This paper presents a framework to automatically estimate the gaze direction of an infant in an infant-parent face-to-face interaction. Commercial devices are sometimes used to produce automated measurement of the subjects' gaze direction. This approach is intrusive, requiring cooperation from the participants, and cannot be employed in interactive face-to-face communication scenarios between a parent and their infant. Alternately, the infant gazes that are at and away from the parent's face may be manually coded from captured videos by a human expert. However, this approach is labor intensive. A preferred alternative would be to automatically estimate the gaze direction of participants from captured videos. The realization of a such a system will help psychological scientists to readily study and understand the early attention of infants. One of the problems in eye region image analysis is the large dimensionality of the visual data. We address this problem by employing the spectral regression technique to project high dimensionality eye region images into a low dimensional sub-space. Represented eye region images in the low dimensional sub-space are utilized to train a Support Vector Machine (SVM) classifier to predict the gaze direction (i.e., either looking at parent's face or looking away from parent's face). The analysis of more than 39,000 video frames of naturalistic gaze shifts of multiple infants demonstrates significant agreement between a human coder and our approach. These results indicate that the proposed system provides an efficient approach to automating the estimation of gaze direction of naturalistic gaze shifts.