Sepsis is a life-threatening medical emergency that can lead to multiple organ dysfunction and even death if not promptly identified and treated. The causes of sepsis are highly complex, and its manifestations vary significantly. Subtle changes in the time-series data of medical variables, including vital signs and laboratory blood test results, reveal critical clues for the early detection of sepsis deterioration. Deep learning networks possess excellent feature-learning capabilities, whereas support vector machines (SVMs) exhibit superior inferential abilities. This study integrates the strengths of both approaches. First, a Temporal Convolutional Network (TCN) is employed to extract key features. Subsequently, an SVM is used to develop an optimal predictive model to enhance the accuracy of early sepsis prediction. Furthermore, given that sepsis prediction comprises two interrelated sub-tasks—predicting whether a patient will develop sepsis (a classification problem) and estimating the time until sepsis onset if the patient is at risk (a regression problem)—this study proposes a novel multi-task support vector machine (MT-SVM) that integrates classification and regression tasks. By learning the shared underlying knowledge between these tasks, the proposed model aims to improve overall predictive performance.