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SUMMARY:A Case for using Trend Filtering over Splines  - Aaditya Ramdas\, 
 Carnegie Mellon University 
DTSTART:20140926T100000Z
DTEND:20140926T110000Z
UID:TALK54835@talks.cam.ac.uk
CONTACT:Microsoft Research Cambridge Talks Admins
DESCRIPTION:This talk will be about fast optimization algorithms (specific
 ally specialized ADMM) for a common practical problem - estimating piecewi
 se constant/linear/quadratic fits to time series data. I will first introd
 uce Trend Filtering\, a recently proposed tool for this problem by Kim\, K
 oh\, Boyd and Gorinevsky (2009)\, and compare it to the popular smoothing 
 splines and locally adaptive regression splines. Tibshirani (2014) showed 
 that trend filtering estimates converge at the minimax optimal if the true
  underlying function (or its derivatives) has bounded total variation. Hen
 ce\, the only roadblock to using it in practice is having robust and effic
 ient algorithms. We take a major step in overcoming this problem\, by prov
 iding a more efficient and robust solution than the current interior point
  methods in use. Furthermore\, the proposed ADMM implementation is very si
 mple\, and importantly\, it is flexible enough to extend to many interesti
 ng related problems\, such as sparse trend filtering and isotonic trend fi
 ltering. Software for our method will be made freely available\, written i
 n C++\, and also in R (see the {\\tt trendfilter} function in the R packag
 e {\\tt genlasso}). 
LOCATION:Auditorium\, Microsoft Research Ltd\, 21 Station Road\, Cambridge
 \, CB1 2FB
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