This paper models residential consumers' energy-consumption behavior by load patterns and distributions and reveals the relationship between consumers' load patterns and socioeconomic features by machine learning. We analyze the real-world smart meter data and extract load patterns using K-Medoids clustering, which is robust to outliers. We develop an analytical framework with feature selection and deep learning models to estimate the relationship between load patterns and socioeconomic features. Specifically, we use an entropy-based feature selection method to identify the critical socioeconomic characteristics that affect load patterns and benefit our method's interpretability. We further develop a customized deep neural network model to characterize the relationship between consumers' load patterns and selected socioeconomic features. Numerical studies validate our proposed framework using Pecan Street smart meter data and survey. We demonstrate that our framework can capture the relationship between load patterns and socioeconomic information and outperform benchmarks such as regression and single DNN models.