12 papers
Parisi Formula for the ground state energy of quantum p-Spin Hamiltonians
Sohom Bhattacharya
Quantum -local spin glass Hamiltonians are natural quantum analogues of the classical spin glass models. We provide an asymptotic characterization of the maximal energy achievab…
LDP for Tensor Forms
Reihaneh Malekian, Sohom Bhattacharya, Nabarun Deb +1
In this paper, we study the large deviation principle (LDP) for a tensor-weighted functional of i.i.d. random variables, when the sequence of tensors converges under a variant of t…
Nonsense associations in Markov random fields with pairwise dependence
Sohom Bhattacharya, Rajarshi Mukherjee, Elizabeth Ogburn
Yule (1926) identified the issue of "nonsense correlations" in time series data, where dependence within each of two random vectors causes overdispersion -- i.e. variance inflation…
Inferences on Mixing Probabilities and Ranking in Mixed-Membership Models
Sohom Bhattacharya, Jianqing Fan, Jikai Hou
Network data is prevalent in numerous big data applications including economics and health networks where it is of prime importance to understand the latent structure of network. I…
Gibbs Measures with Multilinear Forms
Sohom Bhattacharya, Nabarun Deb, Sumit Mukherjee
In this paper, we study a class of multilinear Gibbs measures with Hamiltonian given by a generalized -statistic and with a general base measure. Expressing the asympto…
Deep Neural Networks for Nonparametric Interaction Models with Diverging Dimension
Sohom Bhattacharya, Jianqing Fan, Debarghya Mukherjee
Deep neural networks have achieved tremendous success due to their representation power and adaptation to low-dimensional structures. Their potential for estimating structured regr…
LDP for Inhomogeneous U-Statistics
Sohom Bhattacharya, Nabarun Deb, Sumit Mukherjee
In this paper we derive a Large Deviation Principle (LDP) for inhomogeneous U/V-statistics of a general order. Using this, we derive a LDP for two types of statistics: random multi…
PC Adjusted Testing for Low Dimensional Parameters
Sohom Bhattacharya, Rounak Dey, Rajarshi Mukherjee
In this paper, we investigate the impact of high-dimensional Principal Component (PC) adjustments on inferring the effects of variables on outcomes, with a focus on applications in…
Sharp Signal Detection Under Ferromagnetic Ising Models
Sohom Bhattacharya, Rajarshi Mukherjee, Gourab Ray
In this paper we study the effect of dependence on detecting a class of structured signals in Ferromagnetic Ising models. Natural examples of our class include Ising Models on latt…
Matrix completion with data-dependent missingness probabilities
Sohom Bhattacharya, Sourav Chatterjee
The problem of completing a large matrix with lots of missing entries has received widespread attention in the last couple of decades. Two popular approaches to the matrix completi…
Spectral Edge in Sparse Random Graphs: Upper and Lower Tail Large Deviations
Bhaswar B. Bhattacharya, Sohom Bhattacharya, Shirshendu Ganguly
In this paper we consider the problem of estimating the joint upper and lower tail large deviations of the edge eigenvalues of an Erdős-Rényi random graph , in t…
Upper Tail For Homomorphism Counts In Constrained Sparse Random Graphs
Sohom Bhattacharya, Amir Dembo
Consider the upper tail probability that the homomorphism count of a fixed graph within a large sparse random graph exceeds its expected value by a fixed factor . Go…