Deep anomaly detection has become popular for its capability of handling complex data. However, training a deep detector is fragile to data contamination due to overfitting. In this work, we study the performance of the anomaly detectors under data contamination and construct a data-efficient countermeasure against data contamination. We show that training a deep anomaly detector induces an implicit kernel machine. We then derive an information-theoretic bound of performance degradation with respect to the data contamination ratio. To mitigate the degradation, we propose a contradicting training approach. Apart from learning normality on the contaminated dataset, our approach discourages learning an additional small auxiliary dataset of labeled anomalies. Our approach is much more affordable than constructing a completely clean training dataset. Experiments on public datasets show that our approach significantly improves anomaly detection in the presence of contamination and outperforms some recently proposed detectors.

The restless multi-armed bandit (RMAB) problem is a generalization of the multi-armed bandit with non-stationary rewards. Its optimal solution is intractable due to exponentially large state and action spaces with respect to the number of arms. Existing approximation approaches, e.g., Whittle's index policy, have difficulty in capturing either temporal or spatial factors such as impacts from other arms. We propose considering both factors using the attention mechanism, which has achieved great success in deep learning. Our state-aware value function approximation solution comprises an attention-based value function approximator and a Bellman equation solver. The attention-based coordination module capture both spatial and temporal factors for arm coordination. The Bellman equation solver utilizes the decoupling structure of RMABs to acquire solutions with significantly reduced computation overheads. In particular, the time complexity of our approximation is linear in the number of arms. Finally, we illustrate the effectiveness and investigate the properties of our proposed method with numerical experiments.

This paper introduces a concept of layer aggregation to describe how information from previous layers can be reused to better extract features at the current layer. While DenseNet is a typical example of the layer aggregation mechanism, its redundancy has been commonly criticized in the literature. This motivates us to propose a very light-weighted module, called recurrent layer aggregation (RLA), by making use of the sequential structure of layers in a deep CNN. Our RLA module is compatible with many mainstream deep CNNs, including ResNets, Xception and MobileNetV2, and its effectiveness is verified by our extensive experiments on image classification, object detection and instance segmentation tasks. Specifically, improvements can be uniformly observed on CIFAR, ImageNet and MS COCO datasets, and the corresponding RLA-Nets can surprisingly boost the performances by 2-3% on the object detection task. This evidences the power of our RLA module in helping main CNNs better learn structural information in images.

Autoregressive networks can achieve promising performance in many sequence modeling tasks with short-range dependence. However, when handling high-dimensional inputs and outputs, the massive amount of parameters in the network leads to expensive computational cost and low learning efficiency. The problem can be alleviated slightly by introducing one more narrow hidden layer to the network, but the sample size required to achieve a certain training error is still substantial. To address this challenge, we rearrange the weight matrices of a linear autoregressive network into a tensor form, and then make use of Tucker decomposition to represent low-rank structures. This leads to a novel compact autoregressive network, called Tucker AutoRegressive (TAR) net. Interestingly, the TAR net can be applied to sequences with long-range dependence since the dimension along the sequential order is reduced. Theoretical studies show that the TAR net improves the learning efficiency, and requires much fewer samples for model training. Experiments on synthetic and real-world datasets demonstrate the promising performance of the proposed compact network.

The LSTM network was proposed to overcome the difficulty in learning long-term dependence, and has made significant advancements in applications. With its success and drawbacks in mind, this paper raises the question - do RNN and LSTM have long memory? We answer it partially by proving that RNN and LSTM do not have long memory from a statistical perspective. A new definition for long memory networks is further introduced, and it requires the model weights to decay at a polynomial rate. To verify our theory, we convert RNN and LSTM into long memory networks by making a minimal modification, and their superiority is illustrated in modeling long-term dependence of various datasets.

Many problems in science and engineering can be reduced to the recovery of an unknown large matrix from a small number of random linear measurements. Matrix factorization arguably is the most popular approach for low-rank matrix recovery. Many methods have been proposed using different loss functions, for example the most widely used L2loss, more robust choices such as L1and Huber loss, quantile and expectile loss for skewed data. All of them can be unified into the framework of M-estimation. In this paper, we present a general framework of low-rank matrix factorization based on M-estimation in statistics. The framework mainly involves two steps: firstly we apply Nesterov's smoothing technique to obtain an optimal smooth approximation for non-smooth loss function, such as L1and quantile loss; secondly we exploit an alternative updating scheme along with Nesterov's momentum method at each step to minimize the smoothed loss function. Strong theoretical convergence guarantee has been developed for the general framework, and extensive numerical experiments have been conducted to illustrate the performance of proposed algorithm.