MST-GAT: A Multimodal Spatial-Temporal Graph Attention Network for Time Series Anomaly Detection

Multimodal time series (MTS) anomaly detection is crucial for maintaining the safety and stability of working devices (e.g., water treatment system and spacecraft), whose data are characterized by multivariate time series with diverse modalities. Although recent deep learning methods show great potential in anomaly detection, they do not explicitly capture spatial-temporal relationships between univariate time series of different modalities, resulting in more false negatives and false positives. In this paper, we propose a multimodal spatial-temporal graph attention network (MST-GAT) to tackle this problem. MST-GAT first employs a multimodal graph attention network (M-GAT) and a temporal convolution network to capture the spatial-temporal correlation in multimodal time series. Specifically, M-GAT uses a multi-head attention module and two relational attention modules (i.e., intra- and inter-modal attention) to model modal correlations explicitly. Furthermore, MST-GAT optimizes the reconstruction and prediction modules simultaneously. Experimental results on four multimodal benchmarks demonstrate that MST-GAT outperforms the state-of-the-art baselines. Further analysis indicates that MST-GAT strengthens the interpretability of detected anomalies by locating the most anomalous univariate time series.

GNN-XML: Graph Neural Networks for Extreme Multi-label Text Classification

Extreme multi-label text classification (XMTC) aims to tag a text instance with the most relevant subset of labels from an extremely large label set. XMTC has attracted much recent attention due to massive label sets yielded by modern applications, such as news annotation and product recommendation. The main challenges of XMTC are the data scalability and sparsity, thereby leading to two issues: i) the intractability to scale to the extreme label setting, ii) the presence of long-tailed label distribution, implying that a large fraction of labels have few positive training instances. To overcome these problems, we propose GNN-XML, a scalable graph neural network framework tailored for XMTC problems. Specifically, we exploit label correlations via mining their co-occurrence patterns and build a label graph based on the correlation matrix. We then conduct the attributed graph clustering by performing graph convolution with a low-pass graph filter to jointly model label dependencies and label features, which induces semantic label clusters. We further propose a bilateral-branch graph isomorphism network to decouple representation learning and classifier learning for better modeling tail labels. Experimental results on multiple benchmark datasets show that GNN-XML significantly outperforms state-of-the-art methods while maintaining comparable prediction efficiency and model size.

Manifold Partition Discriminant Analysis

We propose a novel algorithm for supervised dimensionality reduction named Manifold Partition Discriminant Analysis (MPDA). It aims to find a linear embedding space where the within-class similarity is achieved along the direction that is consistent with the local variation of the data manifold, while nearby data belonging to different classes are well separated. By partitioning the data manifold into a number of linear subspaces and utilizing the first-order Taylor expansion, MPDA explicitly parameterizes the connections of tangent spaces and represents the data manifold in a piecewise manner. While graph Laplacian methods capture only the pairwise interaction between data points, our method capture both pairwise and higher order interactions (using regional consistency) between data points. This manifold representation can help to improve the measure of within-class similarity, which further leads to improved performance of dimensionality reduction. Experimental results on multiple real-world data sets demonstrate the effectiveness of the proposed method.

Adversarial Attacks for Multi-view Deep Models

Recent work has highlighted the vulnerability of many deep machine learning models to adversarial examples. It attracts increasing attention to adversarial attacks, which can be used to evaluate the security and robustness of models before they are deployed. However, to our best knowledge, there is no specific research on the adversarial attacks for multi-view deep models. This paper proposes two multi-view attack strategies, two-stage attack (TSA) and end-to-end attack (ETEA). With the mild assumption that the single-view model on which the target multi-view model is based is known, we first propose the TSA strategy. The main idea of TSA is to attack the multi-view model with adversarial examples generated by attacking the associated single-view model, by which state-of-the-art single-view attack methods are directly extended to the multi-view scenario. Then we further propose the ETEA strategy when the multi-view model is provided publicly. The ETEA is applied to accomplish direct attacks on the target multi-view model, where we develop three effective multi-view attack methods. Finally, based on the fact that adversarial examples generalize well among different models, this paper takes the adversarial attack on the multi-view convolutional neural network as an example to validate that the effectiveness of the proposed multi-view attacks. Extensive experimental results demonstrate that our multi-view attack strategies are capable of attacking the multi-view deep models, and we additionally find that multi-view models are more robust than single-view models.

