Cosma Rohilla Shalizi, Kristina Lisa Shalizi, James P. Crutchfield
备注：
26 pages, 5 figures; 5 tables; http://www.santafe.edu/projects/CompMech Added discussion of algorithm parameters; improved treatment of convergence and time complexity; added comparison to older methods
We present a new algorithm for discovering patterns in time series and other sequential data. We exhibit a reliable procedure for building the minimal set of hidden, Markovian states that is statistically capable of producing the behavior exhibited in the data -- the underlying process's causal states. Unlike conventional methods for fitting hidden Markov models (HMMs) to data, our algorithm makes no assumptions about the process's causal architecture (the number of hidden states and their transition structure), but rather infers it from the data. It starts with assumptions of minimal structure and introduces complexity only when the data demand it. Moreover, the causal states it infers have important predictive optimality properties that conventional HMM states lack. We introduce the algorithm, review the theory behind it, prove its asymptotic reliability, use large deviation theory to estimate its rate of convergence, and compare it to other algorithms which also construct HMMs from data. We also illustrate its behavior on an example process, and report selected numerical results from an implementation.
Causal Discovery with Inverted Self-attention for Multivariate Time Series
School of Computer Science, University of Technology Sydney（悉尼科技大学计算机科学学院）；Technical University of Denmark（丹麦技术大学）；TianFu YongXing Laboratory（天府永兴实验室）；Faculty of Data Science, City University of Macau（澳门城市大学数据科学学院）
The SINDy algorithm has been successfully used to identify the governing equations of dynamical systems from time series data. In this paper, we argue that this makes SINDy a potentially useful tool for causal discovery and that existing tools for causal discovery can be used to dramatically improve the performance of SINDy as tool for robust sparse modeling and system identification. We then demonstrate empirically that augmenting the SINDy algorithm with tools from causal discovery can provides engineers with a tool for learning causally robust governing equations.
We present a new R package which takes a numerical matrix format as data input, and computes clusters using a support vector clustering method (SVC). We have implemented an original 2D-grid labeling approach to speed up cluster extraction. In this sense, SVC can be seen as an efficient cluster extraction if clusters are separable in a 2-D map. Secondly we showed that this SVC approach using a Jaccard-Radial base kernel can help to classify well enough a set of terms into ontological classes and help to define regular expression rules for information extraction in documents; our case study conc…
Causal structure discovery in complex dynamical systems is an important challenge for many scientific domains. Although data from (interventional) experiments is usually limited, large amounts of observational time series data sets are usually available. Current methods that learn causal structure from time series often assume linear relationships. Hence, they may fail in realistic settings that contain nonlinear relations between the variables. We propose Neural Additive Vector Autoregression (NAVAR) models, a neural approach to causal structure learning that can discover nonlinear relationsh…
The traditional frequent pattern mining algorithms generate an exponentially large number of patterns of which a substantial proportion are not much significant for many data analysis endeavors. Discovery of a small number of personalized interesting patterns from the large output set according to a particular user's interest is an important as well as challenging task. Existing works on pattern summarization do not solve this problem from the personalization viewpoint. In this work, we propose an interactive pattern discovery framework named PRIIME which identifies a set of interesting patter…
University of California, Riverside（加州大学河滨分校）；University of New Mexico（新墨西哥大学）
The discovery of time series motifs has emerged as one of the most useful primitives in time series data mining. Researchers have shown its utility for exploratory data mining, summarization, visualization, segmentation, classification, clustering, and rule discovery. Although there has been more than a decade of extensive research, there is still no technique to allow the discovery of time series motifs in the presence of missing data, despite the well-documented ubiquity of missing data in scientific, industrial, and medical datasets. In this work, we introduce a technique for motif discover…
Pattern discovery, the process of discovering previously unrecognized patterns, is often performed as an ad-hoc process with little resulting certainty in the quality of the proposed patterns. Pattern validation, the process of validating the accuracy of proposed patterns, remains dominated by the simple heuristic of "the rule of three". This article shows how to use established scientific research methods for the purpose of pattern discovery and validation. We present a specific approach, called the handbook method, that uses the qualitative survey, action research, and case study research fo…
Time-series classification is an important problem for the data mining community due to the wide range of application domains involving time-series data. A recent paradigm, called shapelets, represents patterns that are highly predictive for the target variable. Shapelets are discovered by measuring the prediction accuracy of a set of potential (shapelet) candidates. The candidates typically consist of all the segments of a dataset, therefore, the discovery of shapelets is computationally expensive. This paper proposes a novel method that avoids measuring the prediction accuracy of similar can…
University of Cambridge（剑桥大学）；University of Oxford（牛津大学）；Northeastern University（东北大学）
Existing methods for structure discovery in time series data construct interpretable, compositional kernels for Gaussian process regression models. While the learned Gaussian process model provides posterior mean and variance estimates, typically the structure is learned via a greedy optimization procedure. This restricts the space of possible solutions and leads to over-confident uncertainty estimates. We introduce a fully Bayesian approach, inferring a full posterior over structures, which more reliably captures the uncertainty of the model.
