Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimax Bounds for Distributed Logistic Regression   We consider a distributed logistic regression problem where labeled data
pairs $(X_i,Y_i)\in \mathbb{R}^d\times\{-1,1\}$ for $i=1,\ldots,n$ are
distributed across multiple machines in a network and must be communicated to a
centralized estimator using at most $k$ bits per labeled pair. We assume that
the data $X_i$ come independently from some distribution $P_X$, and that the
distribution of $Y_i$ conditioned on $X_i$ follows a logistic model with some
parameter $\theta\in\mathbb{R}^d$. By using a Fisher information argument, we
give minimax lower bounds for estimating $\theta$ under different assumptions
on the tail of the distribution $P_X$. We consider both $\ell^2$ and logistic
losses, and show that for the logistic loss our sub-Gaussian lower bound is
order-optimal and cannot be improved.

22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph