Home Page of Subhro Ghosh

Subhroshekhar Ghosh
National University of Singapore
Department of Mathematics
Dept of Statistics and Data Science
Institute of Data Science
Singapore

Email:
subhrowork (**at**) gmail.com
matghos (**at**) nus.edu.sg

About me

I am an assistant professor at the National University of Singapore and a faculty affiliate at the Institute of Data Science, NUS. I am broadly interested in stochastics, focussing on problems from statistical physics and the math of data, and their interactions. Before joining NUS, I was a post doc at Princeton University, and prior to that I obtained my PhD from the University of California, Berkeley. Earlier, I received my Bachelor in Statistics and Master in Mathematics degrees from the Indian Statistical Institute.

Research

I am broadly interested in stochastics, focussing on problems from statistical physics and the math of data, and their interactions. These encompass constrained stochastic systems and their applications, including problems of learning under complex structure (e.g., latent group actions), dimension reduction, sampling and optimization, statistical networks and signal processing. Key paradigms include determinantal processes (DPP), strong Rayleigh measures and negative dependence, multi reference alignment (MRA), empirical likelihood, generative priors, Gaussian analytic functions (GAF), random tensors and stochastic geometry. The investigation of these problems naturally brings together a wide array of tools and techniques, including probability, harmonic and complex analysis, persistent homology and the theory of group representations.

For more on my research, please refer to Selected & recent works and my full list of Publications.

Some selected and recent works

Gaussian determinantal processes: A new model for directionality in data, with P. Rigollet,
Proceedings of the National Academy of Sciences, vol. 117, no. 24 (2020), pp. 13207--13213
(Direct Submission)
article

Sparse Multi-Reference Alignment: Phase Retrieval, Uniform Uncertainty Principles and the Beltway Problem, with P. Rigollet
Foundations of Computational Math. (2022). https://doi.org/10.1007/s10208-022-09584-6
preprint

Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD, with R. Bardenet, M. Lin
Spotlight paper (< 3% of all submissions) at NeurIPS 2021
Advances in Neural Information Processing Systems 34 (2021).
preprint

Maximum Likelihood under constraints: Degeneracies and Random Critical Points, with S. Chaudhuri,
preprint

Gaussian complex zeros on the hole event: the emergence of a forbidden region, with A. Nishry,
Communications in Pure Appl. Math., 72, no. 1 (2019): 3-62
preprint

Rigidity and Tolerance in point processes: Gaussian zeroes and Ginibre eigenvalues, with Y. Peres,
Duke Mathematical Journal, 166 (10), 1789-1858
preprint

Determinantal processes and completeness of random exponentials: the critical case,
Probability Theory and Related Fields, 163 (3-4), 643-665
preprint

Generalized stealthy hyperuniform processes: maximal rigidity and the bounded holes conjecture, with J.L. Lebowitz,
Communications in Math. Physics, 363, no. 1 (2018): 97-110
preprint

Fluctuation and Entropy in Spectrally Constrained random fields, with K. Adhikari, J.L. Lebowitz,
Communications in Math. Physics, 386, 749–780 (2021).
preprint

Rigidity hierarchy in random point fields: random polynomials and determinantal processes, with M. Krishnapur,
Communications in Math. Physics , 388, no. 3 (2021): 1205-1234.
preprint

Continuum Percolation for Gaussian zeroes and Ginibre eigenvalues, with M. Krishnapur, Y. Peres,
Annals of Probability, 44 (5), 3357-3384 (2016)
preprint

Towards Sample-Optimal Compressive Phase Retrieval with Sparse and Generative Priors, with Z. Liu, J. Scarlett,
Neural Information Processing Systems (NeurIPS) , 2021
preprint

Signal Analysis via the Stochastic Geometry of Spectrogram Level Sets , with M. Lin, D. Sun
IEEE Transactions on Signal Processing, 70 (2022): 1104-1117.
preprint

Fractal Gaussian Networks: A sparse random graph model based on Gaussian Multiplicative Chaos, with K. Balasubramanian, X. Yamg,
IEEE Transactions on Information Theory, to appear
International Conference on Machine Learning (ICML), 2020
preprint
Disordered complex networks: energy optimal lattices and persistent homology, with N. Miyoshi, T. Shirai,
IEEE Transactions on Information Theory , to appear
preprint

Generative Principal Component Analysis , with Z. Liu, J. Liu, J. Han, J. Scarlett,
International Conference on Learning Representations (ICLR) , 2022
preprint

Learning with latent group sparsity via heat flow dynamics on networks, with S.S. Mukherjee,
preprint

Quantitative Marcinkiewicz's theorem and central limit theorems: applications to spin systems and point processes, with T.C. Dinh, H.S. Tran, M.H. Tran
preprint

Publications

Sparse Multi-Reference Alignment: Phase Retrieval, Uniform Uncertainty Principles and the Beltway Problem, with P. Rigollet
Foundations of Computational Math. (2022). https://doi.org/10.1007/s10208-022-09584-6
preprint

Learning with latent group sparsity via heat flow dynamics on networks, with S.S. Mukherjee,
preprint

Disordered complex networks: energy optimal lattices and persistent homology, with N. Miyoshi, T. Shirai,
IEEE Transactions on Information Theory, to appear
preprint

Signal Analysis via the Stochastic Geometry of Spectrogram Level Sets , with M. Lin, D. Sun
IEEE Transactions on Signal Processing, 70 (2022): 1104-1117.
preprint

Fractal Gaussian Networks: A sparse random graph model based on Gaussian Multiplicative Chaos, with K. Balasubramanian, X. Yang,
IEEE Transactions on Information Theory, to appear
International Conference on Machine Learning (ICML), 2020
preprint
Generative Principal Component Analysis , with Z. Liu, J. Liu, J. Han, J. Scarlett,
International Conference on Learning Representations (ICLR) , 2022
preprint

Rigidity hierarchy in random point fields: random polynomials and determinantal processes, with M. Krishnapur,
Communications in Mathematical Physics, 388, no. 3 (2021): 1205-1234.
preprint

Determinantal point processes based on orthogonal polynomials for sampling minibatches in SGD, with R. Bardenet, M. Lin
Spotlight paper (< 3% of submissions) at NeurIPS 2021
at Advances in Neural Information Processing Systems 34 (2021).
Towards Sample-Optimal Compressive Phase Retrieval with Sparse and Generative Priors, with Z. Liu, J. Scarlett,
Neural Information Processing Systems (NeurIPS), 2021
preprint

Fluctuation and Entropy in Spectrally Constrained random fields, with K. Adhikari, J.L. Lebowitz,
Communications in Math. Physics, 386, 749–780 (2021).
preprint

Quantitative Marcinkiewicz's theorem and central limit theorems: applications to spin systems and point processes, with T.C. Dinh, H.S. Tran, M.H. Tran
preprint

Robust 1-bit Compressive Sensing with Partial Gaussian Circulant Matrices and Generative Priors, with Z. Liu, J. Scarlett
IEEE Information Theory Workshop 2021
preprint

On a Variational Approximation based Empirical Likelihood ABC Method, with S. Chaudhuri, D.J. Nott, K.C. Pham
preprint

Learning from DPPs via Sampling: Beyond HKPV and symmetry, with R. Bardenet
preprint

Transmission and Navigation on Disordered Lattice Networks, Directed Spanning Forests and Brownian Web, with K. Saha,
Journal of Statistical Physics 180, no. 1 (2020): 1167-1205
Special issue in honour of J.L. Lebowitz
preprint

Gaussian determinantal processes: A new model for directionality in data, with P. Rigollet,
Proceedings of the National Academy of Sciences,vol. 117, no. 24 (2020), pp. 13207--13213
article

Maximum Likelihood under constraints: Degeneracies and Random Critical Points, with S. Chaudhuri,
preprint

Gaussian complex zeros on the hole event: the emergence of a forbidden region, with A. Nishry,
Communications in Pure Appl. Math., 72, no. 1 (2019): 3-62
preprint

Generalized stealthy hyperuniform processes: maximal rigidity and the bounded holes conjecture, with J.L. Lebowitz,
Communications in Math. Physics, 363, no. 1 (2018): 97-110
preprint

Point processes, hole events, and large deviations: random complex zeros and Coulomb gases, with A. Nishry,
Constructive Approximation, 48, no. 1 (2018): 101-136.
Special Issue: Approximation and Statistical Physics – Part I
preprint

Fluctuations, large deviations and rigidity in hyperuniform systems: a brief survey, with J.L. Lebowitz
Indian Journal of Pure and Applied Mathematics vol. 48 no. 4 (2017), 609-631
Special issue in honour of B.V. Rao
preprint

