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Learning behavioral patterns for activities of daily living in a smart home environment can be challenged by the limited number of training data that may be available. This may be due to the infrequent repetition of routine activities (e.g., once daily), the expense of using observers to label activities, and the intrusion that would be caused by the presence of observers over long time periods. It is important, therefore, to make as much use of any labeled data that are collected, however, incomplete these data may be. In this paper, we propose an algorithm for learning behavioral patterns for multi-inhabitants living in a single smart home environment, by making full use of all limited labeled activities, including incomplete data resulting from unreliable low-level sensors in this environment. Through maximum-likelihood estimation, using Expectation-Maximization, we build a model that captures both environmental uncertainties from sensor readings and user uncertainties, including variations in how individuals carry out activities. Our algorithm outperforms models that cannot handle data incompleteness, with increasing performance gains as incompleteness increases. The approach also enables the impact of particular sensors to be assessed and can thus inform sensor maintenance and deployment.