Skip to main content

Fast Statistical Analysis Using Machine Learning

  • Chapter
  • First Online:
  • 2946 Accesses

Abstract

In this chapter, we describe a fast statistical yield analysis methodology for memory design. At the heart of its engine is a mixture importance sampling-based methodology which comprises a uniform sampling stage and an importance sampling stage. Logistic regression-based machine learning techniques are employed for modeling the circuit response and speeding up the importance sample points simulations. To avoid overfitting, we rely on a cross-validation-based regularization framework for ordered feature selection. The methodology is comprehensive and computationally efficient. We demonstrate the methodology on an industrial state-of-the-art 14 nm FinFET SRAM design with write-assist circuitry. The results corroborate well with hardware and with the fully circuit-simulation-based approach.

A model is a simplification or approximation of reality and hence will not reflect all of reality Kenneth P. Burnham David R. Anderson

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. X. Li, H. Liu, Statistical regression for efficient high-dimensional modeling of analog and mixed-signal performance variations, in Design Automation Conference, 2008. DAC 2008. 45th ACM/IEEE (IEEE, New York, 2008), pp. 38–43

    Google Scholar 

  2. K. Agarwal, S, Nassif, Statistical analysis of SRAM cell stability, in Proceedings of the 43rd annual Design Automation Conference (ACM, New York, 2006), pp. 57–62

    Google Scholar 

  3. S. Mukhopadhyay, H. Mahmoodi, K. Roy, Statistical design and optimization of SRAM cell for yield enhancement, in Proceedings of the 2004 IEEE/ACM International Conference on Computer-Aided Design (IEEE Computer Society, Washington, DC, 2004), pp. 10–13

    Google Scholar 

  4. A. Singhee, R.A. Rutenbar, Statistical blockade: a novel method for very fast Monte Carlo simulation of rare circuit events, and its application, in Design, Automation, and Test in Europe (Springer, New York, 2008), pp. 235–251

    Google Scholar 

  5. R. Kanj, R. Joshi, S. Nassif, Mixture importance sampling and its application to the analysis of SRAM designs in the presence of rare failure events, in Design Automation Conference, 2006 43rd ACM/IEEE (IEEE, New York, 2006), pp. 69–72

    Google Scholar 

  6. R. Kanj, T. Li, R. Joshi, K. Agarwal, A. Sadigh, D. Winston, S. Nassif, Accelerated statistical simulation via on-demand Hermite spline interpolations, in Proceedings of the International Conference on Computer-Aided Design (IEEE Press, New York, 2011), pp. 353–360

    Google Scholar 

  7. M. Malik, R.V. Joshi, R. Kanj, S. Sun, H. Homayoun, T. Li, Sparse regression driven mixture importance sampling for memory design, in IEEE Transactions on Very Large Scale Integration (VLSI) Systems (2017)

    Google Scholar 

  8. L. Shaer, R. Kanj, R. Joshi, M. Malik, A. Chehab, Regularized logistic regression for fast importance sampling based SRAM yield analysis, in 2017 18th International Symposium on Quality Electronic Design (ISQED) (IEEE, New York, 2017), pp. 119–124

    Google Scholar 

  9. G.E.P. Box, J. Stuart Hunter, W. Gordon Hunter, Statistics for Experimenters: Design, Innovation, and Discovery, vol. 2 (Wiley, New York, 2005)

    MATH  Google Scholar 

  10. J.F. Ramaley, Buffon’s noodle problem. Am. Math. Mon. 76(8), 916–918 (1969)

    Article  MathSciNet  Google Scholar 

  11. N. Metropolis, S. Ulam, The Monte Carlo method. J. Am. Stat. Assoc. 44(247), 335–341 (1949)

    Article  Google Scholar 

  12. C.P. Robert. Monte Carlo Methods (Wiley Online Library, 2004)

    Google Scholar 

  13. T.C. Hesterberg, Advances in importance sampling, PhD Thesis, 1988

    Google Scholar 

  14. D.W Hosmer Jr., S. Lemeshow, R.X. Sturdivant, Applied Logistic Regression, vol. 398 (Wiley, New York, 2013)

    Google Scholar 

  15. A. Mojsilovic, A logistic regression model for small sample classification problems with hidden variables and non-linear relationships: an application in business analytics, in IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005. Proceedings (ICASSP’05), vol. 5 (IEEE, New York, 2005), pp. v–329

    Google Scholar 

  16. S. Ahmad, N.M. Ramli, H. Midi, Outlier detection in logistic regression and its application in medical data analysis, in 2012 IEEE Colloquium on Humanities, Science and Engineering (CHUSER) (IEEE, New York, 2012), pp. 503–507

    Google Scholar 

  17. R.S. Collica, A logistic regression yield model for SRAM bit fail patterns, in The IEEE International Workshop on Defect and Fault Tolerance in VLSI Systems, 1993 (IEEE, New York, 1993), pp. 127–135

    Google Scholar 

  18. X. Li, H. Liu, Statistical regression for efficient high-dimensional modeling of analog and mixed-signal performance variations, in Design Automation Conference, 2008. DAC 2008. 45th ACM/IEEE (IEEE, New York, 2008), pp. 38–43

    Google Scholar 

  19. A. Ng, Cs229 lecture notes (2017). Retrieved from http://cs229.stanford.edu/notes/cs229-notes-all/

  20. X. Li, Finding deterministic solution from underdetermined equation: large-scale performance variability modeling of analog/RF circuits. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 29(11), 1661–1668 (2010)

    Article  Google Scholar 

  21. D. Böhning, Multinomial logistic regression algorithm. Ann. Inst. Stat. Math. 44(1), 197–200 (1992)

    Article  Google Scholar 

  22. D.T, Larose, Data Mining Methods & Models (Wiley, New York, 2006)

    Google Scholar 

  23. T.P. Minka, A comparison of numerical optimizers for logistic regression, Unpublished draft (2003)

    Google Scholar 

  24. S.-I. Lee, H. Lee, P. Abbeel, A.Y. Ng, Efficient L1 regularized logistic regression, in AAAI, vol. 6 (2006), pp. 401–408

    Google Scholar 

  25. S. Perkins, J. Theiler, Online feature selection using grafting, in Proceedings of the 20th International Conference on Machine Learning (ICML-03) (2003), pp. 592–599

    Google Scholar 

  26. R. Kohavi et al., A study of cross-validation and bootstrap for accuracy estimation and model selection. in Proceedings of International Joint Conference on Artificial Intelligence, IJCAI, Stanford, CA, vol. 14 (1995), pp. 1137–1145

    Google Scholar 

  27. R.V. Joshi, M. Ziegler, H. Wetter, C. Wandel, H, Ainspan, 14nm finfet based supply voltage boosting techniques for extreme low v min operation, in 2015 Symposium on VLSI Circuits (VLSI Circuits) (IEEE, Piscataway, 2015), pp. C268–C269

    Book  Google Scholar 

  28. R.V. Joshi, M.M. Ziegler, Programmable supply boosting techniques for near threshold and wide operating voltage SRAM, in 2017 IEEE Custom Integrated Circuits Conference (CICC) (IEEE, Piscataway, 2017), pp. 1–4

    Google Scholar 

  29. R. Joshi, R. Kanj, S. Nassif, D. Plass, Y. Chan et al., Statistical exploration of the dual supply voltage space of a 65nm PD/SOI CMOS SRAM cell, in Proceeding of the 36th European Solid-State Device Research Conference, 2006. ESSDERC 2006 (IEEE, Piscataway, 2006), pp. 315–318

    Google Scholar 

Download references

Acknowledgements

The authors would like to thank the Maroun Semaan Faculty of Engineering and Architecture at the American University of Beirut for supporting Ph.D. student Miss Lama Shaer.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Rouwaida Kanj .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Kanj, R., Joshi, R.V., Shaer, L., Chehab, A., Malik, M. (2019). Fast Statistical Analysis Using Machine Learning. In: Elfadel, I., Boning, D., Li, X. (eds) Machine Learning in VLSI Computer-Aided Design. Springer, Cham. https://doi.org/10.1007/978-3-030-04666-8_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-04666-8_11

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-04665-1

  • Online ISBN: 978-3-030-04666-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics