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 thesignal strength, which is a function of the underlying parametersβ of the logistic regression.

Consider the problem of training deep neural networks on large annotated datasets, such as ImageNet [1]. This problem can be formalized as finding optimal parameters for a given neural networka,parameterized byw,w.r.t.

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