underlying early-and late-life brain disorders promotes the understanding of disorder comorbidities in the lifespan.

In recent years, large amounts of electronic health records (EHRs) concerning chronic diseases, such as cancer, diabetes, and mental disease, have been collected to facilitate medical diagnosis. Modeling the dynamic properties of EHRs related to chronic diseases can be efficiently done using dynamic treatment regimes (DTRs), which are a set of sequential decision rules. While Reinforcement learning (RL) is a widely used method for creating DTRs, there is ongoing research in developing RL algorithms that can effectively handle large amounts of data. In this paper, we present a novel approach, a distributed Q-learning algorithm, for generating DTRs. The novelties of our research are as follows: 1) From a methodological perspective, we present a novel and scalable approach for generating DTRs by combining distributed learning with Q-learning. The proposed approach is specifically designed to handle large amounts of data and effectively generate DTRs. 2) From a theoretical standpoint, we provide generalization error bounds for the proposed distributed Q-learning algorithm, which are derived within the framework of statistical learning theory. These bounds quantify the relationships between sample size, prediction accuracy, and computational burden, providing insights into the performance of the algorithm. 3) From an applied perspective, we demonstrate the effectiveness of our proposed distributed Q-learning algorithm for DTRs by applying it to clinical cancer treatments. The results show that our algorithm outperforms both traditional linear Q-learning and commonly used deep Q-learning in terms of both prediction accuracy and computation cost.

Unrecognized patient deterioration can lead to high morbidity and mortality. Most existing deterioration prediction models require a large number of clinical information, typically collected in hospital settings, such as medical images or comprehensive laboratory tests. This is infeasible for telehealth solutions and highlights a gap in deterioration prediction models that are based on minimal data, which can be recorded at a large scale in any clinic, nursing home, or even at the patient's home. In this study, we propose and develop a prognostic model that predicts if a patient will experience deterioration in the forthcoming 3-24 hours. The model sequentially processes routine triadic vital signs: (a) oxygen saturation, (b) heart rate, and (c) temperature. The model is also provided with basic patient information, including sex, age, vaccination status, vaccination date, and status of obesity, hypertension, or diabetes. We train and evaluate the model using data collected from 37,006 COVID-19 patients at NYU Langone Health in New York, USA. The model achieves an area under the receiver operating characteristic curve (AUROC) of 0.808-0.880 for 3-24 hour deterioration prediction. We also conduct occlusion experiments to evaluate the importance of each input feature, where the results reveal the significance of continuously monitoring the variations of the vital signs. Our results show the prospect of accurate deterioration forecast using a minimum feature set that can be relatively easily obtained using wearable devices and self-reported patient information.

Knowledge graphs (KGs), as structured representations of real world facts, are intelligent databases incorporating human knowledge that can help machine imitate the way of human problem solving. However, due to the nature of rapid iteration as well as incompleteness of data, KGs are usually huge and there are inevitably missing facts in KGs. Link prediction for knowledge graphs is the task aiming to complete missing facts by reasoning based on the existing knowledge. Two main streams of research are widely studied: one learns low-dimensional embeddings for entities and relations that can capture latent patterns, and the other gains good interpretability by mining logical rules. Unfortunately, previous studies rarely pay attention to heterogeneous KGs. In this paper, we propose DegreEmbed, a model that combines embedding-based learning and logic rule mining for inferring on KGs. Specifically, we study the problem of predicting missing links in heterogeneous KGs that involve entities and relations of various types from the perspective of the degrees of nodes. Experimentally, we demonstrate that our DegreEmbed model outperforms the state-of-the-art methods on real world datasets. Meanwhile, the rules mined by our model are of high quality and interpretability.

Large-scale knowledge graphs (KGs) provide structured representations of human knowledge. However, as it is impossible to contain all knowledge, KGs are usually incomplete. Reasoning based on existing facts paves a way to discover missing facts. In this paper, we study the problem of learning logic rules for reasoning on knowledge graphs for completing missing factual triplets. Learning logic rules equips a model with strong interpretability as well as the ability to generalize to similar tasks. We propose a model called MPLR that improves the existing models to fully use training data and multi-target scenarios are considered. In addition, considering the deficiency in evaluating the performance of models and the quality of mined rules, we further propose two novel indicators to help with the problem. Experimental results empirically demonstrate that our MPLR model outperforms state-of-the-art methods on five benchmark datasets. The results also prove the effectiveness of the indicators.

This paper focuses on learning rate analysis of Nystr\"{o}m regularization with sequential sub-sampling for $\tau$-mixing time series. Using a recently developed Banach-valued Bernstein inequality for $\tau$-mixing sequences and an integral operator approach based on second-order decomposition, we succeed in deriving almost optimal learning rates of Nystr\"{o}m regularization with sequential sub-sampling for $\tau$-mixing time series. A series of numerical experiments are carried out to verify our theoretical results, showing the excellent learning performance of Nystr\"{o}m regularization with sequential sub-sampling in learning massive time series data. All these results extend the applicable range of Nystr\"{o}m regularization from i.i.d. samples to non-i.i.d. sequences.

Low-tubal-rank tensor approximation has been proposed to analyze large-scale and multi-dimensional data. However, finding such an accurate approximation is challenging in the streaming setting, due to the limited computational resources. To alleviate this issue, this paper extends a popular matrix sketching technique, namely Frequent Directions, for constructing an efficient and accurate low-tubal-rank tensor approximation from streaming data based on the tensor Singular Value Decomposition (t-SVD). Specifically, the new algorithm allows the tensor data to be observed slice by slice, but only needs to maintain and incrementally update a much smaller sketch which could capture the principal information of the original tensor. The rigorous theoretical analysis shows that the approximation error of the new algorithm can be arbitrarily small when the sketch size grows linearly. Extensive experimental results on both synthetic and real multi-dimensional data further reveal the superiority of the proposed algorithm compared with other sketching algorithms for getting low-tubal-rank approximation, in terms of both efficiency and accuracy.

Compared with avid research activities of deep convolutional neural networks (DCNNs) in practice, the study of theoretical behaviors of DCNNs lags heavily behind. In particular, the universal consistency of DCNNs remains open. In this paper, we prove that implementing empirical risk minimization on DCNNs with expansive convolution (with zero-padding) is strongly universally consistent. Motivated by the universal consistency, we conduct a series of experiments to show that without any fully connected layers, DCNNs with expansive convolution perform not worse than the widely used deep neural networks with hybrid structure containing contracting (without zero-padding) convolution layers and several fully connected layers.

Background. Studies have shown that the conventional left ventricular mechanical dyssynchrony (LVMD) parameters have their own statistical limitations. The purpose of this study is to extract new LVMD parameters from the phase analysis of gated SPECT MPI by deep learning to help CRT patient selection. Methods. One hundred and three patients who underwent rest gated SPECT MPI were enrolled in this study. CRT response was defined as a decrease in left ventricular end-systolic volume (LVESV) >= 15% at 6 +- 1 month follow up. Autoencoder (AE), an unsupervised deep learning method, was trained by the raw LV systolic phase polar maps to extract new LVMD parameters, called AE-based LVMD parameters. Correlation analysis was used to explain the relationships between new parameters with conventional LVMD parameters. Univariate and multivariate analyses were used to establish a multivariate model for predicting CRT response. Results. Complete data were obtained in 102 patients, 44.1% of them were classified as CRT responders. AE-based LVMD parameter was significant in the univariate (OR 1.24, 95% CI 1.07 - 1.44, P = 0.006) and multivariate analyses (OR 1.03, 95% CI 1.01 - 1.06, P = 0.006). Moreover, it had incremental value over PSD (AUC 0.72 vs. 0.63, LH 8.06, P = 0.005) and PBW (AUC 0.72 vs. 0.64, LH 7.87, P = 0.005), combined with significant clinic characteristics, including LVEF and gender. Conclusions. The new LVMD parameters extracted by autoencoder from the baseline gated SPECT MPI has the potential to improve the prediction of CRT response.