In this paper, we present a comprehensive analysis of extreme temperature patterns using emerging statistical machine learning techniques. Our research focuses on exploring and comparing the effectiveness of various statistical models for climate time series forecasting. The models considered include Auto-Regressive Integrated Moving Average, Exponential Smoothing, Multilayer Perceptrons, and Gaussian Processes. We apply these methods to climate time series data from five most populated U.S. cities, utilizing Python and Julia to demonstrate the role of statistical computing in understanding climate change and its impacts. Our findings highlight the differences between the statistical methods and identify Multilayer Perceptrons as the most effective approach. Additionally, we project extreme temperatures using this best-performing method, up to 2030, and examine whether the temperature changes are greater than zero, thereby testing a hypothesis.

Motivated by the need for efficient and personalized learning in mobile health, we investigate the problem of online kernel selection for Gaussian Process regression in the multi-task setting. We propose a novel generative process on the kernel composition for this purpose. Our method demonstrates that trajectories of kernel evolutions can be transferred between users to improve learning and that the kernels themselves are meaningful for an mHealth prediction goal.