Rigidity and Tolerance in point processes: Gaussian zeroes and Ginibre eigenvalues, with Y. Peres,
Duke Mathematical Journal, 1166, no. 10, 1789-1858 (2017)
preprint

Number rigidity in superhomogeneous random point fields, with J. L. Lebowitz,
Journal of Statistical Physics 166 (3-4), 1016-1027 (2017)
Special issue in honour of Y. Sinai
preprint

Multivariate CLT follows from strong Rayleigh property, with T. Liggett,R. Pemantle,
Proceedings of ANALCO, SIAM, 2017
preprint

Continuum Percolation for Gaussian zeroes and Ginibre eigenvalues, with M. Krishnapur, Y. Peres,
Annals of Probability, 44 (5), 3357-3384 (2016)
preprint

Palm measures and rigidity phenomena in point processes,
Electronic Communications in Probability 21 (2016)
preprint

Large deviations for zeros of random polynomials with i.i.d. exponential coefficients, with O. Zeitouni,
Int. Math. Res. Not., (5), 1308-1347 (2016)
preprint

Determinantal processes and completeness of random exponentials: the critical case,
Probability Theory and Related Fields, 163 (3-4), 643-665 (2015)
preprint

Rigidity and Tolerance in Gaussian zeroes and Ginibre eigenvalues: quantitative estimates,
preprint

Exact quantum algorithm to distinguish Boolean functions of different weights, with S.L. Braunstein, B.S. Choi, S. Maitra,
Journal of Physics A: Mathematical and Theoretical, Volume 40, Number 29 (2007)
journal

Symmetry of Bound and Antibound States in the Semiclassical Limit for a General Class of Potentials, with S. Dyatlov,
Proc. Amer. Math. Soc. 138 (2010), 3203-3210
preprint

Rigidity Phenomena in random point sets
PhD Thesis, UC Berkeley (2013)
Thesis

A Random Gallery

Left to right: Surface plot of normalised GAF; and Fractal Gaussian networks

Left to right: Gaussian DPP for clustering Fisher's Iris data; and stochastic geometry of spectrogram level sets

Left to right: Laplace transform based sampling for UK retail data; and DPP based minibatch sampling for Stochastic Gradient Descent

Left to right: Conditional intensity for a Gaussian matrix and for a Gaussian polynomial

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Teaching

Some courses that I have taught:

Stochastic Processes and Algorithms (MA5249) (graduate)

Topics in Undergraduate Mathematics : The Mathematics of Data (MA4292) (advanced undergraduate)

Stochastic Calculus (ORF527) (graduate)

Stochastic Processes (MA3238/ST3236) (undergraduate)

Living with Mathematics (GEH1036) (basic undergraduate)

Research Grants and organisational activities

My research work and organisational activities have been generously supported by :

Complex structures in Statistical Physics and the Math of Data [Singapore Ministry of Education grant T2EP20121-0033; 2022-2025]

Stochastics beyond Independence : A Math of Data Perspective [Singapore Ministry of Education grant R-146-000-312-114; 2020-2023]

Rigidity Phenomena in Random Processes [Singapore Ministry of Education grant R-146-000-250-133; 2017-2022]

The Mathematics of Data (with A. Bandeira, P. Rigollet) [Institute for Mathematical Sciences, Singapore; 02 Jan–26 Jan 2024]

Stat. Phys. of continuum particle systems with strong interactions (with D. Dereudre, A. Hardy, M. Maida) [Institute for Mathematical Sciences, Singapore; Aug29--Sep9 2022]

Random matrices, Stochastic geometry and Related topics (with T. Shirai, K. Suzaki) [J.S.P.S., Instt. for Math. Sc., Singapore & Dept. of Math. (NUS); Mar 14--16, 2019]

Resilience and Growth Programme [NUS, 2020-21]

Graduate students

I have had the pleasure to supervise :

Tran Hoang Son (PhD, 2020 -- )

Tran Man Hung (PhD, 2020 -- )

Bian Xinran (PhD, 2020 -- )

Hugo Simon (PhD, 2022 -- )

Jeremiah Thomson (Masters by research, 2020 -- )

Dongfang Sun (Masters by research, 2020)

Jnaneshwar Baslingekar (Research assistant, 2022)

Research Fellows

I have had the pleasure to mentor :

Meixia Lin

Ujan Gandopadhyay

Soumendu Sundar Mukherjee

Seminar

I organise the Stochastics Seminar together with Ujan Gandopadhyay. If you are interested in giving a talk, please reach out via e-mail.