Fast MLE Computation for the Dirichlet Multinomial

Given a collection of categorical data, we want to find the parameters of a Dirichlet distribution which maximizes the likelihood of that data. Newton's method is typically used for this purpose but current implementations require reading through the entire dataset on each iteration. In this paper, we propose a modification which requires only a single pass through the dataset and substantially decreases running time. Furthermore we analyze both theoretically and empirically the performance of the proposed algorithm, and provide an open source implementation

Four$quare: Hybrid Spaces of Economic Activity

The study of cyberspace in geography is not new; however the nature of digital spaces is changing with the development of mobile technology, social media, and location-based media platforms. Much of the content found online is now user-generated and embedded with geographic coordinate information in what is termed the geoweb. While the geoweb provides extensive databases of digital information, it also represents a pivotal shift in the way that digital space is studied by geographers. Online spaces, and especially those spaces created by location-based social media platforms, represent a hybrid space that meshes the physical information of the offline world with the digital information of the online. As a hybrid space, the internet has the power to shape offline places and spaces as well as the individual decisions people make within those locations. Physical spaces as well shape online space through the creation of these forms of location-based social media by recognizing that people are embodied. This dissertation seeks to employ the hybrid nature of online/offline spaces to look at sites of consumption and economic geography. Using data from the location-based social media platform, Foursquare, this dissertation argues that the nature of consumption is changing. While physical storefronts are a necessity for our lives as physical beings, an online presence on location-based social media platforms is needed for economic growth and success. Those offline areas left out of the online discussion due to the digital divide may continue to fall behind