"Recent years have witnessed the significant growth of spatial and temporal data generated from various disciplines, including geophysical sciences, neuroscience, economics, criminology, and epidemiology. Such data have been extensively used to train spatial and temporal models that can make predictions either at multiple locations simultaneously or along multiple forecasting horizons (lead times). However, training an accurate prediction model in these domains can be challenging especially when there are significant noise and missing values or limited training examples available. The goal of this thesis is to develop novel multi-task learning frameworks that can exploit the spatial and/or temporal dependencies of the data to ensure robust predictions in spite of the data quality and scarcity problems. The first framework developed in this dissertation is designed for multi-task classification of time series data. Specifically, the prediction task here is to continuously classify activities of a human subject based on the multi-modal sensor data collected in a smart home environment. As the classes exhibit strong spatial and temporal dependencies, this makes it an ideal setting for applying a multi-task learning approach. Nevertheless, since the type of sensors deployed often vary from one room (location) to another, this introduces a structured missing value problem, in which blocks of sensor data could be missing when a subject moves from one room to another. To address this challenge, a probabilistic multi-task classification framework is developed to jointly model the activity recognition tasks from all the rooms, taking into account the block-missing value problem. The framework also learns the transitional dependencies between classes to improve its overall prediction accuracy. The second framework is developed for the multi-location time series forecasting problem. Although multi-task learning has been successfully applied to many time series forecasting applications such as climate prediction, conventional approaches aim to minimize only the point-wise residual error of their predictions instead of considering how well their models fit the overall distribution of the response variable. As a result, their predicted distribution may not fully capture the true distribution of the data. In this thesis, a novel distribution-preserving multi-task learning framework is proposed for the multi-location time series forecasting problem. The framework uses a non-parametric density estimation approach to fit the distribution of the response variable and employs an L2-distance function to minimize the divergence between the predicted and true distributions. The third framework proposed in this dissertation is for the multi-step-ahead (long-range) time series prediction problem with application to ensemble forecasting of sea surface temperature. Specifically, our goal is to effectively combine the forecasts generated by various numerical models at different lead times to obtain more precise predictions. Towards this end, a multi-task deep learning framework based on a hierarchical LSTM architecture is proposed to jointly model the ensemble forecasts of different models, taking into account the temporal dependencies between forecasts at different lead times. Experiments performed on 29-year sea surface temperature data from North American Multi-Model Ensemble (NAMME) demonstrate that the proposed architecture significantly outperforms standard LSTM and other MTL approaches."--Pages ii-iii.
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