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CATEGORIES:Statistics
SUMMARY:Complexity analysis of the Lasso regularization pa
th and an application of sparsity to isoform detec
tion in RNA-seq data - Julien Mairal\, INRIA\, Gre
noble
DTSTART;TZID=Europe/London:20150227T160000
DTEND;TZID=Europe/London:20150227T170000
UID:TALK56947AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/56947
DESCRIPTION:This talk will be composed of two independent part
s. In the first part\, we will study an intriguing
phenomenon related to the regularization path of
the Lasso estimator. The regularization path of th
e Lasso can be shown to be piecewise linear\, maki
ng it possible to “follow” and explicitly compute
the entire path. We analyze this popular strategy\
, and prove that its worst case complexity is expo
nential in the number of variables. We then oppose
this pessimistic result to an (optimistic) approx
imate analysis: We show that an approximate path w
ith at most O(1/sqrt(ε)) linear segments can alway
s be obtained\, where every point on the path is g
uaranteed to be optimal up to a relative ε-duality
gap. \n \nIn the second part\, I will present a s
uccessful application of sparsity to the problem o
f isoform identification and quantification from R
NA-Seq data. A gene is composed of several coding
(exon) and non-coding parts (introns). Exons are c
ombined into sequences called isoforms that encode
a protein. An important but computationally chall
enging task consists of discovering isoforms from
the expression of exons. This can be formulated as
a sparse regression problem with an exponential n
umber of features. We propose an approach based o
n an equivalence between the problem of isoform de
tection in sparse regression and the problem of pa
th selection in a directed acyclic graphs\, which
can be solved efficiently using network flow algor
ithms.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberf
orce Road\, Cambridge
CONTACT:
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