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Beyond loworder statistical response surfaces: latent variable regression for efficient, highly nonlinear fitting
 IEEE DAC
, 2007
"... The number and magnitude of process variation sources are increasing as we scale further into the nano regime. Today’s most successful response surface methods limit us to loworder forms linear, quadratic to make the fitting tractable. Unfortunately, not all variational scenarios are well model ..."
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Cited by 9 (1 self)
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The number and magnitude of process variation sources are increasing as we scale further into the nano regime. Today’s most successful response surface methods limit us to loworder forms linear, quadratic to make the fitting tractable. Unfortunately, not all variational scenarios are well modeled with loworder surfaces. We show how to exploit latent variable regression ideas to support efficient extraction of arbitrarily nonlinear statistical response surfaces. An implementation of these ideas called SiLVR, applied to a range of analog and digital circuits, in technologies from 90 to 45nm, shows significant improvements in prediction, with errors reduced by up to 21X, with very reasonable runtime costs.
Biplots in reducedrank regression
 Biom. J
, 1994
"... SUMMARY Regression problems with a number of related response variables are typically analyzed by separate multiple regressions. This paper shows how these regressions can be visualized jointly in a biplot based on reducedrank regression. Reducedrank regression combines multiple regression and pri ..."
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Cited by 5 (0 self)
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SUMMARY Regression problems with a number of related response variables are typically analyzed by separate multiple regressions. This paper shows how these regressions can be visualized jointly in a biplot based on reducedrank regression. Reducedrank regression combines multiple regression and principal components analysis and can therefore be carried out with standard statistical packages. The proposed biplot highlights the major aspects of the regressions by displaying the leastsquares approximation of fitted values, regression coefficients and associated tratio's. The utility and interpretation of the reducedrank regression biplot is demonstrated with an example using public health data that were previously analyzed by separate multiple regressions.
Interpreting canonical correlation analysis through biplots of structural correlations and weights
 Psychometrika
, 1990
"... This paper extends the biplot technique to canonical correlation analysis and redundancy analysis, The plot of structure correlations is shown to be optimal for displaying the pairwise correlations between the variables of the one set and those of the second. The link between multivariate regression ..."
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Cited by 5 (1 self)
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This paper extends the biplot technique to canonical correlation analysis and redundancy analysis, The plot of structure correlations is shown to be optimal for displaying the pairwise correlations between the variables of the one set and those of the second. The link between multivariate regression and canonical correlation analysis/redundancy analysis is exploited for producing an optimal biplot that displays a matrix of regression coefficients. This plot can be made from the canonical weights of the predictors and the structure correlations of the criterion variables. An example is used to show how the proposed biptots may be interpreted. Key words: biplot, canonical correlation analysis, canonical weight, interbattery factor analysis, partial analysis, redundancy analysis, regression coefficient, reduced rank regression, structure correlations.
Multidimensional scaling and regression
 Statistica Applicata
, 1992
"... Constrained multidimensional scaling was put on a firm theoretical basis by Jan De Leeuw and Willem Heiser in the 1980's. There is a simple method of fitting, based on distance via innerproducts, and a numerically more complicated one that is truly based on leastsquares on distances. The unconstrai ..."
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Constrained multidimensional scaling was put on a firm theoretical basis by Jan De Leeuw and Willem Heiser in the 1980's. There is a simple method of fitting, based on distance via innerproducts, and a numerically more complicated one that is truly based on leastsquares on distances. The unconstrained forms are known as principal coordinate analysis and nonmetric multidimensional scaling, respectively. Constraining the solution by external variables brings the power of classical regression analysis back into multidimensional data analysis. This idea is developed and illustrated, with emphasis on constrained principal coordinate analysis.
Novel Algorithms for Fast Statistical Analysis of Scaled Circuits
, 2007
"... As VLSI technology moves to the nanometer scale for transistor feature sizes, the impact of manufacturing imperfections result in large variations in the circuit performance. Traditional CAD tools are not wellequipped to handle this scenario, since they do not model this statistical nature of the c ..."
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As VLSI technology moves to the nanometer scale for transistor feature sizes, the impact of manufacturing imperfections result in large variations in the circuit performance. Traditional CAD tools are not wellequipped to handle this scenario, since they do not model this statistical nature of the circuit parameters and performances, or if they do, the existing techniques tend to be oversimplified or intractably slow. We draw upon ideas for attacking parallel problems in other technical fields, such as computational finance, machine learning and hydrology, and synthesize them with innovative attacks for our problem domain of integrated circuits, to develop novel solutions to problems of efficient statistical analysis of circuits in the nanometer regime. In particular, this thesis makes three contributions: 1) SiLVR, a nonlinear response surface modeling (RSM) and performancedriven dimensionality reduction strategy, that uses the concepts of projection pursuit and latent variable regression to obtain an absolute improvement in modeling error of up to 34% over the best quadratic RSM method. SiLVR also captures the designer’s insight into the circuit behavior, by automatically extracting quantitative measures of relative
A Markov Chain Monte Carlo Method for Approximating 2Way Contingency Tables with Applications in the Stability Analysis of Ecological Ordination
, 1999
"... OF THE DISSERTATION A Markov Chain Monte Carlo Method for Approximating 2Way Contingency Tables with Applications in the Stability Analysis of Ecological Ordination by Stanley S. Bentow Doctor of Philosophy in Statistics University of California, Los Angeles, 1999 Professor N. Donald Ylvisaker, ..."
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OF THE DISSERTATION A Markov Chain Monte Carlo Method for Approximating 2Way Contingency Tables with Applications in the Stability Analysis of Ecological Ordination by Stanley S. Bentow Doctor of Philosophy in Statistics University of California, Los Angeles, 1999 Professor N. Donald Ylvisaker, Chair This dissertation develops a Markov Chain Monte Carlo method for approximating 2way contingency tables with an eye toward assessing the stability of ecological ordination. Ecology is a part of biology that deals with the interrelationships between populations, communities and ecosystems and their environment. It draws on knowledge from many other disciplines such as climatology, physical geography, agronomy, and pedology [52]. Odum [75] prefers the de nition \ Ecology is the study of structure and function of nature," and stresses the role of ecosystem research in relation to the use of nature by man. Krebs [58] prefers to think of Ecology as the scienti c study of the interactions t...