• Corpus ID: 238419483

# High Dimensional Logistic Regression Under Network Dependence

@inproceedings{Mukherjee2021HighDL,
title={High Dimensional Logistic Regression Under Network Dependence},
author={Somabha Mukherjee and Sagnik Halder and Bhaswar B. Bhattacharya and George Michailidis},
year={2021}
}
• Somabha Mukherjee, +1 author G. Michailidis
• Published 7 October 2021
• Mathematics
Abstract. Logistic regression is one of the most fundamental methods for modeling the probability of a binary outcome based on a collection of covariates. However, the classical formulation of logistic regression relies on the independent sampling assumption, which is often violated when the outcomes interact through an underlying network structure, such as over a temporal/spatial domain or on a social network. This necessitates the development of models that can simultaneously handle both the…

## References

SHOWING 1-10 OF 71 REFERENCES
Logistic-Regression with peer-group effects via inference in higher order Ising models
• Mathematics, Computer Science
AISTATS
• 2020
This work model binary outcomes on a network as a higher-order spin glass, where the behavior of an individual depends on a linear function of their own vector of covariates and some polynomial function of others, capturing peer-group effects.
Regression from dependent observations
• Computer Science, Mathematics
STOC
• 2019
This work presents computationally and statistically efficient methods for linear and logistic regression models when the response variables are dependent on a network, and proves strong consistency results for recovering the vector of coefficients and the strength of the dependencies.
High-dimensional Ising model selection using ℓ1-regularized logistic regression
• Mathematics
• 2010
We consider the problem of estimating the graph associated with a binary Ising Markov random field. We describe a method based on $\ell_1$-regularized logistic regression, in which the neighborhood
Optimal Single Sample Tests for Structured versus Unstructured Network Data
• Mathematics, Computer Science
COLT
• 2018
This work develops a new approach that applies to both the Ising and Exponential Random Graph settings based on a general and natural statistical test that can distinguish the hypotheses with high probability above a certain threshold in the (inverse) temperature parameter, and is optimal in that below the threshold no test can distinctions the hypotheses.
Hidden Markov Models and Disease Mapping
• Mathematics
• 2002
We present new methodology to extend hidden Markov models to the spatial domain, and use this class of models to analyze spatial heterogeneity of count data on a rare phenomenon. This situation
A Semiparametric Two-Sample Hypothesis Testing Problem for Random Graphs
• Mathematics
• 2017
ABSTRACT Two-sample hypothesis testing for random graphs arises naturally in neuroscience, social networks, and machine learning. In this article, we consider a semiparametric problem of two-sample
High-dimensional structure estimation in Ising models: Local separation criterion
• Mathematics, Computer Science
• 2012
A novel criterion for tractable graph families, where this method is efficient, based on the presence of sparse local separators between node pairs in the underlying graph, is introduced.
The phase transition for the existence of the maximum likelihood estimate in high-dimensional logistic regression
• Mathematics
• 2018
This paper rigorously establishes that the existence of the maximum likelihood estimate (MLE) in high-dimensional logistic regression models with Gaussian covariates undergoes a sharp `phase
Nonconcave penalized composite conditional likelihood estimation of sparse Ising models
• Mathematics
• 2012
The Ising model is a useful tool for studying complex interactions within a system. The estimation of such a model, however, is rather challenging, especially in the presence of high-dimensional
The likelihood ratio test in high-dimensional logistic regression is asymptotically a rescaled Chi-square
• Computer Science, Mathematics
Probability Theory and Related Fields
• 2019
It is proved that when p is not negligible compared to n, Wilks’ theorem does not hold and that the Chi-square approximation is grossly incorrect; in fact, this approximation produces p-values that are far too small (under the null hypothesis).