Statistics/Machine Learn Thesis Proposal

  • Ph.D. Student
  • Joint Ph.D. Program in Statistics & Machine Learning
  • Carnegie Mellon University
Thesis Proposals

Networks, Point Processes, and Networks of Point Processes

My proposed work for my thesis can be broadly categorized into three projects at the interface of network models and point process models:

  1. Projective, Sparse, and Learnable Latent Position Network Models: in which I extend the latent position network model to account for sparse graph sequences by generating the latent positions according to a Poisson process. I establish that my framework results in a projective family of models that can express any level of sparsity. I also detail conditions under which a restricted maximum likelihood estimator is a consistent estimate of the underlying Poisson process.
  2. Evaluating Random Match Probabilities in Footwear Analysis: in which I propose a new hierarchical Cox process-based framework to model the locations of cuts and scrapes on the soles of shoes. I fit my model to data collected by the Israeli police, demonstrating it outperforms existing approaches for evaluating the strength of evidence through random match probabilities.
  3. A Horseshoe Prior for Network-Structured Sparsity: in which I extend the traditional horseshoe prior methodology to jointly exchangeable arrays, with the goal of efficiently incorporating network-structured sparsity when inferring the triggering matrix for mutually exciting Hawkes processes. I intend to fit this model to neural spike train data.

My talk will focus on projects (1) and (3).

Thesis Committee:
Rob Kass (Co-advisor)
Cosma Shalizi (Co-advisor)
Brian Junker
Jared Murray (University of Texas at Austin)  

Copy of Thesis Proposal Document

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