Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The phase transition for the existence of the maximum likelihood
  estimate in high-dimensional logistic regression   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 transition'. We introduce an
explicit boundary curve $h_{\text{MLE}}$, parameterized by two scalars
measuring the overall magnitude of the unknown sequence of regression
coefficients, with the following property: in the limit of large sample sizes
$n$ and number of features $p$ proportioned in such a way that $p/n \rightarrow
\kappa$, we show that if the problem is sufficiently high dimensional in the
sense that $\kappa > h_{\text{MLE}}$, then the MLE does not exist with
probability one. Conversely, if $\kappa < h_{\text{MLE}}$, the MLE
asymptotically exists with probability one.

33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs