IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i11p1942-d439496.html
   My bibliography  Save this article

Variational Inference over Nonstationary Data Streams for Exponential Family Models

Author

Listed:
  • Andrés R. Masegosa

    (Department of Mathematics and Center for Development and Transfer of Mathematical Research to Industry (CDTIME), University of Almería, 04120 Almería, Spain)

  • Darío Ramos-López

    (Department of Applied Mathematics, Materials Science and Engineering, and Electronic Technology, Rey Juan Carlos University, 28933 Móstoles, Spain)

  • Antonio Salmerón

    (Department of Mathematics and Center for Development and Transfer of Mathematical Research to Industry (CDTIME), University of Almería, 04120 Almería, Spain)

  • Helge Langseth

    (Department of Computer Science, Norwegian University of Science and Technology, 7491 Trondheim, Norway)

  • Thomas D. Nielsen

    (Department of Computer Science, Aalborg University, 9220 Aalborg, Denmark)

Abstract

In many modern data analysis problems, the available data is not static but, instead, comes in a streaming fashion. Performing Bayesian inference on a data stream is challenging for several reasons. First, it requires continuous model updating and the ability to handle a posterior distribution conditioned on an unbounded data set. Secondly, the underlying data distribution may drift from one time step to another, and the classic i.i.d. (independent and identically distributed), or data exchangeability assumption does not hold anymore. In this paper, we present an approximate Bayesian inference approach using variational methods that addresses these issues for conjugate exponential family models with latent variables. Our proposal makes use of a novel scheme based on hierarchical priors to explicitly model temporal changes of the model parameters. We show how this approach induces an exponential forgetting mechanism with adaptive forgetting rates. The method is able to capture the smoothness of the concept drift, ranging from no drift to abrupt drift. The proposed variational inference scheme maintains the computational efficiency of variational methods over conjugate models, which is critical in streaming settings. The approach is validated on four different domains (energy, finance, geolocation, and text) using four real-world data sets.

Suggested Citation

  • Andrés R. Masegosa & Darío Ramos-López & Antonio Salmerón & Helge Langseth & Thomas D. Nielsen, 2020. "Variational Inference over Nonstationary Data Streams for Exponential Family Models," Mathematics, MDPI, vol. 8(11), pages 1-27, November.
  • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1942-:d:439496
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/11/1942/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/8/11/1942/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. David M. Blei & Alp Kucukelbir & Jon D. McAuliffe, 2017. "Variational Inference: A Review for Statisticians," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 859-877, April.
    2. Ibrahim J.G. & Chen M-H. & Sinha D., 2003. "On Optimality Properties of the Power Prior," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 204-213, January.
    3. Michael E. Tipping & Christopher M. Bishop, 1999. "Probabilistic Principal Component Analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 611-622.
    4. Kostas Triantafyllopoulos, 2009. "Inference of Dynamic Generalized Linear Models: On‐Line Computation and Appraisal," International Statistical Review, International Statistical Institute, vol. 77(3), pages 430-450, December.
    5. Xi Chen & Kaoru Irie & David Banks & Robert Haslinger & Jewell Thomas & Mike West, 2018. "Scalable Bayesian Modeling, Monitoring, and Analysis of Dynamic Network Flow Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 519-533, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wang, Yu & Liu, Qiufa & Lu, Wenjian & Peng, Yizhen, 2023. "A general time-varying Wiener process for degradation modeling and RUL estimation under three-source variability," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    2. Antonio Salmerón, 2022. "Comments on: Hybrid semiparametric Bayesian networks," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 331-334, June.
    3. Krzysztof Drachal & Daniel González Cortés, 2022. "Estimation of Lockdowns’ Impact on Well-Being in Selected Countries: An Application of Novel Bayesian Methods and Google Search Queries Data," IJERPH, MDPI, vol. 20(1), pages 1-24, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. José A. Perusquía & Jim E. Griffin & Cristiano Villa, 2022. "Bayesian Models Applied to Cyber Security Anomaly Detection Problems," International Statistical Review, International Statistical Institute, vol. 90(1), pages 78-99, April.
    2. Mike West, 2020. "Bayesian forecasting of multivariate time series: scalability, structure uncertainty and decisions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 1-31, February.
    3. Wang, Zihan & Daeipour, Mohamad & Xu, Hongyi, 2023. "Quantification and propagation of Aleatoric uncertainties in topological structures," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    4. Shen Liu & Hongyan Liu, 2021. "Tagging Items Automatically Based on Both Content Information and Browsing Behaviors," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 882-897, July.
    5. Matteo Barigozzi & Matteo Luciani, 2019. "Quasi Maximum Likelihood Estimation and Inference of Large Approximate Dynamic Factor Models via the EM algorithm," Papers 1910.03821, arXiv.org, revised Sep 2024.
    6. Xin Xu & Yang Lu & Yupeng Zhou & Zhiguo Fu & Yanjie Fu & Minghao Yin, 2021. "An Information-Explainable Random Walk Based Unsupervised Network Representation Learning Framework on Node Classification Tasks," Mathematics, MDPI, vol. 9(15), pages 1-14, July.
    7. Dorota Toczydlowska & Gareth W. Peters & Man Chung Fung & Pavel V. Shevchenko, 2017. "Stochastic Period and Cohort Effect State-Space Mortality Models Incorporating Demographic Factors via Probabilistic Robust Principal Components," Risks, MDPI, vol. 5(3), pages 1-77, July.
    8. Loaiza-Maya, Rubén & Smith, Michael Stanley & Nott, David J. & Danaher, Peter J., 2022. "Fast and accurate variational inference for models with many latent variables," Journal of Econometrics, Elsevier, vol. 230(2), pages 339-362.
    9. Luo, Nanyu & Ji, Feng & Han, Yuting & He, Jinbo & Zhang, Xiaoya, 2024. "Fitting item response theory models using deep learning computational frameworks," OSF Preprints tjxab, Center for Open Science.
    10. Matteo Barigozzi & Marc Hallin, 2023. "Dynamic Factor Models: a Genealogy," Papers 2310.17278, arXiv.org, revised Jan 2024.
    11. Chen, Tao & Martin, Elaine & Montague, Gary, 2009. "Robust probabilistic PCA with missing data and contribution analysis for outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3706-3716, August.
    12. Chen, Andrew Y. & McCoy, Jack, 2024. "Missing values handling for machine learning portfolios," Journal of Financial Economics, Elsevier, vol. 155(C).
    13. Wang, Shao-Hsuan & Huang, Su-Yun, 2022. "Perturbation theory for cross data matrix-based PCA," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    14. Xing Qin & Shuangge Ma & Mengyun Wu, 2023. "Two‐level Bayesian interaction analysis for survival data incorporating pathway information," Biometrics, The International Biometric Society, vol. 79(3), pages 1761-1774, September.
    15. Cook, R. Dennis, 2022. "A slice of multivariate dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    16. Youngseon Lee & Seongil Jo & Jaeyong Lee, 2022. "A variational inference for the Lévy adaptive regression with multiple kernels," Computational Statistics, Springer, vol. 37(5), pages 2493-2515, November.
    17. Liu, Jie & Ye, Zifeng & Chen, Kun & Zhang, Panpan, 2024. "Variational Bayesian inference for bipartite mixed-membership stochastic block model with applications to collaborative filtering," Computational Statistics & Data Analysis, Elsevier, vol. 189(C).
    18. Nathaniel Tomasetti & Catherine Forbes & Anastasios Panagiotelis, 2019. "Updating Variational Bayes: Fast Sequential Posterior Inference," Monash Econometrics and Business Statistics Working Papers 13/19, Monash University, Department of Econometrics and Business Statistics.
    19. Thomas A. Murray & Brian P. Hobbs & Theodore C. Lystig & Bradley P. Carlin, 2014. "Semiparametric Bayesian commensurate survival model for post-market medical device surveillance with non-exchangeable historical data," Biometrics, The International Biometric Society, vol. 70(1), pages 185-191, March.
    20. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1942-:d:439496. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.