Wide deployment of artificial intelligence (AI) is inducing exponentially growing energy consumption. Traditional digital platforms are becoming difficult to fulfill such ever-growing demands on energy efficiency as well as computing latency, which necessitates the development of high efficiency analog hardware platforms for AI. Recently, optical and electrooptic hybrid computing is reactivated as a promising analog hardware alternative because it can accelerate the information processing in an energy-efficient way. Integrated photonic circuits offer such an analog hardware solution for implementing photonic AI and machine learning. For this purpose, we proposed a photonic analog of support vector machine and experimentally demonstrated low-latency and low-energy classification computing, which evidences the latency and energy advantages of optical analog computing over traditional digital computing. We also proposed an electrooptic Hopfield network for classifying and recognizing time-series data. This paper will review our work on implementing classification computing and Hopfield network by leveraging silicon photonic circuits.