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CATEGORIES:Lecture or Presentation
DESCRIPTION:Nishant Mehta\, Assistant professor\nDepartment of Computer Sci
ence\nUniversity of Victoria\n\nI will talk about a new notion of complexit
y\, “COMP”\, that interpolates between and generalizes some existing comple
xity notions from statistical learning theory. I will first derive COMP as
a generalization of the Shtarkov sum\, the normalizer in the normalized max
imum likelihood (NML) distribution. When the NML distribution exists\, the
logarithm of the Shtarkov sum is precisely equal to the minimax regret for
individual sequence prediction under log loss. Next\, via a PAC-Bayesian an
alysis\, I will show how COMP can be used to obtain tight upper bounds on t
he excess risk for randomized estimators (which include generalized Bayesia
n estimators). This excess risk bound will be in terms of COMP itself. Unde
r a certain specialization\, further upper bounding COMP leads to a standar
d PAC-Bayesian excess risk bound whose right hand side is the information c
omplexity (essentially the empirical excess risk plus an additional complex
ity term involving the KL divergence from the posterior distribution to the
prior distribution). Under a different specialization\, the special case o
f empirical risk minimization with VC-type classes and "large classes" (who
se empirical L2 entropy exhibits polynomial growth)\, we will see how COMP
is upper bounded in a way which yields optimal rates of convergence of the
excess risk for such classes. Along the way\, we will see connections to Ra
demacher complexity\, and\, in particular\, we will recover bounds based on
local Rademacher complexity while completely avoiding complicated local Ra
demacher complexity-based arguments. This is joint work with Peter Grünwald
at CWI (in Amsterdam) and Leiden University.\n\nAdditional information: ht
tp://eecs.oregonstate.edu/colloquium-series
DTEND:20180521T235000Z
DTSTAMP:20241014T015010Z
DTSTART:20180521T230000Z
GEO:44.565762;-123.281717
LOCATION:Learning Innovation Center (LINC)\, 200
SEQUENCE:0
SUMMARY:Colloquium: A tight excess risk bound via a new complexity based on
a unification of PAC-Bayesian\, normalized maximum likelihood\, and Radema
cher complexities
UID:tag:localist.com\,2008:EventInstance_3630737
URL:https://events.oregonstate.edu/event/colloquium_a_tight_excess_risk_bou
nd_via_a_new_complexity_based_on_a_unification_of_pac-bayesian_normalized_m
aximum_likelihood_and_rademacher_complexities
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