Description 
An ICTP Hybrid Meeting. You can submit your application for participation in presence or online.
This school on random matrices and graphs, machine learning and statistical physics will emphasize the strong connections between these fields, strenghten the analytical toolbox of the students and provide a modern vision of the challenges in highdimensional statistics.
Inference and learning systems have been studied for decades. But the richness of contemporary highdimensional statistical models (deep neural networks, community detection and inference on graphs, tensor factorization etc) require novel ideas and analytical methods. In particular, blending methods from random matrix theory, statistical physics and information theory is particularly promising. The school aims at providing an overview of recent progresses in this interdisciplinary field by worldwide experts coming from different backgrounds, but who all share a common goal of better modelling complex systems processing large datasets, and understanding their fundamental and algorithmic limitations.
Topics:
Lecturers: C. MALE, Bordeaux University, France
L. MASSOULIÉ, INRIA Paris, France
M. LELARGE, INRIA Paris & Ecole Polytechnique, France
M. POTTERS, Capital Fund Management, France
P. VIVO, King's College London, UK
Grants: A limited number of grants are available to support the attendance of selected participants. There is no registration fee. 
Random Matrices, Random Graphs and Statistical Physics for Machine Learning and Inference  (smr 3703)
Go to day


09:00  09:30

09:00
Registration formalities (in person participants)
30' (
Adriatico Guest House  Registration desk
)
REGISTRATION: Upon arrival, Visitors not staying in the ICTP Guest Houses, are kindly requested to complete registration formalities at the Adriatico Guesthouse as follows: Registration Desk (Lower level) from 9.00 till 9.30.

09:00
Registration formalities (in person participants)
30' (
Adriatico Guest House  Registration desk
)

09:30  11:25
Eigenvector problems in RMT, with applications
Time zone: You can choose your time zone (in place of Europe/Rome) on the top right of the page and the programme time will be modified accordingly.
Location: Adriatico Guest House  Giambiagi Lecture Hall 
09:30
RMT basics: invariant ensembles, eigenvalue density, Stieltjes transform, Rtransform
45'
Speaker: Marc POTTERS (Capital Fund Management, France) Material: Video  10:15 Coffee break 25'

10:40
Rank1 deformation (1): eigenvalue and eigenvector, fluctuations
45'
Speaker: Marc POTTERS (Capital Fund Management, France) Material: Video

09:30
RMT basics: invariant ensembles, eigenvalue density, Stieltjes transform, Rtransform
45'

11:25  16:45
Leastsquare optimization on the sphere: lessons from RMT and replicas

11:25
General setting: minimisation of a quadratic loss function with random coefficients and spherical constraint
45'
Speaker: Pierpaolo VIVO (King's College London, UK) Material: Video  12:10 Lunch Break 1h50'

14:00
The “Procrustes problem”
45'
Speaker: Pierpaolo VIVO (King's College London, UK) Material: Video  14:45 Break 15'

15:00
Recent free probability methods for large random matrices: computational aspects for non standard random matrix ensembles Part I
45'
Speaker: Camille MALE (Bordeaux University, France) Material: Abstract Video  15:45 Break 15'

16:00
Recent free probability methods for large random matrices: computational aspects for non standard random matrix ensembles Part II
45'
Speaker: Camille MALE (Bordeaux University, France) Material: Video

11:25
General setting: minimisation of a quadratic loss function with random coefficients and spherical constraint
45'

09:00  09:30


09:30  16:45
Location: Adriatico Guest House  Giambiagi Lecture Hall 
09:30
Covariance inference (1): Sample Covariance matrices, Free Product, Stransform
45'
Speaker: Marc POTTERS (Capital Fund Management, France) Material: Video  10:15 Coffee break 25'

10:40
Covariance inference (2): Eigenvector overlap and LedoitPeche estimator
45'
Speaker: Marc POTTERS (Capital Fund Management, France) 
11:25
Recent free probability methods for large random matrices: computational aspects for non standard random matrix ensembles Part III
45'
Speaker: Camille MALE (Bordeaux University, France) Material: Video  12:10 Lunch Break 1h50'

14:00
Recent free probability methods for large random matrices: computational aspects for non standard random matrix ensembles Part IV
45'
Speaker: Camille MALE (Bordeaux University, France) Material: Video  14:45 Break 15'

15:00
Counting of stationary points via the Lagrange multipliers method
45'
Speaker: Pierpaolo VIVO (King's College London, UK) Material: Video  15:45 Break 15'

16:00
Statistics of the Lagrange multipliers
45'
Speaker: Pierpaolo VIVO (King's College London, UK) Material: Video

