# 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} }

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 ScienceAISTATS
- 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, MathematicsSTOC
- 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 ScienceCOLT
- 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, MathematicsProbability 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).