[Sds-seminars] S&DS Seminar, Ahmed El Alaoui, 9/19, 4pm-5pm, DL220, "Sampling from the SK measure via algorithmic stochastic localization"

[elizavette.torres at yale.edu]

In-Person seminars will be held at Dunham Lab, 10 Hillhouse Ave., Room 220,
with an option of remote participation via zoom.

 <https://statistics.yale.edu/>     <https://statistics.yale.edu/>
Department of Statistics and Data Science

We invite you to attend our in-person seminar.

Ahmed El Alaoui, Cornell University



Monday, September 19, 2022

4:00PM to 5:00PM

Dunham Lab.

10 Hillhouse Avenue, Rm. 220

New Haven, CT 06511

OR

Via Zoom:
https://yale.zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09  /
Password: 24

https://statistics.yale.edu/seminars/ahmed-el-alaoui





Title: Sampling from the SK measure via algorithmic stochastic localization



Information and Abstract:

The Sherrington-Kirkpatrick measure is a random probability distribution on
the hypercube, which is a central object of study in probability theory and
in the mean-field theory of disordered statistical physics models.



In this talk I will present an algorithm which efficiently samples from the
SK measure with no external field and at high temperature. The approach uses
a discretized version of the stochastic localization process of Eldan,
together with a subroutine for computing the mean vector, or magnetization,
of a family of SK measures tilted by an appropriate external field. This
approach is very general and has wide applicability.



Our analysis shows that the algorithm outputs an approximate sample (in a
certain weak sense) from the SK measure, for all inverse temperatures beta <
1/2. In a recent paper, Celentano (2022) shows that our algorithm succeeds
up to the critical temperature beta < beta_c = 1.



Conversely, we show that in the ‘low temperature’ phase beta >1, no
‘stable’ algorithm can approximately sample from the SK measure. This
exploits a newly established strong version of a property called `disorder
chaos’ exhibited by SK in this regime.



The above two results settle the question of the computational tractability
of sampling from SK for all temperatures except the critical one.



This is based on a  <https://arxiv.org/abs/2203.05093> joint work with
Andrea Montanari and Mark Sellke.



 <x-apple-data-detectors://10/> 3:30pm -   Pre-talk meet and greet.



Zoom Link: Via Zoom: Join from PC, Mac, Linux, iOS or Android: https://yale.
zoom.us/j/92411077917?pwd=aXhnTnFGRXFoaTVDczNjeFFKeWpTQT09

    Password: 24
    Or Telephone：203-432-9666 (2-ZOOM if on-campus) or 646 568 7788
    Meeting ID: 924 1107 7917



For more details and upcoming events visit our website at
<http://statistics.yale.edu/> http://statistics.yale.edu/ .



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