State space models (SSMs) are a popular modeling approach for time series. By augmenting an observed time series with a latent state sequence, SSMs capture complex dynamics with a simpler Markov dependence structure. Unfortunately, inference in SSMs requires passing messages along the entire sequence, which scales poorly for both long and high dimensional time series.
Many current products and systems employ sophisticated mathematical algorithms to automatically make complex decisions, or take action, in real-time. Examples include recommendation engines, search engines, spam filters, on-line advertising systems, fraud detection systems, automated trading engines, revenue management systems, supply chain systems, electricity generator scheduling, flight management systems, and advanced engine controls.
Advisor: Emily Fox
Advisor: Emily Fox Understanding how housing values evolve over time is important to consumers, real estate professionals, and policy makers. Existing methods for constructing housing indices are computed at a coarse spatial granularity, such as metropolitan regions. This coarse granularity does not have the representative power to encode the fine price dynamics apparent in local markets, such as neighborhoods and census tracts, and therefore leads to distorted price predictions.
In dynamic topic modeling, the proportional contribution of a topic to a document depends on the temporal dynamics of that topics overall prevalence in the corpus. We extend the Dynamic Topic Model of Blei and Lafferty (2006) by modeling document-level topic proportions with covariates and dynamic structure that includes polynomial trends and periodicity. A Markov Chain Monte Carlo (MCMC) algorithm that utilizes Polya-Gamma data augmentation is developed for posterior inference.