09:30
Covariance inference (1): Sample Covariance matrices, Free Product, Stransform
45'

09:30  16:45


09:30  15:00
Location: Adriatico Guest House  Giambiagi Lecture Hall 
09:30
Rank1 deformation (2): eigenvalue and eigenvector, fluctuations
45'
Speaker: Marc POTTERS (Capital Fund Management, France) Material: Video  10:15 Coffee break 25'

10:40
Covariance inference (3): Numerical aspects, kernel methods, crossvalidation, applications to finance
45'
Speaker: Marc POTTERS (Capital Fund Management, France) Material: Video 
11:25
Statistical physics and random matrix theory for statistical inference I
45'
Speaker: Marc LELARGE (INRIA Paris & Ecole Polytechnique, France) Material: Abstract Video  12:10 Lunch Break 1h50'

14:00
Statistical physics and random matrix theory for statistical inference II
45'
Speaker: Marc LELARGE (INRIA Paris & Ecole Polytechnique, France) Material: Video  14:45 Break 15'

09:30
Rank1 deformation (2): eigenvalue and eigenvector, fluctuations
45'

15:00  16:45
Community detection and alignment in random graphs’
Location: Adriatico Guest House  Giambiagi Lecture Hall 
15:00
Tree reconstruction : KestenStigum threshold
45'
Speaker: Laurent MASSOULIE (INRIA Paris, France) Material: Video  15:45 Break 15'

16:00
Nonbacktracking spectra of random graphs: community detection above KestenStigum threshold
45'
Speaker: Laurent MASSOULIE (INRIA Paris, France) Material: Video

15:00
Tree reconstruction : KestenStigum threshold
45'

09:30  15:00


09:30  17:30
Location: Adriatico Guest House  Giambiagi Lecture Hall 
09:30
Recent free probability methods for large random matrices: computational aspects for non standard random matrix ensembles Part V
45'
Speaker: Camille MALE (Bordeaux University, France) Material: Video  10:15 Coffee break 25'

10:40
Recent free probability methods for large random matrices: computational aspects for non standard random matrix ensembles Part VI
45'
Speaker: Camille MALE (Bordeaux University, France) Material: Video 
11:25
Statistical physics and random matrix theory for statistical inference III
45'
Speaker: Marc LELARGE (INRIA Paris & Ecole Polytechnique, France) Material: Video  12:10 Lunch Break 1h50'

14:00
Statistical physics and random matrix theory for statistical inference IV
45'
Speaker: Marc LELARGE (INRIA Paris & Ecole Polytechnique, France) Material: Video  14:45 Break 15'

15:00
Links to Ramanujan graphs and BaikBen ArousPéché transition
45'
Speaker: Laurent MASSOULIE (INRIA Paris, France) Material: Video  15:45 Group Photo (online) 5'
 15:50 Break 10'

16:00
Tree matching weight and polynomialtime alignment of correlated graphs
45'
Speaker: Laurent MASSOULIE (INRIA Paris, France) Material: Video

09:30
Recent free probability methods for large random matrices: computational aspects for non standard random matrix ensembles Part V
45'

09:30  17:30


09:30  16:45
Location: Adriatico Guest House  Giambiagi Lecture Hall 
09:30
Statistics of the Lagrange multipliers
45'
Speaker: Pierpaolo VIVO (King's College London, UK) Material: Video  10:15 Coffee break 25'

10:40
Techniques: (i) KacRice formula (ii) minimisation as \beta\to\infty limit of the free energy of an associated canonical problem (iii) replica trick to get rid of the logarithm (iv) Random matrix tools to deal with the randomness in the coefficients
45'
Speaker: Pierpaolo VIVO (King's College London, UK) Material: Video 
11:25
Informationtheoretic limits to graph alignment
45'
Speaker: Laurent MASSOULIE (INRIA Paris, France) Material: Video  12:10 Lunch Break 1h50'

14:00
Polynomialtime graph alignment from feasibility of testing tree correlation
45'
Speaker: Laurent MASSOULIE (INRIA Paris, France) Material: Video  14:45 Break 15'

15:00
Statistical physics and random matrix theory for statistical inference V
45'
Speaker: Marc LELARGE (INRIA Paris & Ecole Polytechnique, France) Material: Video  15:45 Break 15'

16:00
Statistical physics and random matrix theory for statistical inference VI
45'
Speaker: Marc LELARGE (INRIA Paris & Ecole Polytechnique, France) Material: Video

09:30
Statistics of the Lagrange multipliers
45'

09:30  16:45