PPT-Submodular Set Function Maximization

A MiniSurvey Chandra Chekuri Univ of Illinois UrbanaChampaign Submodular Set Functions A function f 2 N R is submodular if fA fB fA B . washingtonedu Jeff Bilmes Department of Electrical Engineering University of Washington bilmesuwashingtonedu Abstract We investigate two new optimization problems minimizing a submodular function subject to a submodular lower bound constraint submod Let denote the function de64257ned as follows First de64257ne a four parameter function by xyztabcd 2 43 Then xyzt 1 sin xyzt 1237566 54783217 1237896431 325123467 37 xyzt 5674235 4067231567 13245678 3748967543 2 xyzt 3867435523 7134893 75 35658 Submodular. Bandits Problem. Yisong Yue. Carnegie Mellon University. Joint work with Carlos Guestrin & Sue Ann Hong. Optimizing Recommender Systems. Must predict what the user finds interesting. Honglei. . Zhuang. , . Yihan. Sun, Jie Tang, Jialin Zhang, Xiaoming Sun. Influence Maximization. 0.6. 0.5. 0.1. 0.4. 0.6. 0.1. 0.8. 0.1. A. B. C. D. E. F. Probability . of . influence. Marketer Alice. Machine Learning. Last Time. Expectation Maximization. Gaussian Mixture Models. Today. EM Proof. Jensen’s Inequality. Clustering sequential data. EM over . HMMs. EM in any Graphical Model. Gibbs Sampling. Submodular. Functions. Grigory. . Yaroslavtsev. Columbia University. October 26, 2012. With . Sofya. . Raskhodnikova. (SODA’13). + Work in progress with Rocco . Servedio. Submodularity. Discrete analog of convexity/concavity, law . Honglei. . Zhuang. , . Yihan. Sun, Jie Tang, Jialin Zhang, Xiaoming Sun. Influence Maximization. 0.6. 0.5. 0.1. 0.4. 0.6. 0.1. 0.8. 0.1. A. B. C. D. E. F. Probability . of . influence. Marketer Alice. Sahil. . Singla. . (Carnegie Mellon University). Joint work with . Aviad. Rubinstein. (18. th. Jan, 2017). Prophet Inequality. 2. Krengel. and . Sucheston. [. KS-BAMS’77]. Given. . distributions. . for Binary . Pairwise. Energies. Lena . Gorelick. . joint work with. . O. . Veksler. I. Ben . Ayed. A. Delong. . Y. . Boykov. Example of Simple Binary Energy. 2. Potts Model. Binary . Pairwise. Winter 2012. Daniel Weld. Slides adapted from Carlos . Guestrin. , Dan Klein & Luke . Zettlemoyer. Machine Learning. 2. Supervised Learning. Parametric. Reinforcement Learning. Unsupervised Learning. of . submodular. and XOS . functions by juntas. Vitaly. Feldman and Jan . Vondrâk. IBM . Research - . Almaden. Prelims:. Submodular. and XOS. Functions; . Learning. $20. $27. Approximation by juntas. Unconstrained Submodular Maximization Moran Feldman The Open University of Israel Based On Maximizing Non-monotone Submodular Functions. Uriel Feige , Vahab S. Mirrokni and Jan Vondrák , SIAM J. TexPoint fonts used in EMF. . Read the TexPoint manual before you delete this box.: . A. A. A. A. A. A. A. A. Maria . Florina. . Balcan. LGO, . 11/16/2010. f(S)+f(T) . ¸. f(S . Å. T) + f(S . [. T), . . The costs that an organization incurs even when there is little or no activity are . fixed costs. , or . overhead. .. Finding Marginal Cost. . Variable costs . are usually associated with labor and raw materials and change with the business’s rate of operation or output..