email: | dasta@andrew.cmu.edu |

office: | 3713 Wean Hall |

Research

My interests fall into two areas: Network Inference and Nonparametric Methods on Non-Euclidean Spaces.

**Network Inference**

Network inference is about inferring a distribution of random graphs (networks) from sample graphs (networks). Network inference is useful, for example, when assessing whether changes in networks over time, environment, or other conditions are significant or mere fluctuations. I am interested in using tools from geometry to describe and infer distributions of random graphs.

C. Shalizi and I have outlined a method for comparing certain real-world, hierarchical networks as L2-differences between densities on the hyperboloid [2]. This builds on previous observations of ours that the abstract structure in social networks, as opposed to the content of messages between users, track CDC flu counts [4]. We are currently working on further building the theory, as well as applying our methods on brain networks, collaboration networks, and other real-world networks.

**Nonparametric Methods on Non-Euclidean Spaces**

Data is usually given as a collection of numbers, but that data is often more naturally regarded as points in a non-Euclidean space. Some examples are directional headings (the space SO(3) of 3x3 special orthogonal matrices), distortions in the spacetime continuum (symmetric positive definite matrices), or latent positions of large-scale networks (hyperbolic spaces). In all such examples, Euclidean distances do not reflect the true distance between the data, regarded as points in a true latent space. I am interested in extending non-parametric estimators on Euclidean space (like kernel density estimators, kernel regression) for the non-Euclidean setting.

I have generalized the standard kernel density estimator for a large class of symmetric spaces (like the space of symmetric positive definite matrices) and have proven a minimax rate that is comparable to the Euclidean case [1]. A special case of the estimator, on the hyperboloid, is used in my work with C. Shalizi on network inference [2]. I am currently working on applying this estimator to problems in brain imaging, astrostatistics, and other settings where the data lives in a non-Euclidean symmetric space.

Papers

[1] D. Asta, "Kernel Density Estimation on Symmetric Spaces,"

*under review*, arXiv preprint 1411.4040, (2014).
[2] D. Asta and C. Shalizi, "Geometric Network Comparisons,"

*under review*, arXiv preprint 1411.1350, (2014).
[3] D. Asta, "Nonparametric Density Estimation on Hyperbolic Space,"

*Neural Information Processing Systems (NIPS) workshop: Modern Nonparametric Methods in Machine Learning*, workshop paper, (2013).
[4] D. Asta and C. Shalizi, "Identifying Influenza Outbreaks via Twitter,"

*Neural Information Processing Systems (NIPS) workshop: Social Network and Social Media Analysis - Methods, Models and Applications*, (2012).
[5] D. Asta and C. Shalizi, "Separating Biological and Social Contagions in Social Media: The Case of Regional Flu Trends in Twitter,"

*manuscript in preparation*, (2013).Teaching

I'm currently TA'ing Advanced Methods for Data Analysis (CMU Stat 36-402). My office hours are Wed 11:00am-12:00pm in Wean Hall 8110.

I've previously TA'ed:

Observational Causal Inference (CMU Stat 36-729) in Fall 2014

Introduction to Engineering and Public Policy (CMU EPP 19-101) in Spring 2013