Xin Li
ABSTRACT
The continuous technology scaling brings about high-dimensional performance variations that cannot be easily captured by the traditional response surface modeling. In this paper we propose a new statistical regression (STAR) technique that applies a novel strategy to address this high dimensionality issue. Unlike most traditional response surface modeling techniques that solve model coefficients from over-determined linear equations, STAR determines all unknown coefficients by moment matching. As such, a large number of (e.g., 103~105) model coefficients can be extracted from a small number of (e.g., 102~103) sampling points without over-fitting. In addition, a novel recursive estimator is proposed to accurately and efficiently predict the moment values. The proposed recursive estimator is facilitated by exploiting the interaction between different moment estimators and formulating the moment estimation problem into a special form that can be iteratively solved. Several circuit examples designed in commercial CMOS processes demonstrate that STAR achieves more than 20x runtime speedup compared with the traditional response surface modeling.
- Semiconductor Industry Associate, International Technology Roadmap for Semiconductors, 2005.Google Scholar
- Dharchoudhury and S. Kang, "Worse-case analysis and optimization of VLSI circuit performance," IEEE Trans. CAD, vol. 14, no. 4, pp. 481--492, Apr. 1995. Google ScholarDigital Library
- F. Schenkel, M. Pronath, S. Zizala, R. Schwencker, H. Graeb and K. Antreich, "Mismatch analysis and direct yield optimization by spec-wise linearization and feasibility-guided search," IEEE DAC, pp. 858--863, 2001. Google ScholarDigital Library
- X. Li, J. Le, P. Gopalakrishnan and L. Pileggi, "Asymptotic probability extraction for nonnormal performance distributions," IEEE TCAD, vol. 26, no. 1, pp. 16--37, Jan. 2007. Google ScholarDigital Library
- X. Li, J. Le, L. Pileggi and A. Strojwas, "Projection-based performance modeling for inter/intra-die variations," IEEE ICCAD, pp. 721--727, 2005. Google ScholarDigital Library
- Z. Feng and P. Li, "Performance-oriented statistical parameter reduction of parameterized systems via reduced rank regression," IEEE ICCAD, pp. 868--875, 2006. Google ScholarDigital Library
- A. Singhee and R. Rutenbar, "Beyond low-order statistical response surfaces: latent variable regression for efficient, highly nonlinear fitting," IEEE DAC, pp. 256--261, 2007. Google ScholarDigital Library
- A. Mitev, M. Marefat, D. Ma and J. Wang, "Principle Hessian direction based parameter reduction for interconnect networks with process variation," IEEE ICCAD, pp. 632--637, 2007. Google ScholarDigital Library
- I. Guyon and A. Elisseeff, "An introduction to variable and feature selection," Journal of Machine Learning Research, vol. 3, pp. 1157--1182, 2003. Google ScholarDigital Library
- G. Seber, Multivariate Observations, Wiley Series, 1984.Google Scholar
- A. Papoulis and S. Pillai, Probability, Random Variables and Stochastic Processes, McGraw-Hill, 2001.Google Scholar
- R. Myers and D. Montgomery, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Wiley-Interscience, 2002. Google ScholarDigital Library
- T. Hastie, R. Tibshirani and J. Friedman, The Elements of Statistical Learning, Springer, 2003.Google Scholar
- G. Sansone, Orthogonal Functions, Dover Publications, 2004.Google Scholar
- S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004. Google ScholarDigital Library
- D. Montgomery, Design and Analysis of Experiments, John Wiley & Sons, 2005. Google ScholarDigital Library
Index Terms
- Statistical regression for efficient high-dimensional modeling of analog and mixed-signal performance variations
Recommendations
Projection-Based Piecewise-Linear Response Surface Modeling for Strongly Nonlinear VLSI Performance Variations
ISQED '08: Proceedings of the 9th international symposium on Quality Electronic DesignLarge-scale process fluctuations (particularly random device mismatches) at nanoscale technologies bring about high-dimensional strongly nonlinear performance variations that cannot be accurately captured by linear or quadratic response surface models. ...
Enhanced algorithm for high-dimensional data classification
Graphical abstractIllustration of the decision hyperplanes generated by TSSVM, MCVSVM, and LMLP on an artificial dataset. Display Omitted HighlightsIn the case of the singularity of the within-class scatter matrix, the drawbacks of both MCVSVM and LMLP ...
Constrained discriminant neighborhood embedding for high dimensional data feature extraction
When handling pattern classification problem such as face recognition and digital handwriting identification, image data is always represented to high dimensional vectors, from which discriminant features are extracted using dimensionality reduction ...
Comments