Physical Sciences and Mathematics Commons^™

Randomized Algorithms For Preconditioner Selection With Applications To Kernel Regression, Conner Dipaolo

HMC Senior Theses

The task of choosing a preconditioner M to use when solving a linear system Ax=b with iterative methods is often tedious and most methods remain ad-hoc. This thesis presents a randomized algorithm to make this chore less painful through use of randomized algorithms for estimating traces. In particular, we show that the preconditioner stability || I - M^-1A ||_F, known to forecast preconditioner quality, can be computed in the time it takes to run a constant number of iterations of conjugate gradients through use of sketching methods. This is in spite of folklore which …

Snap Scholar: The User Experience Of Engaging With Academic Research Through A Tappable Stories Medium, Ieva Burk

CMC Senior Theses

With the shift to learn and consume information through our mobile devices, most academic research is still only presented in long-form text. The Stanford Scholar Initiative has explored the segment of content creation and consumption of academic research through video. However, there has been another popular shift in presenting information from various social media platforms and media outlets in the past few years. Snapchat and Instagram have introduced the concept of tappable “Stories” that have gained popularity in the realm of content consumption.

To accelerate the growth of the creation of these research talks, I propose an alternative to video: …

On Cluster Robust Models, José Bayoán Santiago Calderón

CGU Theses & Dissertations

Cluster robust models are a kind of statistical models that attempt to estimate parameters considering potential heterogeneity in treatment effects. Absent heterogeneity in treatment effects, the partial and average treatment effect are the same. When heterogeneity in treatment effects occurs, the average treatment effect is a function of the various partial treatment effects and the composition of the population of interest. The first chapter explores the performance of common estimators as a function of the presence of heterogeneity in treatment effects and other characteristics that may influence their performance for estimating average treatment effects. The second chapter examines various approaches …