## Probability estimation for PPM (1995)

Venue: | In Proceedings NZCSRSC'95. Available from http://www.cs.waikato.ac.nz/wjt |

Citations: | 12 - 1 self |

### BibTeX

@INPROCEEDINGS{Teahan95probabilityestimation,

author = {W. J. Teahan},

title = {Probability estimation for PPM},

booktitle = {In Proceedings NZCSRSC'95. Available from http://www.cs.waikato.ac.nz/wjt},

year = {1995},

pages = {papers/NZCSRSC.ps.gz}

}

### Years of Citing Articles

### OpenURL

### Abstract

The state of the art in lossless text compression is the PPM data compression scheme. Two approaches to the problem of selecting the context models used in the scheme are described. One uses an a priori upper bound on the lengths of the contexts, while the other method is unbounded. Several techniques that improve the probability estimation are described, including four new methods: partial update exclusions for the unbounded approach, deterministic scaling, recency scaling and multiple probability estimators. Each of these methods improves the performance for both the bounded and unbounded approaches. In addition, further savings are possible by combining the two approaches. 1 Introduction The state of the art in lossless text compression is the PPM data compression scheme [1, 4]. PPM, or prediction by partial matching, is an adaptive statistical modeling technique based on blending together different length context models to predict the next character in the input sequence. The sche...

### Citations

616 |
Text compression
- Bell, Cleary, et al.
- 1990
(Show Context)
Citation Context ...nd unbounded approaches. In addition, further savings are possible by combining the two approaches. 1 Introduction The state of the art in lossless text compression is the PPM data compression scheme =-=[1, 4]-=-. PPM, or prediction by partial matching, is an adaptive statistical modeling technique based on blending together different length context models to predict the next character in the input sequence. ... |

431 |
Algorithms in C
- Sedgewick
- 1990
(Show Context)
Citation Context ... trie memory size for the unbounded approach is also possible by combining nonbranching nodes of the trie into a single node. The resulting compact data structure, which is similar to a patricia trie =-=[7]-=-, is linear with the size of the input string. Local order estimation. Local order estimation using bounded length contexts simply involves selecting the longest context model. However for unbounded c... |

330 | I.: Data compression using adaptive coding and partial string matching
- Cleary, Witten
- 1984
(Show Context)
Citation Context ...nd unbounded approaches. In addition, further savings are possible by combining the two approaches. 1 Introduction The state of the art in lossless text compression is the PPM data compression scheme =-=[1, 4]-=-. PPM, or prediction by partial matching, is an adaptive statistical modeling technique based on blending together different length context models to predict the next character in the input sequence. ... |

227 |
The zero-frequency problem: Estimating the probabilities of novel events in adaptive text compression
- Witten, Bell
- 1991
(Show Context)
Citation Context ...lem with probability estimation is how to encode a novel character, which has not been seen before in the current context. This problem is essentially the zero frequency problem which is described in =-=[8]. PPM uses-=- an escape probability to "escape" to another context model, usually of length one shorter than the current context. For novel characters which have never been seen before in any length mode... |

117 | Implementing the PPM data compression scheme
- Moffat
- 1990
(Show Context)
Citation Context ... unbounded length contexts. There are two approaches to the problem of deciding how long the contexts should be for PPM. The first approach, adopted in the original implementation [4] and later on in =-=[6]-=-, uses an upper bound to the length of the contexts, with the context model of longest length chosen first to estimate the probability. This strategy is surprisingly effective at modelling text, a max... |

111 | Unbounded length contexts for PPM
- Cleary, Teahan
- 1997
(Show Context)
Citation Context ...hought that there was little gain in extending the length of the contexts, as there is a drop off in compression as the maximum order increases beyond length 5. However, a recent approach called PPM* =-=[3]-=- uses a variant of the PPM algorithm that exploits unbounded length contexts. It does this by storing the contexts in a data structure called a context trie. Each context of varying length is stored i... |

49 | The design and analysis of efficient lossless data compression systems
- Howard
- 1993
(Show Context)
Citation Context ...is computed as u=(n + u) where u is the number of unique characters, and n is the total number of characters seen so far. Method C has been found to be superior to methods A and B in practice. Howard =-=[5]-=- proposed a small modification to method C. Instead of adding 1 to both the escape count and the new character's count, each count is incremented by 1 2 , hence the total weight is incremented by 1 as... |

10 | Experiments on the zero frequency problem
- Cleary, Teahan
- 1995
(Show Context)
Citation Context ...or at prediction. The most effective strategy found so far for unbounded contexts is as follows. A context is defined to be "deterministic" when it gives only one prediction. Experiments con=-=ducted by [2]-=- have shown that for such contexts the observed frequency of the deterministic character is much higher than expected based on a uniform prior distribution. This can be exploited by using such context... |