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We study a class of nonconvex nonsmooth optimization problems in which the objective is a sum of two functions: One function is the average of a large number of differentiable functions, while the other function is proper, lower semicontinuous and has a surrogate function that satisfies standard assumptions. Such problems arise in machine learning and regularized empirical risk minimization applications. However, nonconvexity and the large-sum structure are challenging for the design of new algorithms. Consequently, effective algorithms for such scenarios are scarce. We introduce and study three stochastic variance-reduced majorization-minimization (MM) algorithms, combining the general MM principle with new variance-reduced techniques. We provide almost surely subsequential convergence of the generated sequence to a stationary point. We further show that our algorithms possess the best-known complexity bounds in terms of gradient evaluations. We demonstrate the effectiveness of our algorithms on sparse binary classification problems, sparse multi-class logistic regressions, and neural networks by employing several widely-used and publicly available data sets.

In this paper, we propose a new adaptive cross algorithm for computing a low tubal rank approximation of third-order tensors, with less memory and lower computational complexity than the truncated tensor SVD (t-SVD). This makes it applicable for decomposing large-scale tensors. We conduct numerical experiments on synthetic and real-world datasets to confirm the efficiency and feasibility of the proposed algorithm. The simulation results show more than one order of magnitude acceleration in the computation of low tubal rank (t-SVD) for large-scale tensors. An application to pedestrian attribute recognition is also presented.

With the evolution of the fifth-generation (5G) wireless network, smart technology based on the Internet of Things (IoT) has become increasingly popular. As a crucial component of smart technology, IoT systems for service delivery often face concept drift issues in network data stream analytics due to dynamic IoT environments, resulting in performance degradation. In this article, we propose a drift-adaptive framework called Adaptive Exponentially Weighted Average Ensemble (AEWAE) consisting of three stages: IoT data preprocessing, base model learning, and online ensembling. It is a data stream analytics framework that integrates dynamic adjustments of ensemble methods to tackle various scenarios. Experimental results on two public IoT datasets demonstrate that our proposed framework outperforms state-of-the-art methods, achieving high accuracy and efficiency in IoT data stream analytics.

In this paper, we propose two new algorithms for maximum-likelihood estimation (MLE) of high dimensional sparse covariance matrices. Unlike most of the state of-the-art methods, which either use regularization techniques or penalize the likelihood to impose sparsity, we solve the MLE problem based on an estimated covariance graph. More specifically, we propose a two-stage procedure: in the first stage, we determine the sparsity pattern of the target covariance matrix (in other words the marginal independence in the covariance graph under a Gaussian graphical model) using the multiple hypothesis testing method of false discovery rate (FDR), and in the second stage we use either a block coordinate descent approach to estimate the non-zero values or a proximal distance approach that penalizes the distance between the estimated covariance graph and the target covariance matrix. Doing so gives rise to two different methods, each with its own advantage: the coordinate descent approach does not require tuning of any hyper-parameters, whereas the proximal distance approach is computationally fast but requires a careful tuning of the penalty parameter. Both methods are effective even in cases where the number of observed samples is less than the dimension of the data. For performance evaluation, we test the proposed methods on both simulated and real-world data and show that they provide more accurate estimates of the sparse covariance matrix than two state-of-the-art methods.

We develop a method for hybrid analyses that uses external controls to augment internal control arms in randomized controlled trials (RCT) where the degree of borrowing is determined based on similarity between RCT and external control patients to account for systematic differences (e.g. unmeasured confounders). The method represents a novel extension of the power prior where discounting weights are computed separately for each external control based on compatibility with the randomized control data. The discounting weights are determined using the predictive distribution for the external controls derived via the posterior distribution for time-to-event parameters estimated from the RCT. This method is applied using a proportional hazards regression model with piecewise constant baseline hazard. A simulation study and a real-data example are presented based on a completed trial in non-small cell lung cancer. It is shown that the case weighted adaptive power prior provides robust inference under various forms of incompatibility between the external controls and RCT population.

