Process Monitoring involves tracking a system's behaviors, evaluating the current state of the system, and discovering interesting events that require immediate actions. In this paper, we consider monitoring temporal system state sequences to help detect the changes of dynamic systems, check the divergence of the system development, and evaluate the significance of the deviation. We begin with discussions of data reduction, symbolic data representation, and the anomaly detection in temporal discrete sequences. Time-series representation methods are also discussed and used in this paper to discretize raw data into sequences of system states. Markov Chains and stationary state distributions are continuously generated from temporal sequences to represent snapshots of the system dynamics in different time frames. We use generalized Jensen-Shannon Divergence as the measure to monitor changes of the stationary symbol probability distributions and evaluate the significance of system deviations. We prove that the proposed approach is able to detect deviations of the systems we monitor and assess the deviation significance in probabilistic manner.
School of Computing, Electronics and Mathematics, Coventry University UK（考文垂大学计算机、电子与数学系）
Distinguishing between classes of time series sampled from dynamic systems is a common challenge in systems and control engineering, for example in the context of health monitoring, fault detection, and quality control. The challenge is increased when no underlying model of a system is known, measurement noise is present, and long signals need to be interpreted. In this paper we address these issues with a new non parametric classifier based on topological signatures. Our model learns classes as weighted kernel density estimates (KDEs) over persistent homology diagrams and predicts new traject…
Friedrich Schiller University Jena（耶拿弗里德里希·席勒大学）；Carl Zeiss AG（卡尔·蔡司股份公司）
Automatic detection of anomalies in space- and time-varying measurements is an important tool in several fields, e.g., fraud detection, climate analysis, or healthcare monitoring. We present an algorithm for detecting anomalous regions in multivariate spatio-temporal time-series, which allows for spotting the interesting parts in large amounts of data, including video and text data. In opposition to existing techniques for detecting isolated anomalous data points, we propose the "Maximally Divergent Intervals" (MDI) framework for unsupervised detection of coherent spatial regions and time inte…
In this study, we consider a problem of monitoring parameter changes particularly in the presence of outliers. To propose a sequential procedure that is robust against outliers, we use the density power divergence to derive a detector and stopping time that make up our procedure. We first investigate the asymptotic properties of our sequential procedure for i.i.d. sequences, and then extend the proposed procedure to stationary time series models, where we provide a set of sufficient conditions under which the proposed procedure has an asymptotically controlled size and consistency in power. As…
The Conditional Cauchy-Schwarz Divergence with Applications to Time-Series Data and Sequential Decision Making
UiT - The Arctic University of Norway（挪威北极大学）；Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）；University of Florida（佛罗里达大学）；NORCE Norwegian Research Centre（NORCE挪威研究中心）；Copenhagen University（哥本哈根大学）；Norwegian Computing Center（挪威计算中心）
In this paper, we present a new wrapper feature selection approach based on Jensen-Shannon (JS) divergence, termed feature selection with maximum JS-divergence (FSMJ), for text categorization. Unlike most existing feature selection approaches, the proposed FSMJ approach is based on real-valued features which provide more information for discrimination than binary-valued features used in conventional approaches. We show that the FSMJ is a greedy approach and the JS-divergence monotonically increases when more features are selected. We conduct several experiments on real-life data sets, compared…
The University of Tokyo（东京大学）；CyberAgent, Inc.（赛博艾金特公司）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）；Preferred Networks, Inc.（优选网络公司）
This paper provides a unified perspective for the Kullback-Leibler (KL)-divergence and the integral probability metrics (IPMs) from the perspective of maximum likelihood density-ratio estimation (DRE). Both the KL-divergence and the IPMs are widely used in various fields in applications such as generative modeling. However, a unified understanding of these concepts has still been unexplored. In this paper, we show that the KL-divergence and the IPMs can be represented as maximal likelihoods differing only by sampling schemes, and use this result to derive a unified form of the IPMs and a relax…
Dynamic statistical process monitoring methods have been widely studied and applied in modern industrial processes. These methods aim to extract the most predictable temporal information and develop the corresponding dynamic monitoring schemes. However, measurement noise is widespread in real-world industrial processes, and ignoring its effect will lead to sub-optimal modeling and monitoring performance. In this article, a probabilistic predictable feature analysis (PPFA) is proposed for multivariate time series modeling, and a multi-step dynamic predictive monitoring scheme is developed. The …
Maximum likelihood (ML) and adversarial learning are two popular approaches for training generative models, and from many perspectives these techniques are complementary. ML learning encourages the capture of all data modes, and it is typically characterized by stable training. However, ML learning tends to distribute probability mass diffusely over the data space, $e.g.$, yielding blurry synthetic images. Adversarial learning is well known to synthesize highly realistic natural images, despite practical challenges like mode dropping and delicate training. We propose an $α$-Bridge to unify the…
We focus on the maximum regularization parameter for anisotropic total-variation denoising. It corresponds to the minimum value of the regularization parameter above which the solution remains constant. While this value is well know for the Lasso, such a critical value has not been investigated in details for the total-variation. Though, it is of importance when tuning the regularization parameter as it allows fixing an upper-bound on the grid for which the optimal parameter is sought. We establish a closed form expression for the one-dimensional case, as well as an upper-bound for the two-dim…
University of Electronic Science and Technology of China（电子科技大学）；Shandong Normal University（山东师范大学）；Indiana University-Purdue University Indianapolis（印第安纳大学与普渡大学印第安纳波利斯联合分校）
Unsupervised domain adaptation addresses the problem of transferring knowledge from a well-labeled source domain to an unlabeled target domain where the two domains have distinctive data distributions. Thus, the essence of domain adaptation is to mitigate the distribution divergence between the two domains. The state-of-the-art methods practice this very idea by either conducting adversarial training or minimizing a metric which defines the distribution gaps. In this paper, we propose a new domain adaptation method named Adversarial Tight Match (ATM) which enjoys the benefits of both adversari…
A frequent problem in statistical science is how to properly handle missing data in matched paired observations. There is a large body of literature coping with the univariate case. Yet, the ongoing technological progress in measuring biological systems raises the need for addressing more complex data, e.g., graphs, strings and probability distributions, among others. In order to fill this gap, this paper proposes new estimators of the maximum mean discrepancy (MMD) to handle complex matched pairs with missing data. These estimators can detect differences in data distributions under different …
Measuring divergence between two distributions is essential in machine learning and statistics and has various applications including binary classification, change point detection, and two-sample test. Furthermore, in the era of big data, designing divergence measure that is interpretable and can handle high-dimensional and complex data becomes extremely important. In the paper, we propose a post selection inference (PSI) framework for divergence measure, which can select a set of statistically significant features that discriminate two distributions. Specifically, we employ an additive varian…
Recruit Technologies Co., Ltd.（Recruit Technologies株式会社）；National Institute of Advanced Industrial Science and Technology (AIST)（日本产业技术综合研究所）；Kyoto University（京都大学）；Preferred Networks, Inc.（Preferred Networks公司）；ATR Cognitive Mechanisms Laboratories（ATR认知机制实验室）
We propose a new neural sequence model training method in which the objective function is defined by $α$-divergence. We demonstrate that the objective function generalizes the maximum-likelihood (ML)-based and reinforcement learning (RL)-based objective functions as special cases (i.e., ML corresponds to $α\to 0$ and RL to $α\to1$). We also show that the gradient of the objective function can be considered a mixture of ML- and RL-based objective gradients. The experimental results of a machine translation task show that minimizing the objective function with $α> 0$ outperforms $α\to 0$, which …
Queen Mary University of London（伦敦玛丽女王大学）；Aarhus University（奥胡斯大学）；University of Oxford（牛津大学）；University of Lübeck（吕贝克大学）；KU Leuven（鲁汶大学）
Brain waves vary between people. An obvious way to improve automatic sleep staging for longitudinal sleep monitoring is personalization of algorithms based on individual characteristics extracted from the first night of data. As a single night is a very small amount of data to train a sleep staging model, we propose a Kullback-Leibler (KL) divergence regularized transfer learning approach to address this problem. We employ the pretrained SeqSleepNet (i.e. the subject independent model) as a starting point and finetune it with the single-night personalization data to derive the personalized mod…
Carnegie Mellon University（卡内基梅隆大学）；Arm Inc.（安谋公司）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
In this paper, we identify a new phenomenon called activation-divergence which occurs in Federated Learning (FL) due to data heterogeneity (i.e., data being non-IID) across multiple users. Specifically, we argue that the activation vectors in FL can diverge, even if subsets of users share a few common classes with data residing on different devices. To address the activation-divergence issue, we introduce a prior based on the principle of maximum entropy; this prior assumes minimal information about the per-device activation vectors and aims at making the activation vectors of same classes as …
With the rise of machine learning and deep learning based applications in practice, monitoring, i.e. verifying that these operate within specification, has become an important practical problem. An important aspect of this monitoring is to check whether the inputs (or intermediates) have strayed from the distribution they were validated for, which can void the performance assurances obtained during testing. There are two common approaches for this. The, perhaps, more classical one is outlier detection or novelty detection, where, for a single input we ask whether it is an outlier, i.e. exceedi…
Given i.i.d. observations of a random vector $X \in \mathbb{R}^p$, we study the problem of estimating both its covariance matrix $Σ^*$, and its inverse covariance or concentration matrix {$Θ^* = (Σ^*)^{-1}$.} We estimate $Θ^*$ by minimizing an $\ell_1$-penalized log-determinant Bregman divergence; in the multivariate Gaussian case, this approach corresponds to $\ell_1$-penalized maximum likelihood, and the structure of $Θ^*$ is specified by the graph of an associated Gaussian Markov random field. We analyze the performance of this estimator under high-dimensional scaling, in which the number o…
This paper addresses the estimation of the latent dimensionality in nonnegative matrix factorization (NMF) with the β-divergence. The β-divergence is a family of cost functions that includes the squared Euclidean distance, Kullback-Leibler and Itakura-Saito divergences as special cases. Learning the model order is important as it is necessary to strike the right balance between data fidelity and overfitting. We propose a Bayesian model based on automatic relevance determination in which the columns of the dictionary matrix and the rows of the activation matrix are tied together through a commo…
