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277 results on '"Rosenberger, Jay"'

7. Global optimization using mixed integer quadratic programming on non-convex two-way interaction truncated linear multivariate adaptive regression splines

Author

Ju, Xinglong, Rosenberger, Jay M., Chen, Victoria C. P., and Liu, Feng

Subjects
Mathematics - Optimization and Control
Abstract

Multivariate adaptive regression splines (MARS) is a flexible statistical modeling method that has been popular for data mining applications. MARS has also been employed to approxmiate unknown relationships in optimzation for complex systems, including surrogate optimization, dynamic programming, and two-stage stochastic programming. Given the increasing desire to optimize real world systems, this paper presents an approach to globally optimize a MARS model that allows up to two-way interaction terms that are products of truncated linear univariate functions (TITL-MARS). Specifally, such a MARS model consists of linear and quadratic structure. This structure is exploited to formulate a mixed integer quadratic programming problem (TITL-MARS-OPT). To appreciate the contribution of TITL-MARS-OPT, one must recognize that popular heurstic optimization approaches, such as evolutionary algorithms, do not guarantee global optimality and can be computationally slow. The use of MARS maintains the flexibility of modeling within TITL-MARS-OPT while also taking advantage of the linear modeling structure of MARS to enable global optimality. Computational results compare TITL-MARS-OPT with a genetic algorithm for two types of cases. First, a wind farm power distribution case study is described and then other TITL-MARS forms are tested. The results show the superiority of TITL-MARS-OPT over the genetic algorithm in both accuracy and computational time.

Published
2020

11. High-dimensional Black-box Optimization Under Uncertainty

Author

Anahideh, Hadis, Rosenberger, Jay, and Chen, Victoria

Subjects
Mathematics - Optimization and Control, Statistics - Methodology, Statistics - Machine Learning
Abstract

Optimizing expensive black-box systems with limited data is an extremely challenging problem. As a resolution, we present a new surrogate optimization approach by addressing two gaps in prior research -- unimportant input variables and inefficient treatment of uncertainty associated with the black-box output. We first design a new flexible non-interpolating parsimonious surrogate model using a partitioning-based multivariate adaptive regression splines approach, Tree Knot MARS (TK-MARS). The proposed model is specifically designed for optimization by capturing the structure of the function, bending at near-optimal locations, and is capable of screening unimportant input variables. Furthermore, we develop a novel replication approach called \emph{Smart-Replication}, to overcome the uncertainty associated with the black-box output. The Smart-Replication approach identifies promising input points to replicate and avoids unnecessary evaluations of other data points. Smart-Replication is agnostic to the choice of a surrogate and can adapt itself to an unknown noise level. Finally to demonstrate the effectiveness of our proposed approaches we consider different complex global optimization test functions from the surrogate optimization literature. The results indicate that TK-MARS outperforms original MARS within a surrogate optimization algorithm and successfully detects important variables. The results also show that although non-interpolating surrogates can mitigate uncertainty, replication is still beneficial for optimizing highly complex black-box functions. The robustness and the quality of the final optimum solution found through Smart-Replication are competitive with that using no replications in environments with low levels of noise and using a fixed number of replications in highly noisy environments.

Published
2019

31. Estimating Latent Brain Sources with Low-Rank Representation and Graph Regularization

Author

Liu, Feng, Wang, Shouyi, Qin, Jing, Lou, Yifei, Rosenberger, Jay, Hutchison, David, Series Editor, Kanade, Takeo, Series Editor, Kittler, Josef, Series Editor, Kleinberg, Jon M., Series Editor, Mattern, Friedemann, Series Editor, Mitchell, John C., Series Editor, Naor, Moni, Series Editor, Pandu Rangan, C., Series Editor, Steffen, Bernhard, Series Editor, Terzopoulos, Demetri, Series Editor, Tygar, Doug, Series Editor, Weikum, Gerhard, Series Editor, Wang, Shouyi, editor, Yamamoto, Vicky, editor, Su, Jianzhong, editor, Yang, Yang, editor, Jones, Erick, editor, Iasemidis, Leon, editor, and Mitchell, Tom, editor

Published
2018
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33. Supervised EEG Source Imaging with Graph Regularization in Transformed Domain

Author

Liu, Feng, Qin, Jing, Wang, Shouyi, Rosenberger, Jay, Su, Jianzhong, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Zeng, Yi, editor, He, Yong, editor, Kotaleski, Jeanette Hellgren, editor, Martone, Maryann, editor, Xu, Bo, editor, Peng, Hanchuan, editor, and Luo, Qingming, editor

Published
2017
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34. Supervised Discriminative EEG Brain Source Imaging with Graph Regularization

Author

Liu, Feng, Hosseini, Rahilsadat, Rosenberger, Jay, Wang, Shouyi, Su, Jianzhong, Hutchison, David, Editorial Board Member, Kanade, Takeo, Editorial Board Member, Kittler, Josef, Editorial Board Member, Kleinberg, Jon M., Editorial Board Member, Mattern, Friedemann, Editorial Board Member, Mitchell, John C., Editorial Board Member, Naor, Moni, Editorial Board Member, Pandu Rangan, C., Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Terzopoulos, Demetri, Editorial Board Member, Tygar, Doug, Editorial Board Member, Weikum, Gerhard, Series Editor, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Descoteaux, Maxime, editor, Maier-Hein, Lena, editor, Franz, Alfred, editor, Jannin, Pierre, editor, Collins, D. Louis, editor, and Duchesne, Simon, editor

Published
2017
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