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## Response surface modeling

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In this chapter, we discuss several state-of-the-art RSM methods for performance modeling of analog and AMS circuits. RSM aims to approximate a given PoI by the linear combination of a set of basis functions. If the number of training samples is much larger than the number of adopted basis functions, the model coefficients can be accurately estimated by using LS regression. To reduce the number of required training samples and, hence, the modeling cost, we can explore the sparsity of model coefficients and, next, cast performance modeling to an L0-norm regularization problem. Both OMP and L1-norm regularization can be used to efficiently approximate the sparse solution of L0-norm regularization. Alternatively, based on the observation that today's AMS circuits are often designed via a multistage fl ow, BMF attempts to reduce the modeling cost by fusing the early -stage and late -stage data together through Bayesian inference. As an important aspect of future research, a number of recently developed machine learning techniques, such as deep learning, maybe further adopted for RSM for AMS applications.

Chapter Contents:

• 2.1 Introduction
• 2.2 Problem formulation
• 2.3 Least-squares regression
• 2.4 Feature selection
• 2.4.1 Orthogonal matching pursuit
• 2.4.2 L1-norm regularization
• 2.4.3 Cross-validation
• 2.4.4 Least angle regression
• 2.4.5 Numerical experiments
• 2.5 Regularization
• 2.6 Bayesian model fusion
• 2.6.1 Zero-mean prior distribution
• 2.6.2 Nonzero-mean prior distribution
• 2.6.3 Numerical experiments
• 2.7 Summary
• Acknowledgments
• References

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