Masters Thesis Defense

Approximation of Nonintegral Frequency Moments

Brian Pilz

10:00am 30 November 2011, ITE325b

Let a data stream have length m over an alphabet of n letters, with letter i occurring m_i times for i = 1,…,n. For any k, define the frequency moments F_k as F_k = \sum_{i=1}^n m_i^k. Alon, Matias, and Szegedy showed how to estimate F_k for integers k>0 with a one-pass algorithm using O(n^{1-1/k}log n) space for given length m, accuracy, and confidence. Here we extend those results to non-integral k obtaining bounds on the variance giving accuracy and confidence estimates, and giving quantitative results on the algorithm’s space requirements with particular interest to when k is near 1. We also give some performance statistics of the algorithm for these cases and consider an application to entropy estimation. This algorithm is known as a sketching algorithm. Sketching algorithms are probabilistic algorithms generally requiring sublinear space vs. a "classical" O(n) (linear) space requirement, and may have applications for anomaly detection of systems or networks.

Committee:

• Drs. Samuel Lomonaco
• Brooke Stephens
• Kostas Kalpakis (chair)
• Larry Wagoner

Three students were awarded the Second Generation Scholarship on November 9 during the W.E.B. DuBois Lecture featuring speaker Carla L. Peterson of the University of Maryland College Park. The annual lecture is sponsored by the department of Africana Studies.

A group of African-American alumni started the Second Generation Scholarship in 1986 as a means to give back to the campus and become more involved in UMBC. The scholarship provides funding to continuing students whose money for college often decreases the longer they stay in college and graduate. Among the requirements, scholarship candidates must be currently enrolled or have taken a course in Africana studies and demonstrate a commitment to improving the lives of minorities through community service, extracurricular activities or other community involvement.

Learn more about the scholarship here.
The 2011-12 scholarship winners: Oseogie Okojie ’14, Nia Hampton ’13, founder James Wiggins Esq. ’75, and Mahelet Gennene ’13.