Streaming high-quality video over dynamic radio networks is challenging. Dynamic adaptive streaming over HTTP (DASH) is a standard for delivering video in segments, and adapting its quality to adjust to a changing and limited network bandwidth. We present a machine learning-based predictive pre-fetching and caching approach for DASH video streaming, implemented at the multi-access edge computing server. We use ensemble methods for machine learning (ML) based segment request prediction and an integer linear programming (ILP) technique for pre-fetching decisions. Our approach reduces video segment access delay with a cache-hit ratio of 60% and alleviates transport network load by reducing the backhaul link utilization by 69%. We validate the ML model and the pre-fetching algorithm, and present the trade-offs involved in pre-fetching and caching for resource-constrained scenarios.