{"type":"ScholarlyArticle","title":"RobustTrend: A Huber Loss with a Combined First and Second Order Difference Regularization for Time Series Trend Filtering","authors":[{"name":"Qingsong Wen","slug":"qingsong-wen","given":"Qingsong","family":"Wen","affiliation":"Machine Intelligence Technology , Alibaba Group , Bellevue , Washington 98004 , USA"},{"name":"Jingkun Gao","slug":"jingkun-gao","given":"Jingkun","family":"Gao","affiliation":"Machine Intelligence Technology , Alibaba Group , Bellevue , Washington 98004 , USA"},{"name":"Xiaomin Song","slug":"xiaomin-song","given":"Xiaomin","family":"Song","affiliation":"Machine Intelligence Technology , Alibaba Group , Bellevue , Washington 98004 , USA"},{"name":"Liang Sun","slug":"liang-sun","given":"Liang","family":"Sun","affiliation":"Machine Intelligence Technology , Alibaba Group , Bellevue , Washington 98004 , USA"},{"name":"Jian Tan","slug":"jian-tan","given":"Jian","family":"Tan","affiliation":"Machine Intelligence Technology , Alibaba Group , Bellevue , Washington 98004 , USA"}],"abstract":"Extracting the underlying trend signal is a crucial step to facilitate time series analysis like forecasting and anomaly detection. Besides noise signal, time series can contain not only outliers but also abrupt trend changes in real-world scenarios. To deal with these challenges, we propose a robust trend filtering algorithm based on robust statistics and sparse learning. Specifically, we adopt the Huber loss to suppress outliers, and utilize a combination of the first order and second order difference on the trend component as regularization to capture both slow and abrupt trend changes. Furthermore, an efficient method is designed to solve the proposed robust trend filtering based on majorization minimization (MM) and alternative direction method of multipliers (ADMM). We compared our proposed robust trend filter with other nine state-of-the-art trend filtering algorithms on both synthetic and real-world datasets. The experiments demonstrate that our algorithm outperforms existing methods.","doi":"10.24963/ijcai.2019/535","url":"https://ijcai.org/proceedings/2019/535","pdf":"https://ijcai.org/proceedings/2019/0535.pdf","markdown":"https://ijcai.org/proceedings/2019/535.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/535","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Machine Learning M-Z","track":"Main track","number":535,"pages":{"first":3856,"last":3862},"keywords":["Machine Learning: Data Mining","Machine Learning: Unsupervised Learning","Machine Learning: Time-series;Data Streams"],"videos":[],"references":[{"position":1,"raw":"[Afanasyev and Fedorova, 2016] Dmitriy O Afanasyev and Elena A Fedorova. The long-term trends on the electric- ity markets: Comparison of empirical mode and wavelet decompositions. Energy Economics, 56:432-442, 2016.","title":"The long-term trends on the electric-ity markets: Comparison of empirical mode and wavelet decompositions","authors":"O Dmitriy, Elena A Afanasyev, Fedorova","year":"2016","venue":"Energy Economics","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Alexandrov et al., 2012] Theodore Alexandrov, Silvia Bianconcini, Estela Bee Dagum, Peter Maass, and Tucker S McElroy. A review of some modern approaches to the problem of trend extraction. Econometric Reviews, 31(6):593-624, 2012.","title":"A review of some modern approaches to the problem of trend extraction","authors":"Theodore Alexandrov, Silvia Bianconcini, Estela Bee Dagum, Peter Maass, Tucker S Mcelroy","year":"2012","venue":"Econometric Reviews","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Boyd et al., 2011] Stephen Boyd, Neal Parikh, Eric Chu, Borja Peleato, Jonathan Eckstein, et al. Distributed op- timization and statistical learning via the alternating direc- tion method of multipliers. Foundations and Trends in Ma- chine learning, 3(1):1-122, 2011.","title":"Distributed optimization and statistical learning via the alternating direction method of multipliers","authors":"Stephen Boyd, Neal Parikh, Eric Chu, Borja Peleato, Jonathan Eckstein","year":"2011","venue":"Foundations and Trends in Machine learning","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Chan et al., 2001] Tony F Chan, Stanley Osher, and Jian- hong Shen. The digital TV filter and nonlinear denoising. IEEE Transactions on Image processing, 10(2):231-241, 2001.","title":"The digital TV filter and nonlinear denoising","authors":"Stanley Tony F Chan, Jianhong Osher, Shen","year":"2001","venue":"IEEE Transactions on Image processing","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Cleveland et al., 1990] Robert B Cleveland, William S Cleveland, Jean E McRae, and Irma Terpenning. STL: A seasonal-trend decomposition procedure based on loess. Journal of Official Statistics, 6(1):3-73, 1990.","title":"STL: