خانه ریاضیات اصفهان خانه ریاضیات اصفهان
| عنوان: Estimating sparse networks with hubs سخنران: آقای دکتر عباس خلیلی زمان: دوشنبه ۲۳ فروردین ۱۴۰۰ ساعت ۱۷ لینک ورود به وبینار: |
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Abstract:
Graphical modelling techniques based on sparse estimation have been ap-
plied to infer large complex networks in many _elds, including biology and
medicine, engineering, _nance and social sciences. One structural feature of
some of the networks in such applications that poses a challenge for statis-
tical inference is the presence of a small number of strongly interconnected
nodes which are called hubs. For example, in microbiome research hubs or
microbial taxa play a signi_cant role in maintaining stability of the micro-
bial community structure. Methods based on L1- regularization have been
widely used for performing sparse estimation in the graphical modelling con-
text. However, while these methods encourage sparsity, they do not take into
account structural information of the network. In this talk, I will introduce
a new method for estimating networks with hubs that exploits the ability
of (inverse) covariance estimation methods to include structural information
about the underlying network. The proposed method is a weighted LASSO
approach with novel row/column sum weights, which we refer to as the hubs
weighted graphical LASSO. A practical advantage of the new method is that
it leads to an optimization problem that is solved using the e_cient graph-
ical lasso algorithm that is already implemented in the R package glasso. I
will also discuss theoretical properties of the method when the number of
parameters diverges with the sample size, and via simulations show that the
method outperforms competing methods. If time permits, I will illustrate
the method with an application to microbiome data. This work is based on
the PhD thesis of my former student Annaliza McGillivray co-supervised by
David Stephens.