Over the last decade, time series motif discovery has emerged as a useful primitive for many downstream analytical tasks, including clustering, classification, rule discovery, segmentation, and summarization. In parallel, there has been an increased understanding that Dynamic Time Warping (DTW) is the best time series similarity measure in a host of settings. Surprisingly however, there has been virtually no work on using DTW to discover motifs. The most obvious explanation of this is the fact that both motif discovery and the use of DTW can be computationally challenging, and the current best…
University of Amsterdam（阿姆斯特丹大学）；University of Toronto（多伦多大学）；Vector Institute（向量研究所）
On time-series data, most causal discovery methods fit a new model whenever they encounter samples from a new underlying causal graph. However, these samples often share relevant information which is lost when following this approach. Specifically, different samples may share the dynamics which describe the effects of their causal relations. We propose Amortized Causal Discovery, a novel framework that leverages such shared dynamics to learn to infer causal relations from time-series data. This enables us to train a single, amortized model that infers causal relations across samples with diffe…
Causal Discovery from Time-Series Data with Short-Term Invariance-Based Convolutional Neural Networks
Faculty of Computing（计算机学院）；Harbin Institute of Technology（哈尔滨工业大学）；The Artificial Intelligence Institute（人工智能研究所）；The Department of Computer Science（计算机科学系）；The University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）
Going beyond correlations, the understanding and identification of causal relationships in observational time series, an important subfield of Causal Discovery, poses a major challenge. The lack of access to a well-defined ground truth for real-world data creates the need to rely on synthetic data for the evaluation of these methods. Existing benchmarks are limited in their scope, as they either are restricted to a "static" selection of data sets, or do not allow for a granular assessment of the methods' performance when commonly made assumptions are violated. We propose a flexible and simple …
Feedzai（Feedzai公司）；Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术学院）；DCC, Faculdade de Ciêncidas da Universidade do Porto（波尔图大学理学院数据与计算机科学系）；Instituto de Telecomunicações（电信研究所）
Coupled dynamical systems are frequently observed in nature, but often not well understood in terms of their causal structure without additional domain knowledge about the system. Especially when analyzing observational time series data of dynamical systems where it is not possible to conduct controlled experiments, for example time series of climate variables, it can be challenging to determine how features causally influence each other. There are many techniques available to recover causal relationships from data, such as Granger causality, convergent cross mapping, and causal graph structur…
Zhengzhou University（郑州大学）；University of Maryland Baltimore County（马里兰大学巴尔的摩县分校）
Symbolic Aggregation approXimation (SAX) has been the de facto standard representation methods for knowledge discovery in time series on a number of tasks and applications. So far, very little work has been done in empirically investigating the intrinsic properties and statistical mechanics in SAX words. In this paper, we applied several statistical measurements and proposed a new statistical measurement, i.e. information embedding cost (IEC) to analyze the statistical behaviors of the symbolic dynamics. Our experiments on the benchmark datasets and the clinical signals demonstrate that SAX ca…
Reconstructing the causal relationships behind the phenomena we observe is a fundamental challenge in all areas of science. Discovering causal relationships through experiments is often infeasible, unethical, or expensive in complex systems. However, increases in computational power allow us to process the ever-growing amount of data that modern science generates, leading to an emerging interest in the causal discovery problem from observational data. This work evaluates the LPCMCI algorithm, which aims to find generators compatible with a multi-dimensional, highly autocorrelated time series w…
IIIA-CSIC, the Artificial Intelligence Research Institute of the Spanish National Research Council（西班牙国家研究委员会人工智能研究所（IIIA-CSIC））
Efficiently finding similar segments or motifs in time series data is a fundamental task that, due to the ubiquity of these data, is present in a wide range of domains and situations. Because of this, countless solutions have been devised but, to date, none of them seems to be fully satisfactory and flexible. In this article, we propose an innovative standpoint and present a solution coming from it: an anytime multimodal optimization algorithm for time series motif discovery based on particle swarms. By considering data from a variety of domains, we show that this solution is extremely competi…
