1 code implementation • 27 Feb 2024 • Hong T. M. Chu, Subhro Ghosh, Chi Thanh Lam, Soumendu Sundar Mukherjee

In this paper, we explore this problem in the context of more realistic neural networks with a general class of non-linear activation functions, and rigorously demonstrate the implicit regularization phenomenon for such networks in the setting of matrix sensing problems, together with rigorous rate guarantees that ensure exponentially fast convergence of gradient descent. In this vein, we contribute a network architecture called Spectral Neural Networks (abbrv.

no code implementations • 13 Dec 2023 • Subhro Ghosh, Soumendu Sundar Mukherjee, Jing Bin Pan

We demonstrate that the minimax optimal rate of estimation in for the sparse MRA problem in this setting is $\sigma^2/\sqrt{n}$, where $n$ is the sample size.

no code implementations • 4 Aug 2023 • Subhro Ghosh, Soumendu Sundar Mukherjee, Hoang-Son Tran, Ujan Gangopadhyay

In this work, we propose a novel estimator for the weighted network (equivalently, its Laplacian) from repeated measurements of a GFF on the network, based on the Fourier analytic properties of the Gaussian distribution.

no code implementations • 24 Jul 2023 • Soumendu Sundar Mukherjee

Consider the spiked Wigner model \[ X = \sum_{i = 1}^k \lambda_i u_i u_i^\top + \sigma G, \] where $G$ is an $N \times N$ GOE random matrix, and the eigenvalues $\lambda_i$ are all spiked, i. e. above the Baik-Ben Arous-P\'ech\'e (BBP) threshold $\sigma$.

no code implementations • 24 Feb 2023 • Satyaki Mukherjee, Soumendu Sundar Mukherjee, Debarghya Ghoshdastidar

We consider the general dimensionality reduction problem of locating in a high-dimensional data cloud, a $k$-dimensional non-Gaussian subspace of interesting features.

no code implementations • 2 Aug 2022 • Sayak Chatterjee, Shirshendu Chatterjee, Soumendu Sundar Mukherjee, Anirban Nath, Sharmodeep Bhattacharyya

Network-valued time series are currently a common form of network data.

no code implementations • 20 Jan 2022 • Subhroshekhar Ghosh, Soumendu Sundar Mukherjee

Group or cluster structure on explanatory variables in machine learning problems is a very general phenomenon, which has attracted broad interest from practitioners and theoreticians alike.

no code implementations • 29 Nov 2021 • Avinandan Bose, Soumendu Sundar Mukherjee

Changepoint analysis deals with unsupervised detection and/or estimation of time-points in time-series data, when the distribution generating the data changes.

no code implementations • 11 Feb 2021 • Keller Blackwell, Neelima Borade, Arup Bose, Charles Devlin VI, Noah Luntzlara, Renyuan Ma, Steven J. Miller, Soumendu Sundar Mukherjee, Mengxi Wang, Wanqiao Xu

For definiteness we concentrate on the ensemble of palindromic real symmetric Toeplitz (PST) matrices and the ensemble of real symmetric matrices, whose limiting spectral measures are the Gaussian and semi-circular distributions, respectively; these were chosen as they are the two extreme cases in terms of moment calculations.

Probability 15A52 (primary), 60F99, 62H10 (secondary)

no code implementations • 11 Jan 2021 • Soumendu Sundar Mukherjee

We also prove a free probability analogue of Craig's theorem, another well-known result in multivariate statistics on the independence of quadratic functions of Gaussian random matrices.

Point Processes Probability Operator Algebras Statistics Theory Statistics Theory 46L54, 60E05, 62E10

no code implementations • 20 Aug 2020 • Shyamal K. De, Soumendu Sundar Mukherjee

We consider offline detection of a single changepoint in binary and count time-series.

1 code implementation • 2 Jun 2019 • Soumendu Sundar Mukherjee, Sayak Chakrabarti

We consider estimating the edge-probability matrix of a network generated from a graphon model when the full network is not observed---only some overlapping subgraphs are.

no code implementations • ICLR 2019 • Ranjan Mondal, Sanchayan Santra, Soumendu Sundar Mukherjee, Bhabatosh Chanda

A few works have tried to utilize morphological neurons as a part of classification (and regression) networks when the input is a feature vector.

Ranked #1 on Representation Learning on Circle Data (using extra training data)

no code implementations • NeurIPS 2018 • Soumendu Sundar Mukherjee, Purnamrita Sarkar, Y. X. Rachel Wang, Bowei Yan

Variational approximation has been widely used in large-scale Bayesian inference recently, the simplest kind of which involves imposing a mean field assumption to approximate complicated latent structures.

no code implementations • 18 Aug 2017 • Soumendu Sundar Mukherjee, Purnamrita Sarkar, Peter J. Bickel

In this article, we advance divide-and-conquer strategies for solving the community detection problem in networks.

1 code implementation • NeurIPS 2017 • Soumendu Sundar Mukherjee, Purnamrita Sarkar, Lizhen Lin

Community detection, which focuses on clustering nodes or detecting communities in (mostly) a single network, is a problem of considerable practical interest and has received a great deal of attention in the research community.

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