Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On context-tree prediction of individual sequences   Motivated by the evident success of context-tree based methods in lossless
data compression, we explore, in this paper, methods of the same spirit in
universal prediction of individual sequences. By context-tree prediction, we
refer to a family of prediction schemes, where at each time instant $t$, after
having observed all outcomes of the data sequence $x_1,...,x_{t-1}$, but not
yet $x_t$, the prediction is based on a ``context'' (or a state) that consists
of the $k$ most recent past outcomes $x_{t-k},...,x_{t-1}$, where the choice of
$k$ may depend on the contents of a possibly longer, though limited, portion of
the observed past, $x_{t-k_{\max}},...x_{t-1}$. This is different from the
study reported in [1], where general finite-state predictors as well as
``Markov'' (finite-memory) predictors of fixed order, were studied in the
regime of individual sequences.
  Another important difference between this study and [1] is the asymptotic
regime. While in [1], the resources of the predictor (i.e., the number of
states or the memory size) were kept fixed regardless of the length $N$ of the
data sequence, here we investigate situations where the number of contexts or
states is allowed to grow concurrently with $N$. We are primarily interested in
the following fundamental question: What is the critical growth rate of the
number of contexts, below which the performance of the best context-tree
predictor is still universally achievable, but above which it is not? We show
that this critical growth rate is linear in $N$. In particular, we propose a
universal context-tree algorithm that essentially achieves optimum performance
as long as the growth rate is sublinear, and show that, on the other hand, this
is impossible in the linear case.

34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga