The Living Thing / Notebooks :

High dimensional statistics

See compressive sensing for a fruitful sub-field where you are trying to identify sparse models from the data and general nonparametric regression. A major problem here is model selection, which you can’t do in the traditional way, e.g. with stepwise selection or ANOVA.

Or just take the most common option: ignore the details and use a neural net.

Alessandro Rinaldo, Topics in High Dimensional Statistics: * *