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Description
An ICTP Hybrid Meeting

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 high-dimensional statistics.
 
Inference and learning systems have been studied for decades. But the richness of contemporary high-dimensional 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:
  • High-dimensional statistics
  • Random matrix theory
  • Statistical physics
  • Information theory
  • Theoretical machine learning
  • Graph theory

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.

 
 

Material

Random Matrices, Random Graphs and Statistical Physics for Machine Learning and Inference | (smr 3703)
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  • Monday, 16 May 2022
    • 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.
    • 09:30 - 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, R-transform 45'
        Speaker: Marc POTTERS (Capital Fund Management, France)
        Material: Video
      • 10:15 Coffee break 25'
      • 10:40 Rank-1 deformation (1): eigenvalue and eigenvector, fluctuations 45'
        Speaker: Marc POTTERS (Capital Fund Management, France)
        Material: Video
    • 11:25 - 16:45 Least-square 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
  • Tuesday, 17 May 2022
    • 09:30 - 16:45
      Location: Adriatico Guest House - Giambiagi Lecture Hall
      • 09:30 Covariance inference (1): Sample Covariance matrices, Free Product, S-transform 45'
        Speaker: Marc POTTERS (Capital Fund Management, France)
        Material: Video
      • 10:15 Coffee break 25'
      • 10:40 Covariance inference (2): Eigenvector overlap and Ledoit-Peche 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
  • Wednesday, 18 May 2022
    • 09:30 - 15:00
      Location: Adriatico Guest House - Giambiagi Lecture Hall
      • 09:30 Rank-1 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, cross-validation, 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'
    • 15:00 - 16:45 Community detection and alignment in random graphs’
      Location: Adriatico Guest House - Giambiagi Lecture Hall
      • 15:00 Tree reconstruction : Kesten-Stigum threshold 45'
        Speaker: Laurent MASSOULIE (INRIA Paris, France)
        Material: Video
      • 15:45 Break 15'
      • 16:00 Non-backtracking spectra of random graphs: community detection above Kesten-Stigum threshold 45'
        Speaker: Laurent MASSOULIE (INRIA Paris, France)
        Material: Video
  • Thursday, 19 May 2022
    • 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 Baik-Ben Arous-Péché 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 polynomial-time alignment of correlated graphs 45'
        Speaker: Laurent MASSOULIE (INRIA Paris, France)
        Material: Video
  • Friday, 20 May 2022
    • 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) Kac-Rice 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 Information-theoretic limits to graph alignment 45'
        Speaker: Laurent MASSOULIE (INRIA Paris, France)
        Material: Video
      • 12:10 Lunch Break 1h50'
      • 14:00 Polynomial-time 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
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