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SUMMARY:On classification with small Bayes error and the max-margin classi
fier - Professor Sara Van de Geer (ETH Zurich)
DTSTART;VALUE=DATE-TIME:20210429T153000
DTEND;VALUE=DATE-TIME:20210429T163000
UID:https://talks.ox.ac.uk/talks/id/02bef1f8-c7fc-42a3-880b-27342ae1f28a/
DESCRIPTION:This is joint work with Geoffrey Chinot\, Felix Kuchelmeister
and Matthias Löffler.\n\nWe consider the classification problem where one
observes a design matrix X ∈ Rn×p and a binary response variable Y = s
ign(Xβ* +ξ) ∈ {±1}n. Here β* ∈ Rp is an vector of unknown coeffici
ents with llβ*ll2= 1 and ξ ∼ N(0\, σ2I) ∈ Rn is an unobservable noi
se vector independent of X. We will present some theoretical results on th
e misclassification error of a class of estimators β of β* which are bas
ed on L1-regularization or L1-interpolation. The emphasis in this talk wil
l be on the interpolating estimator. It is observed in empirical studies t
hat classification algorithms achieving zero training error can perform we
ll in test sets. We aim at contributing to a theoretical understanding of
this phenomenon in the high-dimensional situation (i.e. p >> n). To allow
for small test error we focus on the case where σ2 is small. In the speci
al setting of i.i.d. Gaussian design\, we examine the minimum L1-norm inte
rpolator or max-margin classifier and its rate of convergence under L1-spa
rsity assumptions. Related is the noisy one-bit compressed sensing problem
\, where we apply the algorithm of Plan and Vershynin [2013] and (re-)esta
blish rates under L0– and L1-sparsity conditions.\n\nReferences\nY. Plan
and R. Vershynin. One-bit compressed sensing by linear programming\nCommu
nications on Pure and Applied Mathematics\, 66(8):1275–1297\, 2013.\nSpe
akers:\nProfessor Sara Van de Geer (ETH Zurich)
LOCATION:24-29 St Giles'\, 24-29 St Giles' OX1 3LB
URL:https://talks.ox.ac.uk/talks/id/02bef1f8-c7fc-42a3-880b-27342ae1f28a/
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DESCRIPTION:Talk:On classification with small Bayes error and the max-marg
in classifier - Professor Sara Van de Geer (ETH Zurich)
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