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. Submodular. Bandits . and their Application to Diversified Retrieval. Yisong Yue (CMU) & Carlos . Guestrin. (CMU). Optimizing Recommender Systems. Every day, users come to news portal. For each user, . 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. Bayesian Submodular Models. Josip . Djolonga. joint work with Andreas Krause. Motivation. inference with higher order potentials. MAP Computation . ✓. Inference? . ✘. We provide a method for inference in such models. 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. on . approximation. of . submodular. and XOS . functions by juntas. Vitaly. Feldman and Jan . Vondrâk. IBM . Research - . Almaden. Prelims:. Submodular. and XOS. Functions; . Learning. $20. $27. 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 . general . submodular. functions. CVPR 2015 . Tutorial. Stefanie Jegelka. MIT. The set function view. 2. cost. of buying items . together, or. utility, . or. probability, …. (. . ). Xinran He . and David Kempe. University of Southern . California. {xinranhe, . dkempe. }@usc.edu. 08/15/2016. The adoption of new products . can . propagate between nodes . in the social network. 0.8. Dictionary Selection. for Sparse Representation. Volkan . Cevher. volkan.cevher@epfl.ch. Laboratory. for Information . . and Inference Systems - . LIONS. & . Idiap. Research Institute. . Joint work with . 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. Approximability. of Combinatorial Optimization Problems with . Submodular. Cost Functions. Based on joint work with . Gagan. . Goel. , . Chinmay. . Karande. , and Wang Lei. Motivation . Network Design Problem.