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"Time Series Analysis": models, code, and papers

tsrobprep -- an R package for robust preprocessing of time series data

Apr 26, 2021
Michał Narajewski, Jens Kley-Holsteg, Florian Ziel

Data cleaning is a crucial part of every data analysis exercise. Yet, the currently available R packages do not provide fast and robust methods for cleaning and preparation of time series data. The open source package tsrobprep introduces efficient methods for handling missing values and outliers using model based approaches. For data imputation a probabilistic replacement model is proposed, which may consist of autoregressive components and external inputs. For outlier detection a clustering algorithm based on finite mixture modelling is introduced, which considers typical time series related properties as features. By assigning to each observation a probability of being an outlying data point, the degree of outlyingness can be determined. The methods work robust and are fully tunable. Moreover, by providing the auto_data_cleaning function the data preprocessing can be carried out in one cast, without manual tuning and providing suitable results. The primary motivation of the package is the preprocessing of energy system data, however, the package is also suited for other moderate and large sized time series data set. We present application for electricity load, wind and solar power data.

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Semantic of Cloud Computing services for Time Series workflows

Feb 01, 2022
Manuel Parra-Royón, Francisco Baldan, Ghislain Atemezing, J. M. Benitez

Time series (TS) are present in many fields of knowledge, research, and engineering. The processing and analysis of TS are essential in order to extract knowledge from the data and to tackle forecasting or predictive maintenance tasks among others The modeling of TS is a challenging task, requiring high statistical expertise as well as outstanding knowledge about the application of Data Mining(DM) and Machine Learning (ML) methods. The overall work with TS is not limited to the linear application of several techniques, but is composed of an open workflow of methods and tests. These workflow, developed mainly on programming languages, are complicated to execute and run effectively on different systems, including Cloud Computing (CC) environments. The adoption of CC can facilitate the integration and portability of services allowing to adopt solutions towards services Internet Technologies (IT) industrialization. The definition and description of workflow services for TS open up a new set of possibilities regarding the reduction of complexity in the deployment of this type of issues in CC environments. In this sense, we have designed an effective proposal based on semantic modeling (or vocabulary) that provides the full description of workflow for Time Series modeling as a CC service. Our proposal includes a broad spectrum of the most extended operations, accommodating any workflow applied to classification, regression, or clustering problems for Time Series, as well as including evaluation measures, information, tests, or machine learning algorithms among others.

* 11 pages, 12 figures 
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Randomized Signature Layers for Signal Extraction in Time Series Data

Jan 02, 2022
Enea Monzio Compagnoni, Luca Biggio, Antonio Orvieto, Thomas Hofmann, Josef Teichmann

Time series analysis is a widespread task in Natural Sciences, Social Sciences, and Engineering. A fundamental problem is finding an expressive yet efficient-to-compute representation of the input time series to use as a starting point to perform arbitrary downstream tasks. In this paper, we build upon recent works that use the Signature of a path as a feature map and investigate a computationally efficient technique to approximate these features based on linear random projections. We present several theoretical results to justify our approach and empirically validate that our random projections can effectively retrieve the underlying Signature of a path. We show the surprising performance of the proposed random features on several tasks, including (1) mapping the controls of stochastic differential equations to the corresponding solutions and (2) using the Randomized Signatures as time series representation for classification tasks. When compared to corresponding truncated Signature approaches, our Randomizes Signatures are more computationally efficient in high dimensions and often lead to better accuracy and faster training. Besides providing a new tool to extract Signatures and further validating the high level of expressiveness of such features, we believe our results provide interesting conceptual links between several existing research areas, suggesting new intriguing directions for future investigations.

