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CATEGORIES:Microsoft Research Cambridge\, public talks
SUMMARY:Probabilistic Latent Tensor Factorisation - Taylan
Cemgil\, Bogazici University
DTSTART;TZID=Europe/London:20121001T110000
DTEND;TZID=Europe/London:20121001T120000
UID:TALK40428AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/40428
DESCRIPTION:Algorithms for decompositions of matrices are of c
entral importance in machine learning\, signal pro
cessing and information retrieval\, with SVD and N
MF (Nonnegative Matrix Factorisation) being the mo
st widely used examples. Probabilistic interpretat
ions of matrix factorisation models are also well
known and are useful in many applications (Salakhu
tdinov and Mnih 2008\; Cemgil 2009\; Fevotte et. a
l. 2009). In the recent years\, decompositions of
multiway arrays\, known as tensor factorisations h
ave gained significant popularity for the analysis
of large data sets with more than two entities (K
olda and Bader\, 2009\; Cichocki et. al. 2008\; Mo
hamed 2011). We will discuss a subset of these mod
els from a statistical modelling perspective\, bui
lding upon probabilistic generative models and gen
eralised linear models (McCulloch and Nelder). In
both views\, the factorisation is implicit in a we
ll-defined statistical model and factorisations ca
n be computed via maximum likelihood.\n\nWe expres
s a tensor factorisation model using a factor grap
h and the factor tensors are optimised iteratively
. In each iteration\, the update equation can be i
mplemented by a message passing algorithm\, remini
scent to variable elimination in a discrete graphi
cal model. This setting provides a structured and
efficient approach that enables very easy developm
ent of application specific custom models\, as wel
l as algorithms for the so called coupled (collect
ive) factorisations where an arbitrary set of tens
ors are factorised simultaneously with shared fact
ors. Extensions to full Bayesian inference for mod
el selection\, via variational approximations or M
CMC are also feasible. Well known models of multiw
ay analysis such as Nonnegative Matrix Factorisati
on (NMF)\, Parafac\, Tucker\, and audio processing
(Convolutive NMF\, NMF2D\, SF-SSNTF) appear as sp
ecial cases and new extensions can easily be devel
oped. We will illustrate the approach with applica
tions in audio and music processing and link predi
ction for recommendation.
LOCATION:Small lecture theatre\, Microsoft Research Ltd\, 7
J J Thomson Avenue (Off Madingley Road)\, Cambrid
ge
CONTACT:Microsoft Research Cambridge Talks Admins
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