APPLIED MATH/ANALYSIS SEMINAR

Speaker Mauro Maggioni, John Hopkins University

Date: Tuesday, April 10, 2018

Time: 3:45p.m. Refreshments (AKW, 1st Floor Break Area)

4:00p.m. Seminar (LOM 206)

Title: “Learning and Geometry for Stochastic Dynamical Systems in high dimensions”

Abstract:

We discuss geometry-based statistical learning techniques for performing model reduction and modeling of certain classes of stochastic high-dimensional dynamical systems. We consider two complementary settings. In the first one, we are given long
trajectories of a system, e.g. from molecular dynamics, and we estimate, in a robust fashion, an effective number of degrees of freedom of the system, which may vary in the state space of then system, and a local scale where the dynamics is well-approximated by a reduced dynamics with a small number of degrees of freedom. We then use these ideas to produce an approximation to the generator of the system and obtain, via eigenfunctions of an empirical Fokker-Planck equation (constructed from data), reaction coordinates for the system that capture the large time behavior of the dynamics. We present various examples from molecular dynamics illustrating these ideas.

In the second setting we only have access to a (large number of expensive) simulators that can return short paths of the stochastic system, and introduce a statistical learning framework for estimating local approximations to the system, that can be (automatically) pieced together to form a fast global reduced model for the system, called ATLAS. ATLAS is guaranteed to be accurate (in the sense of producing stochastic paths whose distribution is close to that of paths generated by the original system) not only at small time scales, but also at large time scales, under suitable assumptions on the dynamics. We discuss applications to homogenization of rough diffusions in low and high dimensions, as well as relatively simple systems with separations of time scales, and deterministic chaotic systems in high-dimensions, that are well-approximated by stochastic
diffusion-like equations.
Mauro Maggioni 4-10 flyer.pdf

Attached please find a seminar announcement for Nobel Laureate, W.E. Moerner on Wednesday, April 11, 2018.

Speaker: W.E. Moerner, Nobel Laureate

Title: “Single Molecules for 3D Super-Resolution Imaging and Single Particle Tracking in Cells: Methods and Applications:

Date: Wednesday, April 11, 2018

Time & Place: 3:30 PM, SCL 110

Host: Biophysics Training Grant Students

Admins Please Post

biostatistics / STATISTICS & DATA SCIENCE Joint SEMINAR

Date: Monday, April 9, 2018

Time: 4:15pm – 5:30pm

Place: Yale Institute for Network Science, 17 Hillhouse Avenue, 3rd Floor, Rm 328

Seminar Speaker: Carey E. Priebe

Department of Applied Mathematics & Statistics, Johns Hopkins University

Personal Website: https://www.ams.jhu.edu/~priebe/

Title: On Spectral Graph Clustering

Abstract: Clustering is a many-splendored thing. As the ill-defined cousin of classification, in which the observation to be classified X comes with a true but unobserved class label Y, clustering is concerned with coherently grouping observations without any explicit concept of true groupings. Spectral graph clustering — clustering the vertices of a graph based on their spectral embedding — is all the rage, and recent theoretical results provide new understanding of the problem and solutions. In particular, we reset the field of spectral graph clustering, demonstrating that spectral graph clustering should not be thought of as kmeans clustering composed with Laplacian spectral embedding, but rather Gaussian mixture model (GMM) clustering composed with either Laplacian or Adjacency spectral embedding (LSE or ASE); in the context of the stochastic blockmodel (SBM), we use eigenvector CLTs & Chernoff analysis to show that (1) GMM dominates kmeans and (2) neither LSE nor ASE dominates, and we present an LSE vs ASE characterization in terms of affinity vs core-periphery SBMs. Along the way, we describe our recent asymptotic efficiency results, as well as an interesting twist on the eigenvector CLT when the block connectivity probability matrix is not positive semidefinite. (And, time permitting, we will touch on essential results using the matrix two-to-infinity norm.) We conclude with a ‘Two Truths’ LSE vs ASE spectral graph clustering result — necessarily including model selection for both embedding dimension & number of clusters — convincingly illustrated via an exciting new diffusion MRI connectome data set: different embedding methods yield different clustering results, with one (ASE) capturing gray matter/white matter separation and the other (LSE) capturing left hemisphere/right hemisphere characterization.

4:00 p.m. Pre-talk Refreshments

4:15 p.m. – 5:30 Seminar, Room 328, 17 Hillhouse Avenue

For more details and upcoming events visit our website at
http://statistics.yale.edu/ .