2013-14 Program on Low-dimensional Structure in High-dimensional Systems (LDHD)

What LDHD do these images illustrate? (click to enlarge image)
Reprinted with permission from Mary A. Rohrdanz, Wenwei Zheng, Mauro Maggioni, Cecelia Clementi, Determination of reaction coordinates via locally scaled diffusion map, Journal of Chemical Physics, vol. 134, Issue 124116 (2011) and Wenwei Zheng, Mary A. Rohrdanz, Mauro Maggioni, Cecelia Clementi, Polymer reversal rate calculated via locally scaled diffusion map, Journal of Chemical Physics, vol. 134, Issue 144108 (2011). Copyright 2011, American Institute of Physics.

 

The LDHD program is devoted to the development of methodological, theoretical, and computational treatment of high-dimensional mathematical and statistical models. Possibly limited amounts of available data pose added challenges in high dimensions. The program will address these challenges by focusing on low-dimensional structures that approximate or encapsulate given high-dimensional data. Cutting edge methods of dimension reduction will be brought together from probability and statistics, geometry, topology, and computer science. These techniques include variable selection, graphical modeling, classification, dimension reduction in matrix estimation, empirical processes, and manifold learning. Working groups during the program will include theoretical discussions of these tools as well as applications to image and signal analysis, graphs and networks, genetics and genomics, dynamical systems, and machine learning.

Representative general research topics include:

  • sparse structures
  • regularization techniques
  • confidence regions and p-values in high dimensions
  • priors that favor concentration of posterior distributions around low-dimensional solutions
  • topological and geometric techniques for data analysis
  • biological and computational applications, such as metagenomics.

Specific research foci will include some or all of the following: statistical inference for low-dimensional structures; graph and network estimation; variable selection, screening, and multiple testing; classification and clustering; graphical models; statistical applications of topology and geometry; dynamical systems; data sketching; low-dimensional representation of genetics and genomics; image and signal analysis; asymptotic geometric analysis; computational aspects; and matrix estimation under complexity constraints.

Description of Activities

Workshops

The program year will start with an Opening Workshop on September 8-12, 2013, preceded by a Summer School in August. There will be several mid-program workshops, as well. The Summer School and at least one of the mid-program workshops will explore connections to the IMA program on Applications of Algebraic Topology.

Courses

One or two semester-long graduate courses will be part of the LDHD program, including "Probability Models, Geometry, and Topology" in Fall 2013 (taught by Sayan Mukherjee).

Working Groups

Working Groups will meet weekly throughout the program to pursue particular research topics, either identified at the Opening Workshop or subsequently chosen by the Working Group participants. Each Working Group consists of researchers associated with SAMSI---as on-site visitors, postdoctoral fellows, graduate students, or off-site participants---in addition to local faculty and scientists. These groups constitute the core of the scientific activities at SAMSI.

Opportunities to Participate

SAMSI is accepting applications from all who are interested in participating, including graduate students, postdocs, junior researchers, and faculty. Click here to see details and instructions for these opportunities.

Further Information

For additional information about the program, send e-mail to ldhd@samsi.info

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