In this paper, we present a novel approach for local exceptionality detection on time series data. This method provides the ability to discover interpretable patterns in the data, which can be used to understand and predict the progression of a time series. This being an exploratory approach, the results can be used to generate hypotheses about the relationships between the variables describing a specific process and its dynamics. We detail our approach in a concrete instantiation and exemplary implementation, specifically in the field of teamwork research. Using a real-world dataset of team i…
University of Waterloo（滑铁卢大学）；ATS Automation（ATS自动化公司）
Causal discovery between collections of time-series data can help diagnose causes of symptoms and hopefully prevent faults before they occur. However, reliable causal discovery can be very challenging, especially when the data acquisition rate varies (i.e., non-uniform data sampling), or in the presence of missing data points (e.g., sparse data sampling). To address these issues, we proposed a new system comprised of two parts, the first part fills missing data with a Gaussian Process Regression, and the second part leverages an Echo State Network, which is a type of reservoir computer (i.e., …
Integrating Statistical Significance and Discriminative Power in Pattern Discovery
INESC-ID and Instituto Superior Técnico, Universidade de Lisboa（INESC-ID 和里斯本大学高等技术学院）；LAQV-REQUIMTE, Department of Chemistry, NOVA School of Science and Technology, Universidade NOVA de Lisboa（LAQV-REQUIMTE，新里斯本大学科学与技术学院化学系）
This article proposes novel rules for false discovery rate control (FDRC) geared towards online anomaly detection in time series. Online FDRC rules allow to control the properties of a sequence of statistical tests. In the context of anomaly detection, the null hypothesis is that an observation is normal and the alternative is that it is anomalous. FDRC rules allow users to target a lower bound on precision in unsupervised settings. The methods proposed in this article overcome short-comings of previous FDRC rules in the context of anomaly detection, in particular ensuring that power remains h…
Tsinghua University（清华大学）；Institute for Brain and Cognitive Science, Tsinghua University (THUIBCS)（清华大学脑与认知科学研究所）；Chinese PLA General Hospital（中国人民解放军总医院）
Causal discovery from time-series data has been a central task in machine learning. Recently, Granger causality inference is gaining momentum due to its good explainability and high compatibility with emerging deep neural networks. However, most existing methods assume structured input data and degenerate greatly when encountering data with randomly missing entries or non-uniform sampling frequencies, which hampers their applications in real scenarios. To address this issue, here we present CUTS, a neural Granger causal discovery algorithm to jointly impute unobserved data points and build cau…
The increasing prominence of weakly labeled data nurtures a growing demand for object detection methods that can cope with minimal supervision. We propose an approach that automatically identifies discriminative configurations of visual patterns that are characteristic of a given object class. We formulate the problem as a constrained submodular optimization problem and demonstrate the benefits of the discovered configurations in remedying mislocalizations and finding informative positive and negative training examples. Together, these lead to state-of-the-art weakly-supervised detection resul…
The growing popularity of wearable sensors has generated large quantities of temporal physiological and activity data. Ability to analyze this data offers new opportunities for real-time health monitoring and forecasting. However, temporal physiological data presents many analytic challenges: the data is noisy, contains many missing values, and each series has a different length. Most methods proposed for time series analysis and classification do not handle datasets with these characteristics nor do they offer interpretability and explainability, a critical requirement in the health domain. W…
CUTS+: High-dimensional Causal Discovery from Irregular Time-series
Tsinghua University（清华大学）；Institute for Brain and Cognitive Science, Tsinghua University (THUIBCS)（清华大学脑与认知科学研究院（THUIBCS））；Chinese PLA General Hospital（中国人民解放军总医院）
AutoCause: A Python framework that automates expert decisions in environmental time-series causal discovery
ISR-Lisbon, Instituto Superior Técnico（里斯本信号与系统研究所，里斯本高等理工学院）；Digital Scholarship at Oxford, University of Oxford（牛津大学牛津数字学术中心）；Jet Propulsion Lab., Caltech（加州理工学院喷气推进实验室）
Stanford University（斯坦福大学）；Cornell University（康奈尔大学）；Joint Center for Artificial Photosynthesis（人工光合作用联合中心）；California Institute of Technology（加州理工学院）
Identifying important components or factors in large amounts of noisy data is a key problem in machine learning and data mining. Motivated by a pattern decomposition problem in materials discovery, aimed at discovering new materials for renewable energy, e.g. for fuel and solar cells, we introduce CombiFD, a framework for factor based pattern decomposition that allows the incorporation of a-priori knowledge as constraints, including complex combinatorial constraints. In addition, we propose a new pattern decomposition algorithm, called AMIQO, based on solving a sequence of (mixed-integer) quad…