A seasonal-trend decomposition procedure based on loess","authors":"William S Robert B Cleveland, Jean E Cleveland, Irma Mcrae, Terpenning","year":"1990","venue":"Journal of Official Statistics","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Craigmile and Percival, 2006] Peter F Craigmile and Don- ald B Percival. Wavelet-based trend detection and estima- tion. Encyclopedia of Environmetrics, 6, 2006.","title":"Wavelet-based trend detection and estimation","authors":"F Peter, Donald B Craigmile, Percival","year":"2006","venue":"Encyclopedia of Environmetrics","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[de Leeuw and Lange, 2009] Jan de Leeuw and Kenneth Lange. Sharp quadratic majorization in one dimension. Computational Statistics & Data Analysis, 53(7):2471- 2484, 2009.","title":"Jan de Leeuw and Kenneth Lange. Sharp quadratic majorization in one dimension","authors":"De Leeuw, Lange","year":"2009","venue":"Computational Statistics & Data Analysis","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[De Livera et al., 2011] Alysha M De Livera, Rob J Hyn- dman, and Ralph D Snyder. Forecasting time series with complex seasonal patterns using exponential smooth- ing. Journal of the American Statistical Association, 106(496):1513-1527, 2011.","title":"Forecasting time series with complex seasonal patterns using exponential smoothing","authors":"Alysha M De Livera, Rob J Hyndman, Ralph D Snyder","year":"2011","venue":"Journal of the American Statistical Association","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Eckstein and Bertsekas, 1992] Jonathan Eckstein and Dim- itri P Bertsekas. On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators. Mathematical Programming, 55(1- 3):293-318, 1992.","title":"On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators","authors":"Bertsekas Eckstein, Jonathan Eckstein, Dimitri P Bertsekas","year":"1992","venue":"Mathematical Programming","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Fried et al., 2018] Roland Fried, Karen Schet- tlinger, and Matthias Borowski. robfilter: Ro- bust time series filters. URL: https://cran.r- project.org/web/packages/robfilter/index.html. R package version 4.1.1. (visited on 11/11/2018), 2018.","title":"robfilter: Robust time series filters","authors":"Roland Fried, Karen Schettlinger, Matthias Borowski","year":"2018","venue":null,"doi":null,"url":"https://cran.r-project.org/web/packages/robfilter/index.html.Rpackageversion4.1.1","internal_url":null},{"position":11,"raw":"[Fried, 2004] Roland Fried. Robust filtering of time series with trends. Journal of Nonparametric Statistics, 16(3- 4):313-328, 2004.","title":"Robust filtering of time series with trends","authors":"Roland Fried, Fried","year":"2004","venue":"Journal of Nonparametric Statistics","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Hodrick and Prescott, 1997] Robert J Hodrick and Ed- ward C Prescott. Postwar US business cycles: an empiri- cal investigation. Journal of Money, Credit, and Banking, pages 1-16, 1997.","title":"Postwar US business cycles: an empirical investigation","authors":"J Robert, Edward C Hodrick, Prescott","year":"1997","venue":"Journal of Money, Credit, and Banking","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Huber and Ronchetti, 2009] Peter J. Huber and Elvezio M. Ronchetti. Robust statistics. John Wiley & Sons, New Jersey, 2nd edition, 2009.","title":"Robust statistics","authors":"J Peter, Elvezio M Huber, Ronchetti","year":"2009","venue":null,"doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Kim et al., 2009] Seung-Jean Kim, Kwangmoo Koh, Stephen Boyd, and Dimitry Gorinevsky. ℓ 1 trend filtering. SIAM Review, 51(2):339-360, 2009.","title":"ℓ 1 trend filtering","authors":"Seung-Jean Kim, Kwangmoo Koh, Stephen Boyd, Dimitry Gorinevsky","year":"2009","venue":"SIAM Review","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Moghtaderi et al., 2011] Azadeh Moghtaderi, Pierre Borgnat, and Patrick Flandrin. Trend filtering: empirical mode decompositions versus ℓ 1 and Hodrick-Prescott. Advances in Adaptive Data Analysis, 3(01n02):41-61, 2011.","title":"Trend filtering: empirical mode decompositions versus ℓ 1 and Hodrick-Prescott","authors":"Azadeh Moghtaderi, Pierre Borgnat, Patrick Flandrin","year":"2011","venue":"Advances in Adaptive Data Analysis","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Papafitsoros and Schönlieb, 2014] Konstantinos Papafit- soros and Carola-Bibiane Schönlieb. A combined first and second order variational approach for image recon- struction. Journal of Mathematical Imaging and Vision, 48(2):308-338, Feb 2014.","title":"A combined first and second order variational approach for image reconstruction","authors":"Konstantinos Papafitsoros, Carola-Bibiane Schönlieb","year":"2014","venue":"Journal of Mathematical Imaging and Vision","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Pham and Venkatesh, 2013] Duc-Son Pham and Svetha Venkatesh. Efficient algorithms for robust recovery of im- ages from compressed data. IEEE transactions on image processing, 22(12):4724-4737, 2013.","title":"Efficient algorithms for robust recovery of images from compressed data","authors":"Venkatesh ; Duc-Son Pham, Svetha Pham, Venkatesh","year":"2013","venue":"IEEE transactions on image processing","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Polson and Scott, 2016] Nicholas G Polson and James G Scott. Mixtures, envelopes and hierarchical duality. Jour- nal of the Royal Statistical Society: Series B (Statistical Methodology), 78(4):701-727, 2016.","title":"Mixtures, envelopes and hierarchical duality","authors":"G Nicholas, James G Polson, Scott","year":"2016","venue":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Ramdas and Tibshirani, 2016] Aaditya Ramdas and Ryan J Tibshirani. Fast and flexible ADMM algorithms for trend filtering. Journal of Computational and Graphical Statis- tics, 25(3):839-858, 2016.","title":"Fast and flexible ADMM algorithms for trend filtering","authors":"Aaditya Ramdas, Ryan J Tibshirani","year":"2016","venue":"Journal of Computational and Graphical Statistics","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Siegel, 1982] Andrew F Siegel. Robust regression using re- peated medians. Biometrika, 69(1):242-244, 1982.","title":"Robust regression using repeated medians","authors":"F Andrew, Siegel","year":"1982","venue":"Biometrika","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Sun et al., 2017] Ying Sun, Prabhu Babu, and Daniel P Palomar. Majorization-minimization algorithms in signal processing, communications, and machine learning. IEEE Transactions on Signal Processing, 65(3):794-816, Feb 2017.","title":"Majorization-minimization algorithms in signal processing, communications, and machine learning","authors":"Ying Sun, Prabhu Babu, Daniel P Palomar","year":"2017","venue":"IEEE Transactions on Signal Processing","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Tibshirani et al., 2005] Robert Tibshirani, Michael Saun- ders, Saharon Rosset, Ji Zhu, and Keith Knight. Spar- sity and smoothness via the fused lasso. Journal of the Royal Statistical Society: Series B (Statistical Methodol- ogy), 67(1):91-108, 2005.","title":"Sparsity and smoothness via the fused lasso","authors":"Robert Tibshirani, Michael Saunders, Saharon Rosset, Ji Zhu, Keith Knight","year":"2005","venue":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Tibshirani, 2014] Ryan Tibshirani. Adaptive piecewise polynomial estimation via trend filtering. The Annals of Statistics, 42(1):285-323, 2014.","title":"Adaptive piecewise polynomial estimation via trend filtering","authors":"Ryan Tibshirani","year":"2014","venue":"The Annals of Statistics","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Wang et al., 2007] Hansheng Wang, Guodong Li, and Guo- hua Jiang. Robust regression shrinkage and consistent variable selection through the LAD-Lasso. Journal of Business & Economic Statistics, 25(3):347-355, 2007.","title":"Robust regression shrinkage and consistent variable selection through the LAD-Lasso","authors":"Wang","year":"2007","venue":"Journal of Business & Economic Statistics","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Wen et al., 2019] Qingsong Wen, Jingkun Gao, Xiaomin Song, Liang Sun, Huan Xu, and Shenghuo Zhu. Robust- STL: A robust seasonal-trend decomposition algorithm for long time series. In AAAI, pages 1501-1509, 2019.","title":"Robust-STL: A robust seasonal-trend decomposition algorithm for long time series","authors":"Qingsong Wen, Jingkun Gao, Xiaomin Song, Liang Sun, Huan Xu, Shenghuo Zhu","year":"2019","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Wu and Huang, 2009] Zhaohua Wu and Norden E Huang. Ensemble empirical mode decomposition: a noise-assisted data analysis method. Advances in Adaptive Data Analy- sis, 1(01):1-41, 2009.","title":"Ensemble empirical mode decomposition: a noise-assisted data analysis method","authors":"Huang ; ] Zhaohua Wu, Norden E Wu, Huang","year":"2009","venue":"Advances in Adaptive Data Analysis","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Wu et al., 2007] Zhaohua Wu, Norden E Huang, Steven R Long, and Chung-Kang Peng. On the trend, detrending, and variability of nonlinear and nonstationary time se- ries. Proceedings of the National Academy of Sciences, 104(38):14889-14894, 2007.","title":"On the trend, detrending, and variability of nonlinear and nonstationary time series","authors":"Zhaohua Wu, Norden E Huang, Steven R Long, Chung-Kang Peng","year":"2007","venue":"Proceedings of the National Academy of Sciences","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}