Case researchers discover methods to find 'needles in haystack' in data

December 05, 2005

A Case Western Reserve University research team from physics and statistics has recently created innovative statistical techniques that improve the chances of detecting a signal in large data sets. The new techniques can not only search for the "needle in the haystack" in particle physics, but also have applications in discovering a new galaxy, monitoring transactions for fraud and security risk, identifying the carrier of a virulent disease among millions of people or detecting cancerous tissues in a mammogram.

Case faculty members Ramani Pilla and Catherine Loader from statistics and Cyrus Taylor from physics report their findings in the article, "A New Technique for Finding Needles in Haystacks: A Geometric Approach to Distinguishing between a New Source and Random Fluctuations," December 2, in the journal, Physical Review Letters.

"As haystacks of information grow ever larger--and the needles ever smaller--the search for a signal becomes increasingly difficult to find using traditional approaches. There is a need for sophisticated new statistical methods," the researchers report.

Researchers working with large amounts of data encounter the fundamental problem of determining a real signal from random variation in the data. In many practical problems, a suspected signal may only be a small blip in a noisy experimental background.

The Case team discovered a technique that is built on the principle of comparing a set of summary characteristics for any sub region of the observations with the background variation. From these characteristics, attempts are made to find small regions that appear significantly different from the background--a difference that cannot simply be attributed to random chance.

"Methods used in high-energy particle physics problems traditionally have searched for any departure from a background model; that is, anything that is not a haystack," said Pilla, the project leader. "Our method efficiently incorporates information about the type of disorder expected, thereby enabling us to find the signal of interest more accurately."

At the core of the breakthrough is the idea of posing the problem in terms of a "hypothesis-based testing" paradigm to detect statistical disorder in the data. The method further exploits the flexibility behind a long-established geometric formula in creating a technique that significantly enhances the ability to distinguish a signal.

The researchers said the challenge is two-fold: defining efficient test statistics, and determining the critical cut-off. That is, to help the scientist find what is random variation as opposed to what is the signal. The detection problem involves a large number of comparisons, and the researchers caution that experimentalists should not be fooled into false discoveries by random variation.

"The experimenter wants to control the experiment-wise error rate: if there is nothing in the data, then there must be minimal probability of falsely discovering a signal. On the other hand, we want to maximize our chance of discovering any real signal that may be present in the massive data set," said Loader.

"The probabilistic problem associated with this scenario is reduced to one of finding the areas of certain regions on the surface of high-dimensional spheres," explains Pilla.

The Case researchers then exploit the geometric methods pioneered in 1939 by Harold Hotelling and Hermann Weyl. They tested the statistical techniques by using computer simulated particle physics experiments that mimic the real experiments conducted in colliders to demonstrate that the new technique significantly increased detection probabilities.

"In high-energy particle physics and astrophysics problems, chi-square goodness-of-fit tests are widely employed, although they have relatively low power to detect the signal," notes Taylor. "Through my collaborative work with Professors Pilla and Loader, we will be able to develop powerful statistical tests for detecting a signal from noisy data with high probability, a fundamental problem encountered in many scientific disciplines."

Taylor added that "conducting experiments in a particle collider may cost tens of millions of dollars. Improving efficiency in the analysis of experimental results can lead to enormous cost savings. Furthermore, we can obtain the same results with much smaller experiments, or effectively find much smaller departures from the background model."

"Detecting a real signal (the needle) present in random and chaotic data (the haystack) will lead to scientific success," conclude the researchers.
-end-
Funding for this research received support from the National Science Foundation and the Office of Naval Research. For information, contact Pilla at 216-368-5013 or visit http://stat.case.edu/~pillar/PRL/PRL.htm.

Case Western Reserve University is among the nation's leading research institutions. Founded in 1826 and shaped by the unique merger of the Case Institute of Technology and Western Reserve University, Case is distinguished by its strengths in education, research, service, and experiential learning. Located in Cleveland, Case offers nationally recognized programs in the Arts and Sciences, Dental Medicine, Engineering, Law, Management, Medicine, Nursing, and Social Sciences. http://www.case.edu.

Case Western Reserve University

Related Physics Articles from Brightsurf:

Helium, a little atom for big physics
Helium is the simplest multi-body atom. Its energy levels can be calculated with extremely high precision only relying on a few fundamental physical constants and the quantum electrodynamics (QED) theory.

Hyperbolic metamaterials exhibit 2T physics
According to Igor Smolyaninov of the University of Maryland, ''One of the more unusual applications of metamaterials was a theoretical proposal to construct a physical system that would exhibit two-time physics behavior on small scales.''

Challenges and opportunities for women in physics
Women in the United States hold fewer than 25% of bachelor's degrees, 20% of doctoral degrees and 19% of faculty positions in physics.

Indeterminist physics for an open world
Classical physics is characterized by the equations describing the world.

Leptons help in tracking new physics
Electrons with 'colleagues' -- other leptons - are one of many products of collisions observed in the LHCb experiment at the Large Hadron Collider.

Has physics ever been deterministic?
Researchers from the Austrian Academy of Sciences, the University of Vienna and the University of Geneva, have proposed a new interpretation of classical physics without real numbers.

Twisted physics
A new study in the journal Nature shows that superconductivity in bilayer graphene can be turned on or off with a small voltage change, increasing its usefulness for electronic devices.

Physics vs. asthma
A research team from the MIPT Center for Molecular Mechanisms of Aging and Age-Related Diseases has collaborated with colleagues from the U.S., Canada, France, and Germany to determine the spatial structure of the CysLT1 receptor.

2D topological physics from shaking a 1D wire
Published in Physical Review X, this new study propose a realistic scheme to observe a 'cold-atomic quantum Hall effect.'

Helping physics teachers who don't know physics
A shortage of high school physics teachers has led to teachers with little-to-no training taking over physics classrooms, reports show.

Read More: Physics News and Physics Current Events
Brightsurf.com is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com.