Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Clustering Time Series and the Surprising Robustness of HMMs   Suppose that we are given a time series where consecutive samples are
believed to come from a probabilistic source, that the source changes from time
to time and that the total number of sources is fixed. Our objective is to
estimate the distributions of the sources. A standard approach to this problem
is to model the data as a hidden Markov model (HMM). However, since the data
often lacks the Markov or the stationarity properties of an HMM, one can ask
whether this approach is still suitable or perhaps another approach is
required. In this paper we show that a maximum likelihood HMM estimator can be
used to approximate the source distributions in a much larger class of models
than HMMs. Specifically, we propose a natural and fairly general non-stationary
model of the data, where the only restriction is that the sources do not change
too often. Our main result shows that for this model, a maximum-likelihood HMM
estimator produces the correct second moment of the data, and the results can
be extended to higher moments.

23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg