Early diagnosis of Autism Spectrum Disorder (ASD) is crucial for best outcomes to interventions. In this paper, we present a machine learning (ML) approach to ASD diagnosis based on identifying specific behaviors from videos of infants of ages 6 through 36 months. The behaviors of interest include directed gaze towards faces or objects of interest, positive affect, and vocalization. The dataset consists of 2000 videos of 3-minute duration with these behaviors manually coded by expert raters. Moreover, the dataset has statistical features including duration and frequency of the above mentioned behaviors in the video collection as well as independent ASD diagnosis by clinicians. We tackle the ML problem in a two-stage approach. Firstly, we develop deep learning models for automatic identification of clinically relevant behaviors exhibited by infants in a one-on-one interaction setting with parents or expert clinicians. We report baseline results of behavior classification using two methods: (1) image based model (2) facial behavior features based model. We achieve 70% accuracy for smile, 68% accuracy for look face, 67% for look object and 53% accuracy for vocalization. Secondly, we focus on ASD diagnosis prediction by applying a feature selection process to identify the most significant statistical behavioral features and a over and under sampling process to mitigate the class imbalance, followed by developing a baseline ML classifier to achieve an accuracy of 82% for ASD diagnosis.