Kaggle has a few datasets, including I believe mammographs and proteomes if you want to do breast cancer specifically. If you're not in it for the money, or if

Kaggle has a few datasets, including I believe mammographs and proteomes if you want to do breast cancer specifically. If you're not in it for the money, or if just fame is enough, I'd suggest to go upriver: individual diagnostic data is rare because of medical privacy and market forces, but there is boundless open data in, for example genomics and proteomics. If you search for [bioinformatics competition], you should find a nice selection of opportunities with good data availability and clearly defined objectives. ML is slowly revolutionising this field, although it's a good idea to pay attention to what happened before–there were some seriously smart people working on these problems for a long time, and they found some rather ways to extract the most value from data with the tools available at the time.