Physics-inspired neural networks are proven to be an effective modeling method by giving more physically plausible results with less data dependency. However, their application in robotics is limited due to the non-conservative nature of robot dynamics and the difficulty in friction modeling. Moreover, these physics-inspired neural networks do not account for complex input matrices, such as those found in underactuated soft robots. This paper solves these problems by extending Lagrangian and Hamiltonian neural networks by including dissipation and a simplified input matrix. Additionally, the loss function is processed using the Runge-Kutta algorithm, circumventing the inaccuracies and environmental susceptibility inherent in direct acceleration measurements. First, the effectiveness of the proposed method is validated via simulations of soft and rigid robots. Then, the proposed approach is validated experimentally in a tendon-driven soft robot and a Panda robot. The simulations and experimental results show that the modified neural networks can model different robots while the learned model enables decent anticipatory control.

Most multivariate outlier detection procedures ignore the spatial dependency of observations, which is present in many real data sets from various application areas. This paper introduces a new outlier detection method that accounts for a (continuously) varying covariance structure, depending on the spatial neighborhood of the observations. The underlying estimator thus constitutes a compromise between a unified global covariance estimation, and local covariances estimated for individual neighborhoods. Theoretical properties of the estimator are presented, in particular related to robustness properties, and an efficient algorithm for its computation is introduced. The performance of the method is evaluated and compared based on simulated data and for a data set recorded from Austrian weather stations.

This work deals with developing two fast randomized algorithms for computing the generalized tensor singular value decomposition (GTSVD) based on the tubal product (t-product). The random projection method is utilized to compute the important actions of the underlying data tensors and use them to get small sketches of the original data tensors, which are easier to be handled. Due to the small size of the sketch tensors, deterministic approaches are applied to them to compute their GTSVDs. Then, from the GTSVD of the small sketch tensors, the GTSVD of the original large-scale data tensors is recovered. Some experiments are conducted to show the effectiveness of the proposed approach.

Graph convolutional network (GCN) has been successfully applied to many graph-based applications; however, training a large-scale GCN remains challenging. Current SGD-based algorithms suffer from either a high computational cost that exponentially grows with number of GCN layers, or a large space requirement for keeping the entire graph and the embedding of each node in memory. In this paper, we propose Cluster-GCN, a novel GCN algorithm that is suitable for SGD-based training by exploiting the graph clustering structure. Cluster-GCN works as the following: at each step, it samples a block of nodes that associate with a dense subgraph identified by a graph clustering algorithm, and restricts the neighborhood search within this subgraph. This simple but effective strategy leads to significantly improved memory and computational efficiency while being able to achieve comparable test accuracy with previous algorithms. To test the scalability of our algorithm, we create a new Amazon2M data with 2 million nodes and 61 million edges which is more than 5 times larger than the previous largest publicly available dataset (Reddit). For training a 3-layer GCN on this data, Cluster-GCN is faster than the previous state-of-the-art VR-GCN (1523 seconds vs 1961 seconds) and using much less memory (2.2GB vs 11.2GB). Furthermore, for training 4 layer GCN on this data, our algorithm can finish in around 36 minutes while all the existing GCN training algorithms fail to train due to the out-of-memory issue. Furthermore, Cluster-GCN allows us to train much deeper GCN without much time and memory overhead, which leads to improved prediction accuracy---using a 5-layer Cluster-GCN, we achieve state-of-the-art test F1 score 99.36 on the PPI dataset, while the previous best result was 98.71 by [16]. Our codes are publicly available at //github.com/google-research/google-research/tree/master/cluster_gcn.

Benefit from the quick development of deep learning techniques, salient object detection has achieved remarkable progresses recently. However, there still exists following two major challenges that hinder its application in embedded devices, low resolution output and heavy model weight. To this end, this paper presents an accurate yet compact deep network for efficient salient object detection. More specifically, given a coarse saliency prediction in the deepest layer, we first employ residual learning to learn side-output residual features for saliency refinement, which can be achieved with very limited convolutional parameters while keep accuracy. Secondly, we further propose reverse attention to guide such side-output residual learning in a top-down manner. By erasing the current predicted salient regions from side-output features, the network can eventually explore the missing object parts and details which results in high resolution and accuracy. Experiments on six benchmark datasets demonstrate that the proposed approach compares favorably against state-of-the-art methods, and with advantages in terms of simplicity, efficiency (45 FPS) and model size (81 MB).