English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we study high-dimensional estimation from truncated samples.We focus on two fundamental and classical problems: (i) inference of sparseGaussian graphical models and (ii) support recovery of sparse linear models.  (i) For Gaussian graphical models, suppose $d$-dimensional samples ${\bf x}$are generated from a Gaussian $N(\mu,\Sigma)$ and observed only if they belongto a subset $S \subseteq \mathbb{R}^d$. We show that ${\mu}$ and ${\Sigma}$ canbe estimated with error $\epsilon$ in the Frobenius norm, using$\tilde{O}\left(\frac{\textrm{nz}({\Sigma}^{-1})}{\epsilon^2}\right)$ samplesfrom a truncated $\mathcal{N}({\mu},{\Sigma})$ and having access to amembership oracle for $S$. The set $S$ is assumed to have non-trivial measureunder the unknown distribution but is otherwise arbitrary.  (ii) For sparse linear regression, suppose samples $({\bf x},y)$ aregenerated where $y = {\bf x}^\top{{\Omega}^*} + \mathcal{N}(0,1)$ and $({\bfx}, y)$ is seen only if $y$ belongs to a truncation set $S \subseteq\mathbb{R}$. We consider the case that ${\Omega}^*$ is sparse with a supportset of size $k$. Our main result is to establish precise conditions on theproblem dimension $d$, the support size $k$, the number of observations $n$,and properties of the samples and the truncation that are sufficient to recoverthe support of ${\Omega}^*$. Specifically, we show that under some mildassumptions, only $O(k^2 \log d)$ samples are needed to estimate ${\Omega}^*$in the $\ell_\infty$-norm up to a bounded error.  For both problems, our estimator minimizes the sum of the finite populationnegative log-likelihood function and an $\ell_1$-regularization term.

Efficient Statistics for Sparse Graphical Models from Truncated Samples