[Ml-stat-talks] Fwd: Wilks Statistics Seminar: Arian Maleki, Today, November. 13th @ 12:30pm, Sherrerd Hall 101

Barbara Engelhardt bee at princeton.edu
Fri Nov 13 09:00:07 EST 2015

Talk of interest today.


---------- Forwarded message ----------
From: Carol Smith <carols at princeton.edu>
Date: Fri, Nov 13, 2015 at 8:50 AM
Subject: Wilks Statistics Seminar: Arian Maleki, Today, November. 13th @
12:30pm, Sherrerd Hall 101
To: wilks-seminar at princeton.edu

***   Wilks Statistics Seminar   ***

DATE:  Today, November 13, 2015

TIME:   12:30pm

LOCATION:   Sherrerd Hall, room 101

SPEAKER:    Arian Maleki, Columbia University

TITLE:   On The Asymptotic Performance of ℓ q   -regularized Least Squares

ABSTRACT:   In many application areas ranging from bioinformatics to
imaging we are faced with the following question: Can we recover a sparse
vector β o ∈R p   from its undersampled set of noisy observations y∈R n   ,
y=Xβ+ϵ  . The last decade has witnessed a surge of algorithms to address
this question. One of the most popular algorithms is the ℓ q   -regularized
least squares given by the following formulation:
β ^ (λ,q)=argmin β 12 |y−Xβ| 2 2 +λ|β| q q .
Despite the non-convexity of these optimization problems for 0<q<1  , they
are still appealing for their closer proximity to the ``ideal'' ℓ 0
-regularized least squares. In this talk, we adopt the asymptotic framework
p→∞  and n/p→δ  and analyze the properties of the global minimizer of (???)
  under the optimal tuning of the parameter λ  . In particular, we discuss
the phase transition and noise sensitivity of these optimization problems.
If time permits, we discuss algorithms that can reach to the global minima
of these problems in certain regimes and explain how their performance is
compared with the popular LASSO.
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