Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification error in multiclass discrimination from Markov data   As a model for an on-line classification setting we consider a stochastic
process $(X_{-n},Y_{-n})_{n}$, the present time-point being denoted by 0, with
observables $ \ldots,X_{-n},X_{-n+1},\ldots, X_{-1}, X_0$ from which the
pattern $Y_0$ is to be inferred. So in this classification setting, in addition
to the present observation $X_0$ a number $l$ of preceding observations may be
used for classification, thus taking a possible dependence structure into
account as it occurs e.g. in an ongoing classification of handwritten
characters. We treat the question how the performance of classifiers is
improved by using such additional information. For our analysis, a hidden
Markov model is used. Letting $R_l$ denote the minimal risk of
misclassification using $l$ preceding observations we show that the difference
$\sup_k |R_l - R_{l+k}|$ decreases exponentially fast as $l$ increases. This
suggests that a small $l$ might already lead to a noticeable improvement. To
follow this point we look at the use of past observations for kernel
classification rules. Our practical findings in simulated hidden Markov models
and in the classification of handwritten characters indicate that using $l=1$,
i.e. just the last preceding observation in addition to $X_0$, can lead to a
substantial reduction of the risk of misclassification. So, in the presence of
stochastic dependencies, we advocate to use $ X_{-1},X_0$ for finding the
pattern $Y_0$ instead of only $X_0$ as one would in the independent situation.

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The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio