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SUMMARY:Nonparametric classification with missing data - Tim Cannings\, Un
 iversity of Edinburgh
DTSTART:20240614T130000Z
DTEND:20240614T140000Z
UID:TALK213478@talks.cam.ac.uk
CONTACT:Dr Sergio Bacallado
DESCRIPTION:We introduce a new nonparametric framework for classification 
 problems in the presence of missing data. The key aspect of our framework 
 is that the regression function decomposes into an anova-type sum of ortho
 gonal functions\, of which some (or even many) may be zero. Working under 
 a general missingness setting\, which allows features to be missing not at
  random\, our main goal is to derive the minimax rate for the excess risk 
 in this problem. In addition to the decomposition property\, the rate depe
 nds on parameters that control the tail behaviour of the marginal feature 
 distributions\, the smoothness of the regression function and a margin con
 dition. The ambient data dimension does not appear in the minimax rate\, w
 hich can therefore be faster than in the classical nonparametric setting. 
 We further propose a new method\, called the Hard-thresholding Anova Missi
 ng data (HAM) classifier\, based on a careful combination of a k-nearest n
 eighbour algorithm and a thresholding step. The HAM classifier attains the
  minimax rate up to polylogarithmic factors and numerical experiments furt
 her illustrate its utility.
LOCATION:MR12\, Centre for Mathematical Sciences
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