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Closed-Form Diffeomorphic Transformations for Time Series Alignment

Jun 16, 2022
Iñigo Martinez, Elisabeth Viles, Igor G. Olaizola

Time series alignment methods call for highly expressive, differentiable and invertible warping functions which preserve temporal topology, i.e diffeomorphisms. Diffeomorphic warping functions can be generated from the integration of velocity fields governed by an ordinary differential equation (ODE). Gradient-based optimization frameworks containing diffeomorphic transformations require to calculate derivatives to the differential equation's solution with respect to the model parameters, i.e. sensitivity analysis. Unfortunately, deep learning frameworks typically lack automatic-differentiation-compatible sensitivity analysis methods; and implicit functions, such as the solution of ODE, require particular care. Current solutions appeal to adjoint sensitivity methods, ad-hoc numerical solvers or ResNet's Eulerian discretization. In this work, we present a closed-form expression for the ODE solution and its gradient under continuous piecewise-affine (CPA) velocity functions. We present a highly optimized implementation of the results on CPU and GPU. Furthermore, we conduct extensive experiments on several datasets to validate the generalization ability of our model to unseen data for time-series joint alignment. Results show significant improvements both in terms of efficiency and accuracy.

* 37 pages, 24 figures, 4 tables. Accepted at International Conference on Machine Learning ICML 2022 
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Privacy Amplification by Subsampling in Time Domain

Jan 13, 2022
Tatsuki Koga, Casey Meehan, Kamalika Chaudhuri

Aggregate time-series data like traffic flow and site occupancy repeatedly sample statistics from a population across time. Such data can be profoundly useful for understanding trends within a given population, but also pose a significant privacy risk, potentially revealing e.g., who spends time where. Producing a private version of a time-series satisfying the standard definition of Differential Privacy (DP) is challenging due to the large influence a single participant can have on the sequence: if an individual can contribute to each time step, the amount of additive noise needed to satisfy privacy increases linearly with the number of time steps sampled. As such, if a signal spans a long duration or is oversampled, an excessive amount of noise must be added, drowning out underlying trends. However, in many applications an individual realistically cannot participate at every time step. When this is the case, we observe that the influence of a single participant (sensitivity) can be reduced by subsampling and/or filtering in time, while still meeting privacy requirements. Using a novel analysis, we show this significant reduction in sensitivity and propose a corresponding class of privacy mechanisms. We demonstrate the utility benefits of these techniques empirically with real-world and synthetic time-series data.

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Iteratively reweighted adaptive lasso for conditional heteroscedastic time series with applications to AR-ARCH type processes

Dec 05, 2015
Florian Ziel

Shrinkage algorithms are of great importance in almost every area of statistics due to the increasing impact of big data. Especially time series analysis benefits from efficient and rapid estimation techniques such as the lasso. However, currently lasso type estimators for autoregressive time series models still focus on models with homoscedastic residuals. Therefore, an iteratively reweighted adaptive lasso algorithm for the estimation of time series models under conditional heteroscedasticity is presented in a high-dimensional setting. The asymptotic behaviour of the resulting estimator is analysed. It is found that the proposed estimation procedure performs substantially better than its homoscedastic counterpart. A special case of the algorithm is suitable to compute the estimated multivariate AR-ARCH type models efficiently. Extensions to the model like periodic AR-ARCH, threshold AR-ARCH or ARMA-GARCH are discussed. Finally, different simulation results and applications to electricity market data and returns of metal prices are shown.

* Computational Statistics & Data Analysis, 100 (2016) 773-793 
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Root Cause Detection Among Anomalous Time Series Using Temporal State Alignment

Jan 04, 2020
Sayan Chakraborty, Smit Shah, Kiumars Soltani, Anna Swigart

The recent increase in the scale and complexity of software systems has introduced new challenges to the time series monitoring and anomaly detection process. A major drawback of existing anomaly detection methods is that they lack contextual information to help stakeholders identify the cause of anomalies. This problem, known as root cause detection, is particularly challenging to undertake in today's complex distributed software systems since the metrics under consideration generally have multiple internal and external dependencies. Significant manual analysis and strong domain expertise is required to isolate the correct cause of the problem. In this paper, we propose a method that isolates the root cause of an anomaly by analyzing the patterns in time series fluctuations. Our method considers the time series as observations from an underlying process passing through a sequence of discretized hidden states. The idea is to track the propagation of the effect when a given problem causes unaligned but homogeneous shifts of the underlying states. We evaluate our approach by finding the root cause of anomalies in Zillows clickstream data by identifying causal patterns among a set of observed fluctuations.

