10 March 2017 |
Title:
Sketching as a Tool for Linear Algebra
Date: 10 March 2017 (Friday)
Time:
1.30pm to 2.30pm
Venue: LT 5, (SPMS-03-08), School of Physical and Mathematical Sciences
Speaker: Dr David Woodruff
IBM Almaden Research Center San Jose, CA, USA
Abstract: We give near optimal algorithms for regression, low rank approximation, and robust variants of these problems. Our results are based on the sketch and solve paradigm, which is a tool for quickly compressing a problem to a smaller version of itself, for which one can then run a slow algorithm on the smaller problem. These lead to the fastest known algorithms for fundamental machine learning and numerical linear algebra problems, which run in time proportional to the number of non-zero entries of the input. We first give algorithms for least squares regression, and robust variants such as l_p regression and M-Estimator loss functions. Then we give algorithms for approximate singular value decomposition, and robust variants such as minimizing sum of distances to a subspace, rather than sum of squared distances, as well as minimizing entrywise l_1-distance, etc.
Speaker Biography:
David Woodruff joined IBM Almaden Research Center in 2007 after completing his Ph.D. at MIT in theoretical computer science. He has been at IBM Almaden ever since. His research interests include data streams, machine learning, numerical linear algebra, sketching, and sparse recovery. He is the recipient of the 2014 Presburger Award and Best Paper Awards at STOC 2013 and PODS 2010. At IBM he is a member of the Academy of Technology and a Master Inventor.
Host: Division of Mathematical Sciences, School of Physical and Mathematical Sciences |

3 February 2017 |
Title:
Topological modeling and analysis
of complex data in biomolecules
Date: 3 February 2017 (Friday)
Time:
1.15pm to 2.15pm
Venue: LT 5, (SPMS-03-08), School of Physical and Mathematical Sciences
Speaker: Assistant Professor Xia Kelin
Division of Mathematical Sciences School of Physical and Mathematical Sciences
Abstract: The understanding of biomolecular structure, flexibility, function, and dynamics is one
of the most challenging tasks in biological science. We introduce persistent homology
for extracting molecular topological fingerprints (MTFs) based on the persistence of
molecular topological invariants. MTFs are utilized for protein characterization,
identification, and classification. The multidimensional persistent homology is
proposed and further used to quantitatively predict the stability of protein folding
configurations generated by steered molecular dynamics. An excellent consistence
between my persistent homology prediction and molecular dynamics simulation is
found. Further, we introduce multiresolution persistent homology to handle complex
biomolecular data. By appropriately tuning the resolution of a density function, we are
able to focus the topological lens on the scale of interest. The proposed
multiresolution -topological method has potential applications in arbitrary data sets,
such as social networks, biological networks and graphs.
Speaker Biography:
Dr. Kelin Xia obtained his PhD degree from the Chinese Academy of Sciences in Jan
2013. He was a visiting scholar in the Department of Mathematics, Michigan State
University from Dec 2009-Dec 2012. From Jan 2013 to May 2016, he worked as a
visiting assistant professor at Michigan State University. He joined Nanyang
Technological University at Jun 2016. His research focused on scientific computation,
mathematical molecular biology, and topological data analysis (TDA), particularly
complex data in biomolecular systems.
Host: Division of Mathematical Sciences, School of Physical and Mathematical Sciences |