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 Terahertz spectroscopy goes nano
20.10.2017 | Brown University

nachricht New software speeds origami structure designs
12.10.2017 | Georgia Institute of Technology

All articles from Information Technology >>>

The most recent press releases about innovation >>>

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

Im Focus: Neutron star merger directly observed for the first time

University of Maryland researchers contribute to historic detection of gravitational waves and light created by event

On August 17, 2017, at 12:41:04 UTC, scientists made the first direct observation of a merger between two neutron stars--the dense, collapsed cores that remain...

Im Focus: Breaking: the first light from two neutron stars merging

Seven new papers describe the first-ever detection of light from a gravitational wave source. The event, caused by two neutron stars colliding and merging together, was dubbed GW170817 because it sent ripples through space-time that reached Earth on 2017 August 17. Around the world, hundreds of excited astronomers mobilized quickly and were able to observe the event using numerous telescopes, providing a wealth of new data.

Previous detections of gravitational waves have all involved the merger of two black holes, a feat that won the 2017 Nobel Prize in Physics earlier this month....

Im Focus: Smart sensors for efficient processes

Material defects in end products can quickly result in failures in many areas of industry, and have a massive impact on the safe use of their products. This is why, in the field of quality assurance, intelligent, nondestructive sensor systems play a key role. They allow testing components and parts in a rapid and cost-efficient manner without destroying the actual product or changing its surface. Experts from the Fraunhofer IZFP in Saarbrücken will be presenting two exhibits at the Blechexpo in Stuttgart from 7–10 November 2017 that allow fast, reliable, and automated characterization of materials and detection of defects (Hall 5, Booth 5306).

When quality testing uses time-consuming destructive test methods, it can result in enormous costs due to damaging or destroying the products. And given that...

Im Focus: Cold molecules on collision course

Using a new cooling technique MPQ scientists succeed at observing collisions in a dense beam of cold and slow dipolar molecules.

How do chemical reactions proceed at extremely low temperatures? The answer requires the investigation of molecular samples that are cold, dense, and slow at...

Im Focus: Shrinking the proton again!

Scientists from the Max Planck Institute of Quantum Optics, using high precision laser spectroscopy of atomic hydrogen, confirm the surprisingly small value of the proton radius determined from muonic hydrogen.

It was one of the breakthroughs of the year 2010: Laser spectroscopy of muonic hydrogen resulted in a value for the proton charge radius that was significantly...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

ASEAN Member States discuss the future role of renewable energy

17.10.2017 | Event News

World Health Summit 2017: International experts set the course for the future of Global Health

10.10.2017 | Event News

Climate Engineering Conference 2017 Opens in Berlin

10.10.2017 | Event News

 
Latest News

Terahertz spectroscopy goes nano

20.10.2017 | Information Technology

Strange but true: Turning a material upside down can sometimes make it softer

20.10.2017 | Materials Sciences

NRL clarifies valley polarization for electronic and optoelectronic technologies

20.10.2017 | Interdisciplinary Research

VideoLinks
B2B-VideoLinks
More VideoLinks >>>