Corpus ID: 14316098

ON THE STOCHASTIC COMPLEXITY FOR ORDER-1 MARKOV CHAINS AND THE CATALAN CONSTANT

@inproceedings{Giurc2007ONTS,
  title={ON THE STOCHASTIC COMPLEXITY FOR ORDER-1 MARKOV CHAINS AND THE CATALAN CONSTANT},
  author={Ciprian Doru Giurc and neanu and D. Mihalache and M. Omarjee and M. Tetiva},
  year={2007}
}
The stochastic complexity (SC) selects from a given family of parametric models the one that yields the shortest code length for the available measurements. Theoretical developments have made possible the evolution of the SC from the “two-part code” formula to the most recent expression based on the so-called Normalized Maximum Likelihood (NML) distribution. The application of the NML criterion is recommended especially in the case of small sample size, but high computational burdens prevent… Expand

Figures and Tables from this paper

ON THE USE OF THE FISHER INFORMATION IN COMPUTING THE STOCHASTIC COMPLEXITY
Because the evaluation of the stochastic complexity is difficult for most of the models, various approximations have been proposed during the last two decades. In this article, we focus on twoExpand
Keep it simple stupid — On the effect of lower-order terms in BIC-like criteria
  • T. Roos, Yuan Zou
  • Mathematics, Computer Science
  • 2013 Information Theory and Applications Workshop (ITA)
  • 2013
TLDR
It is observed that the constant can sometimes be a huge negative number that dominates the other terms in the criterion for moderate sample sizes, at least in the case of Markov sources, which dramatically degrades model selection accuracy. Expand

References

SHOWING 1-10 OF 14 REFERENCES
The asymptotic redundancy of Bayes rules for Markov chains
  • K. Atteson
  • Mathematics, Computer Science
  • IEEE Trans. Inf. Theory
  • 1999
We derive the asymptotics of the redundancy of Bayes rules for Markov chains of fixed order over a finite alphabet, extending the work of Barron and Clarke (1990) on independent and identicallyExpand
Markov types and minimax redundancy for Markov sources
TLDR
It is proved that the maximal minimax redundancy for Markov sources of order r is asymptotically equal to 1/2m/sup r/(m-1)log/sub 2/n+log/ sub 2/A/sub m//sup r/, where n is the length of a source sequence, m is the size of the alphabet, and A/ sub m//Sup r/ is an explicit constant. Expand
The optimal error exponent for Markov order estimation
TLDR
A consistent estimator is constructed, based on Kullback-Leibler divergences, which achieves the best exponent of asymptotically exponential decay of the probability of underestimation of the order of a stationary ergodic Markov chain. Expand
The Minimum Description Length Principle in Coding and Modeling
TLDR
The normalized maximized likelihood, mixture, and predictive codings are each shown to achieve the stochastic complexity to within asymptotically vanishing terms. Expand
Fisher information and stochastic complexity
  • J. Rissanen
  • Mathematics, Computer Science
  • IEEE Trans. Inf. Theory
  • 1996
TLDR
A sharper code length is obtained as the stochastic complexity and the associated universal process are derived for a class of parametric processes by taking into account the Fisher information and removing an inherent redundancy in earlier two-part codes. Expand
Applications of MDL to Selected Families of Models
Evaluating models that approximate complex data distributions is a core problem in data understanding. In this pedagogical review, we describe how the Minimum Description Length principle (MDL) canExpand
Elements of Information Theory
TLDR
The author examines the role of entropy, inequality, and randomness in the design of codes and the construction of codes in the rapidly changing environment. Expand
MDL Denoising
  • J. Rissanen
  • Mathematics, Computer Science
  • IEEE Trans. Inf. Theory
  • 2000
'The so-called denoising problem, relative to normal models for noise, is formalized such that "noise" is defined as the incompressible part in the data while the compressible part defines theExpand
Modeling By Shortest Data Description*
The number of digits it takes to write down an observed sequence x1,...,xN of a time series depends on the model with its parameters that one assumes to have generated the observed data. Accordingly,Expand
Representations of Catalan's Constant
Here, we assemble a fairly exhaustive list of formulae involving Catalan's constant. There are single integral, double integral, innnite series, continued fraction, and asymptotic representations, asExpand
...
1
2
...