Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On PyTorch Implementation of Density Estimators for von Mises-Fisher and
  Its Mixture   The von Mises-Fisher (vMF) is a well-known density model for directional
random variables. The recent surge of the deep embedding methodologies for
high-dimensional structured data such as images or texts, aimed at extracting
salient directional information, can make the vMF model even more popular. In
this article, we will review the vMF model and its mixture, provide detailed
recipes of how to train the models, focusing on the maximum likelihood
estimators, in Python/PyTorch. In particular, implementation of vMF typically
suffers from the notorious numerical issue of the Bessel function evaluation in
the density normalizer, especially when the dimensionality is high, and we
address the issue using the MPMath library that supports arbitrary precision.
For the mixture learning, we provide both minibatch-based large-scale SGD
learning, as well as the EM algorithm which is a full batch estimator. For each
estimator/methodology, we test our implementation on some synthetic data, while
we also demonstrate the use case in a more realistic scenario of image
clustering. Our code is publicly available in
https://github.com/minyoungkim21/vmf-lib.

27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn