Predictive modeling on big data set that can't fit into memory
Whether you're using this for a hobby or for your job, I would recommend EMR on Amazon Web Services. The name is anachronistic (it's no longer just for map reduce), but EMR enables you to quickly stand up an Apache Spark cluster of several machines. Spark comes with machine learning libraries for building trees, and can scale to however many machines you need (to the point that you no longer face memory constraints). EMR is cheap because you're charged hourly and don't have to buy your own hardware. Apache Spark is great for your resume, and it's also a practical skill because it's generally the first tool most data scientists turn to when working with data sets that are too large for a single machine.