Random Coordinate Descent Methods for Minimizing Decomposable Submodular Functions

Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have high running times and are unsuitable for large-scale problems. Recent work have used convex optimization techniques to obtain very practical algorithms for minimizing functions that are sums of ``simple" functions. In this paper, we use random coordinate descent methods to obtain algorithms with faster linear convergence rates and cheaper iteration costs. Compared to alternating projection methods, our algorithms do not rely on full-dimensional vector operations and they converge in significantly fewer iterations

Constrained Submodular Maximization: Beyond 1/e

In this work, we present a new algorithm for maximizing a non-monotone submodular function subject to a general constraint. Our algorithm finds an approximate fractional solution for maximizing the multilinear extension of the function over a down-closed polytope. The approximation guarantee is 0.372 and it is the first improvement over the 1/e approximation achieved by the unified Continuous Greedy algorithm [Feldman et al., FOCS 2011]

Institutional Investors, Insiders and the Firm

This dissertation is comprised of three chapters that focus on three topics related to institutional investors’ and registered insiders’ trading activities around corporate announcements. The purpose of the research is to provide more insights into the trading behavior of institutions and insiders around corporate events when they are influenced by the anticipation and arrival of new information. Data samples are stratified, regression models are estimated, and control variables are added to ensure the results are significant and robust. The first chapter discusses the information signaling hypothesis around share repurchase announcements. I examine if institutions can trade profitability around the announcement time using signals from insiders and the firm. I find that only transient institutional investors are able to adjust their portfolios to take advantage of the post-announcement price run-up. The second chapter explores the relationship between information asymmetry and the information acquisition process. It appears that institutions prefer using lower cost, small, round lot, 100-share multiples when they can acquire information in advance of the event as in earnings announcements. The last chapter looks at if the information hierarchy hypothesis holds true at the very top of the corporate pyramid. I find that CEO trades are largely ignored and president net purchases have positive effects on merger post-announcement returns. In summary, institutions, insiders, and the firm play important roles in the information dissemination and acquisition process. Hence, their decisions have profound effects on their complicated, interconnected relationships