
A note on "MLE in logistic regression with a diverging dimension"
This short note is to point the reader to notice that the proof of high ...
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The Impact of Regularization on Highdimensional Logistic Regression
Logistic regression is commonly used for modeling dichotomous outcomes. ...
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A modern maximumlikelihood theory for highdimensional logistic regression
Every student in statistics or data science learns early on that when th...
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The Likelihood Ratio Test in HighDimensional Logistic Regression Is Asymptotically a Rescaled ChiSquare
Logistic regression is used thousands of times a day to fit data, predic...
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The Asymptotic Distribution of the MLE in Highdimensional Logistic Models: Arbitrary Covariance
We study the distribution of the maximum likelihood estimate (MLE) in hi...
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A NonIntrusive Correction Algorithm for Classification Problems with Corrupted Data
A novel correction algorithm is proposed for multiclass classification ...
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Optimal link prediction with matrix logistic regression
We consider the problem of link prediction, based on partial observation...
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SLOE: A Faster Method for Statistical Inference in HighDimensional Logistic Regression
Logistic regression remains one of the most widely used tools in applied statistics, machine learning and data science. However, in moderately highdimensional problems, where the number of features d is a nonnegligible fraction of the sample size n, the logistic regression maximum likelihood estimator (MLE), and statistical procedures based the largesample approximation of its distribution, behave poorly. Recently, Sur and Candès (2019) showed that these issues can be corrected by applying a new approximation of the MLE's sampling distribution in this highdimensional regime. Unfortunately, these corrections are difficult to implement in practice, because they require an estimate of the signal strength, which is a function of the underlying parameters β of the logistic regression. To address this issue, we propose SLOE, a fast and straightforward approach to estimate the signal strength in logistic regression. The key insight of SLOE is that the Sur and Candès (2019) correction can be reparameterized in terms of the corrupted signal strength, which is only a function of the estimated parameters β. We propose an estimator for this quantity, prove that it is consistent in the relevant highdimensional regime, and show that dimensionality correction using SLOE is accurate in finite samples. Compared to the existing ProbeFrontier heuristic, SLOE is conceptually simpler and orders of magnitude faster, making it suitable for routine use. We demonstrate the importance of routine dimensionality correction in the Heart Disease dataset from the UCI repository, and a genomics application using data from the UK Biobank. We provide an open source package for this method, available at <https://github.com/googleresearch/sloelogistic>.
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