Feature Selection with NP-dimensionality
by Jianqing Fan
Abstract: Ultrahigh-dimensionality characterizes many contemporary statistical problems from genomics and genetics to finance and economics. We first outline a unified approach to ultrahigh dimensional variable selection problems and then focus on penalized likelihood methods which are fundamentally important building blocks to ultra-high dimensional variable selection.
- How high a dimensionality can such methods handle?
- What is the role of penalty functions?
- How to analyze ultrahigh dimensional data and what are possible suprious relations due to ultrahigh dimensionality?
This talk will provide some insights into these problems. The focus will be on the model selection consistency and oracle properties for a class of penalized likelihood approaches using folded-concave penalty functions. The advantages over convex penalty will be clearly demonstrated. The coordinate optimization is implemented for finding the solution paths, whose performance is evaluated by a few simulation examples and the real data analysis. The recent results on independence screening will also be summarized.
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