Personal assistive robots to be realized in the near future should have the ability to seamlessly coexist with humans in unconstrained environments, with the robot's capability to understand and interpret the human behavior during human-robot cohabitation significantly contributing towards this end. Still, the understanding of human behavior through a robot is a challenging task as it necessitates a comprehensive representation of the high-level structure of the human's behavior from the robot's low-level sensory input. The paper at hand tackles this problem by demonstrating a robotic agent capable of apprehending human daily activities through a method, the Interaction Unit analysis, that enables activities' decomposition into a sequence of units, each one associated with a behavioral factor. The modelling of human behavior is addressed with a Dynamic Bayesian Network that operates on top of the Interaction Unit, offering quantification of the behavioral factors and the formulation of the human's behavioral model. In addition, lightweight human action and object manipulation monitoring strategies have been developed, based on RGB-D and laser sensors, tailored for onboard robot operation. As a proof of concept, we used our robot to evaluate the ability of the method to differentiate among the examined human activities, as well as to assess the capability of behavior modeling of people with Mild Cognitive Impairment. Moreover, we deployed our robot in 12 real