We consider maximization of stochastic monotone continuous submodular functions (CSF) with a diminishing return property. Existing algorithms only guarantee the performance in expectation, and do not bound the probability of getting a bad solution. This implies that for a particular run of the algorithms, the solution may be much worse than the provided guarantee in expectation. In this paper, we first empirically verify that this is indeed the case. Then, we provide the first high-probability analysis of the existing methods for stochastic CSF maximization, namely PGA, boosted PGA, SCG, and SCG++. Finally, we provide an improved high-probability bound for SCG, under slightly stronger assumptions, with a better convergence rate than that of the expected solution. Through extensive experiments on non-concave quadratic programming (NQP) and optimal budget allocation, we confirm the validity of our bounds and show that even in the worst-case, PGA converges to $OPT/2$, and boosted PGA, SCG, SCG++ converge to $(1 - 1/e)OPT$, but at a slower rate than that of the expected solution.

Generative Adversarial Networks (GANs) are a widely-used tool for generative modeling of complex data. Despite their empirical success, the training of GANs is not fully understood due to the joint training of the generator and discriminator. This paper analyzes these joint dynamics when the true samples, as well as the generated samples, are discrete, finite sets, and the discriminator is kernel-based. A simple yet expressive framework for analyzing training called the $\textit{Isolated Points Model}$ is introduced. In the proposed model, the distance between true samples greatly exceeds the kernel width so that each generated point is influenced by at most one true point. The model enables precise characterization of the conditions for convergence both to good and bad minima. In particular, the analysis explains two common failure modes: (i) an approximate mode collapse and (ii) divergence. Numerical simulations are provided that predictably replicate these behaviors.

At the present, there is a significant lack of programs or resources at the high school level to prepare students for a data driven future. Data Jam is a high school outreach program, that introduces students to data science. The program is organized by members of academia (Carnegie Mellon University, University of Pittsburgh) and industry and research (IBM, Teradata, Pittsburgh Computing Center). Over a period of four months (Oct-Feb of the school year), teachers and students explore the concepts of data science and big data via workshops, exercises, a field trip, and a team project. Data Jam is currently in its fifth year. Participation has grown from an initial pool of seven teams to twenty-five teams last year. Based on teacher and student feedback, we are pleased with the program's success. This poster discusses the goals and structure of Data Jam, its execution, participant feedback, and lessons learned.