Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bayesian Anomaly Detection and Classification   Statistical uncertainties are rarely incorporated in machine learning
algorithms, especially for anomaly detection. Here we present the Bayesian
Anomaly Detection And Classification (BADAC) formalism, which provides a
unified statistical approach to classification and anomaly detection within a
hierarchical Bayesian framework. BADAC deals with uncertainties by
marginalising over the unknown, true, value of the data. Using simulated data
with Gaussian noise, BADAC is shown to be superior to standard algorithms in
both classification and anomaly detection performance in the presence of
uncertainties, though with significantly increased computational cost.
Additionally, BADAC provides well-calibrated classification probabilities,
valuable for use in scientific pipelines. We show that BADAC can work in online
mode and is fairly robust to model errors, which can be diagnosed through
model-selection methods. In addition it can perform unsupervised new class
detection and can naturally be extended to search for anomalous subsets of
data. BADAC is therefore ideal where computational cost is not a limiting
factor and statistical rigour is important. We discuss approximations to speed
up BADAC, such as the use of Gaussian processes, and finally introduce a new
metric, the Rank-Weighted Score (RWS), that is particularly suited to
evaluating the ability of algorithms to detect anomalies.

12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom