Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

UCSD scientists explain and improve upon ’enigmatic’ probability formula

17.10.2003


Findings could have implications for speech recognition, machine learning, information retrieval



Scientists at the University of California, San Diego (UCSD) have developed new insight into a formula that helped British cryptanalysts crack the German Enigma code in World War II. Writing in the Oct. 17 edition of the journal Science, UCSD Jacobs School of Engineering professor Alon Orlitsky and graduate students Narayana P. Santhanam and Junan Zhang shed light on a lingering mathematical mystery and propose a new solution that could help improve automatic speech recognition, natural language processing, and other machine learning software.

In the article, Orlitsky and his colleagues unlock some of the secrets of the "Good-Turing estimator," a formula for estimating the probability of elements based on observed data. The formula is named after famed mathematicians I.J. Good and Alan Turing who, during WWII, were among a group of cryptanalysts charged with breaking the Enigma cipher -- the code used to encrypt German military communications. Working at Bletchley Park outside of London, their work has been credited by some with shortening the war by several years. (It also led to the development of the first modern computer, and was documented in a number of books and movies.)


The cryptanalysts were greatly aided by their possession of the Kengruppenbuch, the German cipher book that contained all possible secret keys to Enigma, and had been previously captured by British Intelligence. They documented the keys used by various U-boat commanders in previously decrypted messages and used this information to estimate the distributions of pages from which commanders picked their secret keys.

The prevailing technique at the time estimated the likelihood of each page by simply using its empirical frequency, the fraction of the time it had been picked in the past. But Good and Turing developed an unintuitive formula that bore little resemblance to conventional estimators. Surprisingly, this Good-Turing estimator outperformed the more intuitive approaches. Following the war, Good published the formula, mentioning that Turing had an "intuitive demonstration" for its power, but not describing what that demonstration entailed.

Since then, Good-Turing has been incorporated into a variety of applications such as information retrieval, spell-checking, and speech recognition software, where it is used to learn automatically the underlying structure of the language. But despite its usefulness, "its performance has remained something of an enigma itself," said Orlitsky, a professor in the Electrical and Computer Engineering department. While some partial explanations were given as to why Good-Turing may work well, no objective evaluation or results have been established for its optimality. Additionally, scientists observed that while it worked well under many circumstances, at times, its performance was lacking.

Now, Orlitsky, Santhanam, and Zhang believe they have unraveled some of the mystery surrounding Good-Turing, and constructed a new estimator that, unlike the historic formula, is reliable under all conditions. Motivated by information-theoretic and machine-learning considerations, they propose a natural measure for the performance of an estimator. Called attenuation, it evaluates the highest possible ratio between the probability assigned to each symbol in a sequence by any distribution, and the corresponding probability assigned by the estimator.

The UCSD researchers show that intuitive estimators, such as empirical frequency, can attenuate the probability of a symbol by an arbitrary amount. They also prove that Good-Turing performs well in general. While it can attenuate the probability of symbols by a factor of 1.39, it never attenuates by a factor of more than 2. Motivated by these observations, they derived an estimator whose attenuation is 1. This means that as the length of any sequence increases, the probability assigned to each symbol by the new estimator is as high as that assigned to it by any distribution.

"While there is a considerable amount of work to be done in simplifying and further improving the new estimator," concluded Orlitsky, "we hope that this new framework will eventually improve language modeling and hence lead to better speech recognition and data mining software."


* "Always Good-Turing: Asymptotically Optimal Probability Estimation," Science Magazine. http://www.sciencemag.org/

Media Contact: Doug Ramsey 858-822-5825 dramsey@ucsd.edu

Doug Ramsey | EurekAlert!
Further information:
http://www.ucsd.edu/

More articles from Information Technology:

nachricht Drones can almost see in the dark
20.09.2017 | Universität Zürich

nachricht World first: 'Storing lightning inside thunder'
18.09.2017 | University of Sydney

All articles from Information Technology >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Tiny lasers from a gallery of whispers

New technique promises tunable laser devices

Whispering gallery mode (WGM) resonators are used to make tiny micro-lasers, sensors, switches, routers and other devices. These tiny structures rely on a...

Im Focus: Ultrafast snapshots of relaxing electrons in solids

Using ultrafast flashes of laser and x-ray radiation, scientists at the Max Planck Institute of Quantum Optics (Garching, Germany) took snapshots of the briefest electron motion inside a solid material to date. The electron motion lasted only 750 billionths of the billionth of a second before it fainted, setting a new record of human capability to capture ultrafast processes inside solids!

When x-rays shine onto solid materials or large molecules, an electron is pushed away from its original place near the nucleus of the atom, leaving a hole...

Im Focus: Quantum Sensors Decipher Magnetic Ordering in a New Semiconducting Material

For the first time, physicists have successfully imaged spiral magnetic ordering in a multiferroic material. These materials are considered highly promising candidates for future data storage media. The researchers were able to prove their findings using unique quantum sensors that were developed at Basel University and that can analyze electromagnetic fields on the nanometer scale. The results – obtained by scientists from the University of Basel’s Department of Physics, the Swiss Nanoscience Institute, the University of Montpellier and several laboratories from University Paris-Saclay – were recently published in the journal Nature.

Multiferroics are materials that simultaneously react to electric and magnetic fields. These two properties are rarely found together, and their combined...

Im Focus: Fast, convenient & standardized: New lab innovation for automated tissue engineering & drug

MBM ScienceBridge GmbH successfully negotiated a license agreement between University Medical Center Göttingen (UMG) and the biotech company Tissue Systems Holding GmbH about commercial use of a multi-well tissue plate for automated and reliable tissue engineering & drug testing.

MBM ScienceBridge GmbH successfully negotiated a license agreement between University Medical Center Göttingen (UMG) and the biotech company Tissue Systems...

Im Focus: Silencing bacteria

HZI researchers pave the way for new agents that render hospital pathogens mute

Pathogenic bacteria are becoming resistant to common antibiotics to an ever increasing degree. One of the most difficult germs is Pseudomonas aeruginosa, a...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

“Lasers in Composites Symposium” in Aachen – from Science to Application

19.09.2017 | Event News

I-ESA 2018 – Call for Papers

12.09.2017 | Event News

EMBO at Basel Life, a new conference on current and emerging life science research

06.09.2017 | Event News

 
Latest News

Molecular Force Sensors

20.09.2017 | Life Sciences

Producing electricity during flight

20.09.2017 | Power and Electrical Engineering

Tiny lasers from a gallery of whispers

20.09.2017 | Physics and Astronomy

VideoLinks
B2B-VideoLinks
More VideoLinks >>>