[Forum SIS] Webinar in Statistics YUN WEI - 26/2, ore 17

[Pierpaolo De Blasi]

WEBINARS IN STATISTICS @ COLLEGIO CARLO ALBERTO
<https://www.carloalberto.org/events/category/seminars/seminars-in-statistics/?tribe-bar-date=2019-09-01>

Venerdi 26 Febbraio 2021, alle ore 17:00, si terrà  il seguente webinar:

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Speaker: *Yun Wei (*Samsi and Duke University, USA)


Title: *Obtaining faster convergence rates in finite mixture models by
taking repeated measures*


Zoom link:

https://us02web.zoom.us/j/89954920036?pwd=dndsQnZqQ2crZzVlRW1pM0Q2RGo1Zz09

Meeting ID: 899 5492 0036

Passcode: 418668

Abstract:
It is known that some finite mixture models suffer from slow rates for
estimating the component parameters. Examples are mixtures of the weakly
identifiable families in the sense of [Ho and Nguyen 2016]. To obtain
faster parameter convergence rates, we propose to collect more samples from
each mixture component, hence each data is a vector of samples from the
same mixture component. Such a model is known in the literature as a finite
mixture model of repeated measures, which has been applied in psychological
study and topic modeling. This model also belongs to the mixture of product
distributions, with the special structure that the product distributions in
each mixture component are also identical. In this setup, each data
consists of conditionally independent and identically distributed samples
and thus is an exchangeable sequence.
We show that by taking repeated measures (collecting more samples from each
mixture component), a finite mixture model that is not originally
identifiable becomes identifiable. Moreover, the posterior contraction
rates for the parameter estimation are also obtained, demonstrating that
repeated measures are beneficial for estimating the component parameters.
Our results hold for general probability families including all regular
exponential families and can also be applied to hierarchical models. The
key tool to develop the results is by establishing an inverse inequality to
upper bound a suitable distance between mixing measures by the total
variational distance between the corresponding mixture densities.
Based on joint work with Xuanlong Nguyen (University of Michigan).
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Il webinar è organizzato dalla "de Castro" Statistics Initiative

www.carloalberto.org/stats

in collaborazione con il Collegio Carlo Alberto e rientra nel Complex Data
Modeling Research Network

midas.mat.uc.cl/network


Cordiali saluti,

Pierpaolo De Blasi

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University of Torino & Collegio Carlo Alberto

carloalberto.org/pdeblasi
<https://sites.google.com/a/carloalberto.org/pdeblasi/>
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