Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Analysis of EM for truncated mixtures of two Gaussians   Motivated by a recent result of Daskalakis et al. 2018, we analyze the
population version of Expectation-Maximization (EM) algorithm for the case of
\textit{truncated} mixtures of two Gaussians. Truncated samples from a
$d$-dimensional mixture of two Gaussians $\frac{1}{2} \mathcal{N}(\vec{\mu},
\vec{\Sigma})+ \frac{1}{2} \mathcal{N}(-\vec{\mu}, \vec{\Sigma})$ means that a
sample is only revealed if it falls in some subset $S \subset \mathbb{R}^d$ of
positive (Lebesgue) measure. We show that for $d=1$, EM converges almost surely
(under random initialization) to the true mean (variance $\sigma^2$ is known)
for any measurable set $S$. Moreover, for $d>1$ we show EM almost surely
converges to the true mean for any measurable set $S$ when the map of EM has
only three fixed points, namely $-\vec{\mu}, \vec{0}, \vec{\mu}$ (covariance
matrix $\vec{\Sigma}$ is known), and prove local convergence if there are more
than three fixed points. We also provide convergence rates of our findings. Our
techniques deviate from those of Daskalakis et al. 2017, which heavily depend
on symmetry that the untruncated problem exhibits. For example, for an
arbitrary measurable set $S$, it is impossible to compute a closed form of the
update rule of EM. Moreover, arbitrarily truncating the mixture, induces
further correlations among the variables. We circumvent these challenges by
using techniques from dynamical systems, probability and statistics; implicit
function theorem, stability analysis around the fixed points of the update rule
of EM and correlation inequalities (FKG).

23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol