IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i23p3091-d692124.html
   My bibliography  Save this article

Iterative Algorithm for Parameterization of Two-Region Piecewise Uniform Quantizer for the Laplacian Source

Author

Listed:
  • Jelena Nikolić

    (Faculty of Electronic Engineering, University of Nis, Aleksandra Medvedeva 14, 18000 Nis, Serbia)

  • Danijela Aleksić

    (Department of Mobile Network Nis, Telekom Srbija, Vozdova 11, 18000 Nis, Serbia)

  • Zoran Perić

    (Faculty of Electronic Engineering, University of Nis, Aleksandra Medvedeva 14, 18000 Nis, Serbia)

  • Milan Dinčić

    (Faculty of Electronic Engineering, University of Nis, Aleksandra Medvedeva 14, 18000 Nis, Serbia)

Abstract

Motivated by the fact that uniform quantization is not suitable for signals having non-uniform probability density functions (pdfs), as the Laplacian pdf is, in this paper we have divided the support region of the quantizer into two disjunctive regions and utilized the simplest uniform quantization with equal bit-rates within both regions. In particular, we assumed a narrow central granular region (CGR) covering the peak of the Laplacian pdf and a wider peripheral granular region (PGR) where the pdf is predominantly tailed. We performed optimization of the widths of CGR and PGR via distortion optimization per border–clipping threshold scaling ratio which resulted in an iterative formula enabling the parametrization of our piecewise uniform quantizer (PWUQ). For medium and high bit-rates, we demonstrated the convenience of our PWUQ over the uniform quantizer, paying special attention to the case where 99.99% of the signal amplitudes belong to the support region or clipping region. We believe that the resulting formulas for PWUQ design and performance assessment are greatly beneficial in neural networks where weights and activations are typically modelled by the Laplacian distribution, and where uniform quantization is commonly used to decrease memory footprint.

Suggested Citation

  • Jelena Nikolić & Danijela Aleksić & Zoran Perić & Milan Dinčić, 2021. "Iterative Algorithm for Parameterization of Two-Region Piecewise Uniform Quantizer for the Laplacian Source," Mathematics, MDPI, vol. 9(23), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3091-:d:692124
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/23/3091/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/23/3091/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. W. R. Gilks & N. G. Best & K. K. C. Tan, 1995. "Adaptive Rejection Metropolis Sampling Within Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(4), pages 455-472, December.
    2. Zoran Perić & Jelena Nikolić & Danijela Aleksić & Anastasija Perić, 2021. "Symmetric Quantile Quantizer Parameterization for the Laplacian Source: Qualification for Contemporary Quantization Solutions," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-12, February.
    3. W. R. Gilks & P. Wild, 1992. "Adaptive Rejection Sampling for Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 337-348, June.
    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. Zoran Perić & Danijela Aleksić & Jelena Nikolić & Stefan Tomić, 2022. "Two Novel Non-Uniform Quantizers with Application in Post-Training Quantization," Mathematics, MDPI, vol. 10(19), pages 1-21, September.

    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. H. Abebe & F. Tan & G. Breukelen & M. Berger, 2014. "Robustness of Bayesian D-optimal design for the logistic mixed model against misspecification of autocorrelation," Computational Statistics, Springer, vol. 29(6), pages 1667-1690, December.
    2. Yu Yue & Paul Speckman & Dongchu Sun, 2012. "Priors for Bayesian adaptive spline smoothing," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 577-613, June.
    3. Hazan, Alon & Landsman, Zinoviy & E Makov, Udi, 2003. "Robustness via a mixture of exponential power distributions," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 111-121, February.
    4. Cappuccio Nunzio & Lubian Diego & Raggi Davide, 2004. "MCMC Bayesian Estimation of a Skew-GED Stochastic Volatility Model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-31, May.
    5. Xiao Li & Michele Guindani & Chaan S. Ng & Brian P. Hobbs, 2021. "A Bayesian nonparametric model for textural pattern heterogeneity," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(2), pages 459-480, March.
    6. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    7. Chunling Wang & Xiaoyan Lin, 2022. "Bayesian Semiparametric Regression Analysis of Multivariate Panel Count Data," Stats, MDPI, vol. 5(2), pages 1-17, May.
    8. White, Gentry & Porter, Michael D., 2014. "GPU accelerated MCMC for modeling terrorist activity," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 643-651.
    9. Meyer, Renate & Cai, Bo & Perron, François, 2008. "Adaptive rejection Metropolis sampling using Lagrange interpolation polynomials of degree 2," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3408-3423, March.
    10. Neville Francis & Laura E. Jackson & Michael T. Owyang, 2018. "Countercyclical Policy and the Speed of Recovery after Recessions," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 50(4), pages 675-704, June.
    11. Helio Migon & Alexandra Schmidt & Romy Ravines & João Pereira, 2013. "An efficient sampling scheme for dynamic generalized models," Computational Statistics, Springer, vol. 28(5), pages 2267-2293, October.
    12. Cai, Bo & Lin, Xiaoyan & Wang, Lianming, 2011. "Bayesian proportional hazards model for current status data with monotone splines," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2644-2651, September.
    13. Huaiye Zhang & Inyoung Kim, 2016. "Adaptive Rejection Metropolis Simulated Annealing for Detecting Global Maximum Regions," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 1-19, March.
    14. Mazucheli, Josmar & Louzada-Neto, Francisco & Achcar, Jorge A., 2001. "Bayesian inference for polyhazard models in the presence of covariates," Computational Statistics & Data Analysis, Elsevier, vol. 38(1), pages 1-14, November.
    15. Pan, Chun & Cai, Bo & Wang, Lianming & Lin, Xiaoyan, 2014. "Bayesian semiparametric model for spatially correlated interval-censored survival data," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 198-208.
    16. Yi-Ping Chang & Chih-Tun Yu, 2014. "Bayesian confidence intervals for probability of default and asset correlation of portfolio credit risk," Computational Statistics, Springer, vol. 29(1), pages 331-361, February.
    17. Gareth W. Peters & Pavel V. Shevchenko & Mario V. Wuthrich, 2009. "Dynamic operational risk: modeling dependence and combining different sources of information," Papers 0904.4074, arXiv.org, revised Jul 2009.
    18. Abebe, Haftom T. & Tan, Frans E.S. & Van Breukelen, Gerard J.P. & Berger, Martijn P.F., 2014. "Bayesian D-optimal designs for the two parameter logistic mixed effects model," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1066-1076.
    19. England, Peter, 2002. "Addendum to "Analytic and bootstrap estimates of prediction errors in claims reserving"," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 461-466, December.
    20. Pang, W. K. & Yang, Z. H. & Hou, S. H. & Leung, P. K., 2002. "Non-uniform random variate generation by the vertical strip method," European Journal of Operational Research, Elsevier, vol. 142(3), pages 595-609, November.

    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:9:y:2021:i:23:p:3091-:d:692124. 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.