Dissertation Research Topic

**Multiresolution Analysis of Graphs:**Network analysis today grapples with learning graph structure of larger datasets than ever before. Manageable challenges from a decade ago -- such as graph partitioning or graph-based semi-supervised learning -- have become much more challenging. Applying even recently developed techniques for tasks such as community detection require approximations if they are expected to remain useful in the coming years. Multiresolution analysis provides a unique lens through which to consider these problems. Many of the questions in network analysis reduce to the consideration of network properties at a certain level of resolution. By applying techniques from multiresolution analysis (in an efficient manner) to graphs, questions dealing with global graph structure (such as graph partitioning) and local graph structure (such as community detection) may be addressed in a constructive manner. Several methods for constructing wavelets on graphs are already in use, along with the mechanisms for translating graph wavelets into analytical tools. I hope to build on this world by applying MMF to this world of research.**Multiresolution Matrix Factorization (MMF):**Currently working with Risi Kondor on applications of a novel decomposition tool from computational harmonic analysis. By factorizing large symmetric matrices into a dictionary of sparse wavelets, scenarios that tend to require a matrix's full eigenvalue decomposition may be approximated by a wavelet decomposition. A publicly available library for implementing a parallelized MMF computation is available here.

**Gaussian Processes (GPs) for large datasets:**: Many applications of GPs, such as GP regression (GPR), are currently hampered by computational bottlenecks, such as matrix inversion and determinant computation. I am interested in investigating approaches to approximating covariance matrices in ways that make matrix computations scale to massive datasets.**Retrospective data-analysis and medical decision-making:**As data collection becomes easier, the size and scope of hospitals' patient-oriennted databases continues to grow without forseeable limits. I am interested in ways to use modern nonparametric methods to make robust predictions that scale well with the number of database records. Specifically, I am interested in time-series data of patients' intraoperative vitals and how they can be used to make recommendations to anesthesiologists regarding medication dosage.

Last modified: Tue Nov 21 2017