Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Down the Rabbit Hole: Robust Proximity Search and Density Estimation in
  Sublinear Space   For a set of $n$ points in $\Re^d$, and parameters $k$ and $\eps$, we present
a data structure that answers $(1+\eps,k)$-\ANN queries in logarithmic time.
Surprisingly, the space used by the data-structure is $\Otilde (n /k)$; that
is, the space used is sublinear in the input size if $k$ is sufficiently large.
Our approach provides a novel way to summarize geometric data, such that
meaningful proximity queries on the data can be carried out using this sketch.
Using this, we provide a sublinear space data-structure that can estimate the
density of a point set under various measures, including:
  \begin{inparaenum}[(i)]
  \item sum of distances of $k$ closest points to the query point, and
  \item sum of squared distances of $k$ closest points to the query point.
  \end{inparaenum}
  Our approach generalizes to other distance based estimation of densities of
similar flavor. We also study the problem of approximating some of these
quantities when using sampling. In particular, we show that a sample of size
$\Otilde (n /k)$ is sufficient, in some restricted cases, to estimate the above
quantities. Remarkably, the sample size has only linear dependency on the
dimension.

23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga