High dimensional statistics

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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.

Alessandro Rinaldo, Topics in High Dimensional Statistics
http://www.stat.cmu.edu/~arinaldo/36788/
http://www.stat.cmu.edu/~arinaldo/36789/

See original: The Living Thing / Notebooks High dimensional statistics