* 6 pages, 7 figures, 2019 18th IEEE International Conference on Machine Learning and Applications (ICMLA) 
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Anomaly Detection of Wind Turbine Time Series using Variational Recurrent Autoencoders

Dec 05, 2021
Alan Preciado-Grijalva, Victor Rodrigo Iza-Teran

Ice accumulation in the blades of wind turbines can cause them to describe anomalous rotations or no rotations at all, thus affecting the generation of electricity and power output. In this work, we investigate the problem of ice accumulation in wind turbines by framing it as anomaly detection of multi-variate time series. Our approach focuses on two main parts: first, learning low-dimensional representations of time series using a Variational Recurrent Autoencoder (VRAE), and second, using unsupervised clustering algorithms to classify the learned representations as normal (no ice accumulated) or abnormal (ice accumulated). We have evaluated our approach on a custom wind turbine time series dataset, for the two-classes problem (one normal versus one abnormal class), we obtained a classification accuracy of up to 96$\%$ on test data. For the multiple-class problem (one normal versus multiple abnormal classes), we present a qualitative analysis of the low-dimensional learned latent space, providing insights into the capacities of our approach to tackle such problem. The code to reproduce this work can be found here

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Statistically Significant Detection of Linguistic Change

Nov 12, 2014
Vivek Kulkarni, Rami Al-Rfou, Bryan Perozzi, Steven Skiena

We propose a new computational approach for tracking and detecting statistically significant linguistic shifts in the meaning and usage of words. Such linguistic shifts are especially prevalent on the Internet, where the rapid exchange of ideas can quickly change a word's meaning. Our meta-analysis approach constructs property time series of word usage, and then uses statistically sound change point detection algorithms to identify significant linguistic shifts. We consider and analyze three approaches of increasing complexity to generate such linguistic property time series, the culmination of which uses distributional characteristics inferred from word co-occurrences. Using recently proposed deep neural language models, we first train vector representations of words for each time period. Second, we warp the vector spaces into one unified coordinate system. Finally, we construct a distance-based distributional time series for each word to track it's linguistic displacement over time. We demonstrate that our approach is scalable by tracking linguistic change across years of micro-blogging using Twitter, a decade of product reviews using a corpus of movie reviews from Amazon, and a century of written books using the Google Book-ngrams. Our analysis reveals interesting patterns of language usage change commensurate with each medium.

* 11 pages, 7 figures, 4 tables 
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A Causal-based Framework for Multimodal Multivariate Time Series Validation Enhanced by Unsupervised Deep Learning as an Enabler for Industry 4.0

Aug 05, 2020
Cedric Schockaert

An advanced conceptual validation framework for multimodal multivariate time series defines a multi-level contextual anomaly detection ranging from an univariate context definition, to a multimodal abstract context representation learnt by an Autoencoder from heterogeneous data (images, time series, sounds, etc.) associated to an industrial process. Each level of the framework is either applicable to historical data and/or live data. The ultimate level is based on causal discovery to identify causal relations in observational data in order to exclude biased data to train machine learning models and provide means to the domain expert to discover unknown causal relations in the underlying process represented by the data sample. A Long Short-Term Memory Autoencoder is successfully evaluated on multivariate time series to validate the learnt representation of abstract contexts associated to multiple assets of a blast furnace. A research roadmap is identified to combine causal discovery and representation learning as an enabler for unsupervised Root Cause Analysis applied to the process industry.

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