Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:


UCSD scientists explain and improve upon ’enigmatic’ probability formula


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.

Media Contact: Doug Ramsey 858-822-5825

Doug Ramsey | EurekAlert!
Further information:

All articles from Information Technology >>>

The most recent press releases about innovation >>>

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

Im Focus: New 3-D wiring technique brings scalable quantum computers closer to reality

Researchers from the Institute for Quantum Computing (IQC) at the University of Waterloo led the development of a new extensible wiring technique capable of controlling superconducting quantum bits, representing a significant step towards to the realization of a scalable quantum computer.

"The quantum socket is a wiring method that uses three-dimensional wires based on spring-loaded pins to address individual qubits," said Jeremy Béjanin, a PhD...

Im Focus: Scientists develop a semiconductor nanocomposite material that moves in response to light

In a paper in Scientific Reports, a research team at Worcester Polytechnic Institute describes a novel light-activated phenomenon that could become the basis for applications as diverse as microscopic robotic grippers and more efficient solar cells.

A research team at Worcester Polytechnic Institute (WPI) has developed a revolutionary, light-activated semiconductor nanocomposite material that can be used...

Im Focus: Diamonds aren't forever: Sandia, Harvard team create first quantum computer bridge

By forcefully embedding two silicon atoms in a diamond matrix, Sandia researchers have demonstrated for the first time on a single chip all the components needed to create a quantum bridge to link quantum computers together.

"People have already built small quantum computers," says Sandia researcher Ryan Camacho. "Maybe the first useful one won't be a single giant quantum computer...

Im Focus: New Products - Highlights of COMPAMED 2016

COMPAMED has become the leading international marketplace for suppliers of medical manufacturing. The trade fair, which takes place every November and is co-located to MEDICA in Dusseldorf, has been steadily growing over the past years and shows that medical technology remains a rapidly growing market.

In 2016, the joint pavilion by the IVAM Microtechnology Network, the Product Market “High-tech for Medical Devices”, will be located in Hall 8a again and will...

Im Focus: Ultra-thin ferroelectric material for next-generation electronics

'Ferroelectric' materials can switch between different states of electrical polarization in response to an external electric field. This flexibility means they show promise for many applications, for example in electronic devices and computer memory. Current ferroelectric materials are highly valued for their thermal and chemical stability and rapid electro-mechanical responses, but creating a material that is scalable down to the tiny sizes needed for technologies like silicon-based semiconductors (Si-based CMOS) has proven challenging.

Now, Hiroshi Funakubo and co-workers at the Tokyo Institute of Technology, in collaboration with researchers across Japan, have conducted experiments to...

All Focus news of the innovation-report >>>



Event News

#IC2S2: When Social Science meets Computer Science - GESIS will host the IC2S2 conference 2017

14.10.2016 | Event News

Agricultural Trade Developments and Potentials in Central Asia and the South Caucasus

14.10.2016 | Event News

World Health Summit – Day Three: A Call to Action

12.10.2016 | Event News

Latest News

Resolving the mystery of preeclampsia

21.10.2016 | Health and Medicine

Stanford researchers create new special-purpose computer that may someday save us billions

21.10.2016 | Information Technology

From ancient fossils to future cars

21.10.2016 | Materials Sciences

More VideoLinks >>>