Frequent temporal patterns discovered in time-interval-based multivariate data, although syntactically correct, might be non-transparent: For some pattern instances, there might exist intervals for the same entity that contradict the pattern's usual meaning. We conjecture that non-transparent patterns are also less useful as classification or prediction features. We propose a new pruning constraint during a frequent temporal-pattern discovery process, the Semantic Adjacency Criterion [SAC], which exploits domain knowledge to filter out patterns that contain potentially semantically contradicto…
The last decade has seen a flurry of research on all-pairs-similarity-search (or, self-join) for text, DNA, and a handful of other datatypes, and these systems have been applied to many diverse data mining problems. Surprisingly, however, little progress has been made on addressing this problem for time series subsequences. In this thesis, we have introduced a near universal time series data mining tool called matrix profile which solves the all-pairs-similarity-search problem and caches the output in an easy-to-access fashion. The proposed algorithm is not only parameter-free, exact and scala…
INRIA（法国国家信息与自动化研究所）；Université Paris Saclay（巴黎萨克雷大学）
Convolutional dictionary learning (CDL) estimates shift invariant basis adapted to multidimensional data. CDL has proven useful for image denoising or inpainting, as well as for pattern discovery on multivariate signals. As estimated patterns can be positioned anywhere in signals or images, optimization techniques face the difficulty of working in extremely high dimensions with millions of pixels or time samples, contrarily to standard patch-based dictionary learning. To address this optimization problem, this work proposes a distributed and asynchronous algorithm, employing locally greedy coo…
Sorbonne Universités, UPMC Univ Paris 06, CNRS, LIP6 UMR 7606（索邦大学、巴黎第六大学、法国国家科学研究中心、巴黎第六大学计算机科学实验室（UMR 7606））；Vedecom Institute（维德科姆研究所）
We introduce a dynamical spatio-temporal model formalized as a recurrent neural network for forecasting time series of spatial processes, i.e. series of observations sharing temporal and spatial dependencies. The model learns these dependencies through a structured latent dynamical component, while a decoder predicts the observations from the latent representations. We consider several variants of this model, corresponding to different prior hypothesis about the spatial relations between the series. The model is evaluated and compared to state-of-the-art baselines, on a variety of forecasting …
Data-Driven Discovery of Feature Groups in Clinical Time Series
ETH Zurich（苏黎世联邦理工学院）；Helmholtz AI（亥姆霍兹人工智能研究所）；University of Lucerne（卢塞恩大学）；TU Munich（慕尼黑工业大学）；Munich Center for Machine Learning（慕尼黑机器学习中心）；AI Center, ETH Zurich（苏黎世联邦理工学院人工智能中心）；Swiss Institute for Bioinformatics（瑞士生物信息学研究所）；University Hospital Zurich（苏黎世大学医院）
Time series shapelets are discriminative subsequences and their similarity to a time series can be used for time series classification. Since the discovery of time series shapelets is costly in terms of time, the applicability on long or multivariate time series is difficult. In this work we propose Ultra-Fast Shapelets that uses a number of random shapelets. It is shown that Ultra-Fast Shapelets yield the same prediction quality as current state-of-the-art shapelet-based time series classifiers that carefully select the shapelets by being by up to three orders of magnitudes. Since this method…
COMPASS is a longitudinal, prospective cohort study collecting data annually from students attending high school in jurisdictions across Canada. We aimed to discover significant frequent/rare associations of behavioral factors among Canadian adolescents related to cannabis use. We use a subset of COMPASS dataset which contains 18,761 records of students in grades 9 to 12 with 31 selected features (attributes) involving various characteristics, from living habits to academic performance. We then used the Pattern Discovery and Disentanglement (PDD) algorithm that we have developed to detect stro…
Program in Applied and Computational Mathematics, Princeton University（普林斯顿大学应用与计算数学项目）；IBM Research（IBM研究）
We consider the Granger causal structure learning problem from time series data. Granger causal algorithms predict a 'Granger causal effect' between two variables by testing if prediction error of one decreases significantly in the absence of the other variable among the predictor covariates. Almost all existing Granger causal algorithms condition on a large number of variables (all but two variables) to test for effects between a pair of variables. We propose a new structure learning algorithm called MMPC-p inspired by the well known MMHC algorithm for non-time series data. We show that under…
A new algorithm for Subgroup Set Discovery based on Information Gain
Centro de Tecnología Biomédica（生物医学技术中心）；Escuela Técnica Superior de Ingenieros Informáticos（高等信息工程学院）；Hospital Universitario Puerta de Hierro Majadahonda（马哈拉翁达铁之门大学医院）
