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Samory Kpotufe, Princeton

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Exploiting structures in data: some adaptivity and tradeoff results.
15 October 2015 from 4:00 PM to 5:00 PM
201 Thomas Building
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Predictive procedures are being adopted in a variety of application domains 

in the natural sciences and engineering. However it is difficult to use these procedures 

"off-the-shelf" as they typically require human effort to properly tune to the structure 

of the particular application data at hand. Furthermore, many domain constraints 

(e.g. time and space constraints) have to be met, and practitioners often resort to 

various heuristics with few or no guarantees on tradeoffs. 


In this talk we are interested in “local” prediction methods such as 

kernel, k-NN, or tree-based classification or regression. Using these predictors 

as examples, we first develop insights into automatically exploiting hidden structure 

in the input X space (e.g. manifolds, sparsity) to improve prediction accuracy. 


We then discuss simple approaches — rooted in existing heuristics — 

that can exploit hidden structure in X to guarantee good tradeoffs between 

estimation time and accuracy; these tradeoffs are explicitly given in terms of a ‘knob’ 

which can be dialed up or down to favor either time or accuracy. 


Finally, given the local nature of the predictors discussed, we will discuss “self-tuning” 

to unknown local structures in the data. For self-tuning (or local adaptivity)

we combine intuition from so-called Lepski’s methods (adaptive to local smoothness in Y) 

with new insights on adapting to local structures in X. The resulting  

adaptive (pointwise) risks are independent of the ambient dimension of X. 


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