Adversarial Attack with Pattern Replacement

We propose a generative model for adversarial attack. The model generates subtle but predictive patterns from the input. To perform an attack, it replaces the patterns of the input with those generated based on examples from some other class. We demonstrate our model by attacking CNN on MNIST.

A Survey of Optimization Methods from a Machine Learning Perspective

Machine learning develops rapidly, which has made many theoretical breakthroughs and is widely applied in various fields. Optimization, as an important part of machine learning, has attracted much attention of researchers. With the exponential growth of data amount and the increase of model complexity, optimization methods in machine learning face more and more challenges. A lot of work on solving optimization problems or improving optimization methods in machine learning has been proposed successively. The systematic retrospect and summary of the optimization methods from the perspective of machine learning are of great significance, which can offer guidance for both developments of optimization and machine learning research. In this paper, we first describe the optimization problems in machine learning. Then, we introduce the principles and progresses of commonly used optimization methods. Next, we summarize the applications and developments of optimization methods in some popular machine learning fields. Finally, we explore and give some challenges and open problems for the optimization in machine learning.

A Variant of Gaussian Process Dynamical Systems

In order to better model high-dimensional sequential data, we propose a collaborative multi-output Gaussian process dynamical system (CGPDS), which is a novel variant of GPDSs. The proposed model assumes that the output on each dimension is controlled by a shared global latent process and a private local latent process. Thus, the dependence among different dimensions of the sequences can be captured, and the unique characteristics of each dimension of the sequences can be maintained. For training models and making prediction, we introduce inducing points and adopt stochastic variational inference methods.

Variational Langevin Hamiltonian Monte Carlo for Distant Multi-modal Sampling

The Hamiltonian Monte Carlo (HMC) sampling algorithm exploits Hamiltonian dynamics to construct efficient Markov Chain Monte Carlo (MCMC), which has become increasingly popular in machine learning and statistics. Since HMC uses the gradient information of the target distribution, it can explore the state space much more efficiently than the random-walk proposals. However, probabilistic inference involving multi-modal distributions is very difficult for standard HMC method, especially when the modes are far away from each other. Sampling algorithms are then often incapable of traveling across the places of low probability. In this paper, we propose a novel MCMC algorithm which aims to sample from multi-modal distributions effectively. The method improves Hamiltonian dynamics to reduce the autocorrelation of the samples and uses a variational distribution to explore the phase space and find new modes. A formal proof is provided which shows that the proposed method can converge to target distributions. Both synthetic and real datasets are used to evaluate its properties and performance. The experimental results verify the theory and show superior performance in multi-modal sampling.

Online Anomaly Detection with Sparse Gaussian Processes

Online anomaly detection of time-series data is an important and challenging task in machine learning. Gaussian processes (GPs) are powerful and flexible models for modeling time-series data. However, the high time complexity of GPs limits their applications in online anomaly detection. Attributed to some internal or external changes, concept drift usually occurs in time-series data, where the characteristics of data and meanings of abnormal behaviors alter over time. Online anomaly detection methods should have the ability to adapt to concept drift. Motivated by the above facts, this paper proposes the method of sparse Gaussian processes with Q-function (SGP-Q). The SGP-Q employs sparse Gaussian processes (SGPs) whose time complexity is lower than that of GPs, thus significantly speeding up online anomaly detection. By using Q-function properly, the SGP-Q can adapt to concept drift well. Moreover, the SGP-Q makes use of few abnormal data in the training data by its strategy of updating training data, resulting in more accurate sparse Gaussian process regression models and better anomaly detection results. We evaluate the SGP-Q on various artificial and real-world datasets. Experimental results validate the effectiveness of the SGP-Q.

PAC-Bayes bounds for stable algorithms with instance-dependent priors

PAC-Bayes bounds have been proposed to get risk estimates based on a training sample. In this paper the PAC-Bayes approach is combined with stability of the hypothesis learned by a Hilbert space valued algorithm. The PAC-Bayes setting is used with a Gaussian prior centered at the expected output. Thus a novelty of our paper is using priors defined in terms of the data-generating distribution. Our main result estimates the risk of the randomized algorithm in terms of the hypothesis stability coefficients. We also provide a new bound for the SVM classifier, which is compared to other known bounds experimentally. Ours appears to be the first stability-based bound that evaluates to non-trivial values.