UIUC and Purdue

Abstract: Mobile health has emerged as a major success to track individual health status, due to the popularity and power of smartphones and wearable devices. This also brings a great challenge in handling heterogeneous multi-resolution data which arise ubiquitously in mobile health due to irregular multivariate measurements collected from individuals. In this paper, we propose an individualized dynamic latent factor model (IDLFM) for irregular multi-resolution time series data to interpolate unsampled measurements of time series with low-resolution. The proposed method utilizes individualized dynamic latent factors to capture the underlying longitudinal trajectory of each subject. One major advantage of the proposed method is the capability to integrate not only multiple time series but also multiple subjects by mapping the irregular multi-resolution time series to the latent space. In addition, the proposed IDLFM model is applicable for time series with a complex trajectory, such as a non-stationary process or time series with abrupt changes. In theory, we provide the interpolation error bound of the proposed estimator and derive the convergence rate with the non-parametric approximation methods.  Both simulation studies and the application of Garmin watch data demonstrate the superior performance of the proposed method compared to existing methods. 

Abstract: We motivate a new methodological framework for era-adjusting baseball statistics. Our methodological framework is a crystallization of the conceptual ideas put forward by Stephen Jay Gould, and we name it the Full House Model in his honor. The Full House Model works by balancing the achievements of Major League Baseball (MLB) players within a given season and the size of the MLB eligible population. We demonstrate the utility of our Full House Model in an application of comparing baseball players' performance statistics across eras. Our results reveal a radical reranking of baseball's greatest players that is consistent with what one would expect under a sensible uniform talent generation assumption. Most importantly, we find that the greatest African American and Latino players now sit atop the greatest all-time lists of historical baseball players while conventional wisdom ranks such players lower. Our conclusions largely refute a consensus of baseball greatness that is reinforced by nostalgic bias, recorded statistics, and statistical methodologies which we argue are not suited to the task of comparing players across eras.

Abstract: Topic models provide a useful text-mining tool for learning, extracting, and discovering latent structures in large text corpora. Although a plethora of methods has been proposed for topic modeling, a formal theoretical investigation on the statistical identifiability and accuracy of latent topic estimation is lacking in the literature. In this work, we propose a maximum likelihood estimator (MLE) of latent topics based on a specific integrated likelihood, which is naturally connected to the concept of volume minimization in computational geometry. Theoretically, we introduce a new set of geometric conditions for topic model identifiability, which are weaker than conventional separability conditions relying on the existence of anchor words or pure topic documents. We conduct finite-sample error analysis for the proposed estimator and discuss the connection of our results with existing ones. We conclude with empirical studies on both simulated and real datasets. This talk is based on joint work with Yinyin Chen, Shishuang He, and Yun Yang.