Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constant Time EXPected Similarity Estimation using Stochastic
  Optimization   A new algorithm named EXPected Similarity Estimation (EXPoSE) was recently
proposed to solve the problem of large-scale anomaly detection. It is a
non-parametric and distribution free kernel method based on the Hilbert space
embedding of probability measures. Given a dataset of $n$ samples, EXPoSE needs
only $\mathcal{O}(n)$ (linear time) to build a model and $\mathcal{O}(1)$
(constant time) to make a prediction. In this work we improve the linear
computational complexity and show that an $\epsilon$-accurate model can be
estimated in constant time, which has significant implications for large-scale
learning problems. To achieve this goal, we cast the original EXPoSE
formulation into a stochastic optimization problem. It is crucial that this
approach allows us to determine the number of iteration based on a desired
accuracy $\epsilon$, independent of the dataset size $n$. We will show that the
proposed stochastic gradient descent algorithm works in general (possible
infinite-dimensional) Hilbert spaces, is easy to implement and requires no
additional step-size parameters.

2
The categories of this paper are: math
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an