The phase transition for the existence of the maximum likelihood estimate in high-dimensional logistic regression

DOI10.1214/18-AOS1789zbMath1439.62171arXiv1804.09753OpenAlexW3007237875MaRDI QIDQ2176606

Emmanuel J. Candès, Pragya Sur

Publication date: 5 May 2020

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.09753

zbMATH Keywords

decision surfacehigh-dimensional logistic regressionmaximum likelihood estimate (MLE) phase transitionmultivariate centered normal distribution

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Asymptotic distribution theory in statistics (62E20) Generalized linear models (logistic models) (62J12) General considerations in statistical decision theory (62C05)

Related Items

Stochastic Tverberg Theorems With Applications in Multiclass Logistic Regression, Separability, and Centerpoints of Data, The asymptotic distribution of the MLE in high-dimensional logistic models: arbitrary covariance, Learning curves of generic features maps for realistic datasets with a teacher-student model*, A precise high-dimensional asymptotic theory for boosting and minimum-\(\ell_1\)-norm interpolated classifiers, Automatic bias correction for testing in high‐dimensional linear models, A Scale-Free Approach for False Discovery Rate Control in Generalized Linear Models, Unnamed Item, On functional logistic regression: some conceptual issues, Tractability from overparametrization: the example of the negative perceptron, The existence of maximum likelihood estimate in high-dimensional binary response generalized linear models, Unnamed Item, Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach, Computationally efficient likelihood inference in exponential families when the maximum likelihood estimator does not exist, Global and Simultaneous Hypothesis Testing for High-Dimensional Logistic Regression Models, Unnamed Item, Precise statistical analysis of classification accuracies for adversarial training, Large scale analysis of generalization error in learning using margin based classification methods, Large dimensional analysis of general margin based classification methods, A Unifying Tutorial on Approximate Message Passing, Generalisation error in learning with random features and the hidden manifold model*

Cites Work

• A new perspective on least squares under convex constraint
• The likelihood ratio test in high-dimensional logistic regression is asymptotically a rescaled Chi-square
• On the existence of maximum likelihood estimates in logistic regression models
• Stochastic and Integral Geometry
• A note on A. Albert and J. A. Anderson's conditions for the existence of maximum likelihood estimates in logistic regression models
• On existence and uniqueness of a vector minimizing a convex function
• Infinite Parameter Estimates in Logistic Regression, with Application to Approximate Conditional Inference
• Living on the edge: phase transitions in convex programs with random data
• A modern maximum-likelihood theory for high-dimensional logistic regression
• Universality laws for randomized dimension reduction, with applications
• Enumeration of Seven-Argument Threshold Functions
• Measuring overlap in binary regression.
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item