Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterizing predictable classes of processes   The problem is sequence prediction in the following setting. A sequence
x1,..., xn,... of discrete-valued observations is generated according to some
unknown probabilistic law (measure) mu. After observing each outcome, it is
required to give the conditional probabilities of the next observation. The
measure mu belongs to an arbitrary class C of stochastic processes. We are
interested in predictors ? whose conditional probabilities converge to the
'true' mu-conditional probabilities if any mu { C is chosen to generate the
data. We show that if such a predictor exists, then a predictor can also be
obtained as a convex combination of a countably many elements of C. In other
words, it can be obtained as a Bayesian predictor whose prior is concentrated
on a countable set. This result is established for two very different measures
of performance of prediction, one of which is very strong, namely, total
variation, and the other is very weak, namely, prediction in expected average
Kullback-Leibler divergence.

29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph