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CATEGORIES:Statistics
SUMMARY:On Estimation of Unnormalized Density Models - Son
g Liu — University of Bristol
DTSTART;TZID=Europe/London:20191025T140000
DTEND;TZID=Europe/London:20191025T150000
UID:TALK130054AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/130054
DESCRIPTION:In many machine learning applications\, complicate
d parametric density models such as Deep Neural Ne
tworks are favoured due to their flexibility and e
xpressiveness. However\, unlike classic density mo
dels\, these density functions cannot be easily no
rmalised. Thus\, Maximum Likelihood Estimation (ML
E) cannot be easily applied for model parameter es
timation. If the dimensionality of the input varia
ble is high\, MCMC based MLE may also fail. In the
machine learning community\, some Stein Identity
based methods have risen in popularity due to thei
r ability to measure the "goodness of fit" of unno
rmalisable models. In the first part of the talk [
1]\, we study the performance of a parameter estim
ator using Stein's identity. Particularly\, we con
struct a Stein density ratio estimator\, which est
imates the ratio function between a data distribut
ion and a model distribution. Then we minimise the
fitted likelihood ratio to estimate model paramet
ers. In the second part of the talk [2]\, I discus
s a specific type of unnormalised density model: T
runcated densities. We show how an augmented score
matching estimator can be applied to estimate par
ameters of density models with a complex truncatio
n domain (such as a polytope in R^2). \n\n[1] Liu\
, S.\, Kanamori\, T.\, Jitkrittum\, W.\, Chen\, Y\
; Fisher Efficient Inference of Intractable Models
\; arxiv:1805.07454\, 2019.\n[2] Liu\, S.\, Kanamo
ri\, T.\, Estimating Density Models with Complex T
runcation Boundaries\; arXiv:1910.03834\, 2019.
LOCATION:MR12
CONTACT:Dr Sergio Bacallado
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