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GGAM Exit Seminar:

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Speaker: Dmitry Shemetov
Start time: Fri, Apr 16 2021, 2:10PM

In this dissertation, we consider three statistical problems unified by an underlying graph structure.

The first problem concerns graph scan statistics.

Scan statistics can be used for early detection of outbreaks in animal populations by testing large regions for faint but detectable abnormal measurements.

Traditional scan statistic implementations, such as the SaTScan software, fuse neighboring measurements to obtain more powerful global null tests.

In this project, we provide an algorithm for detecting and localizing elevated levels in graph data.

Our method can provably control the family-wise error rate while detecting an outbreak and control the false discovery rate while localizing outbreaks.

The second problem concerns distributed communication with memory constraints.

Memory constraints are common in modern statistical systems like those occurring in wireless sensor networks.

We consider a model system of sensors communicating in a tree structure under bit-rate constraints to solve a hypothesis testing problem.

We obtain bounds on the hypothesis testing error rate for a central class of decision rules as functions of the bitrate, tree width, and depth.

These bounds give fundamental tradeoffs on memory and communication in areas such as wireless sensor networks.

The final problem concerns random graph model fitting.

Exponential random graph models (ERGMs) are a family of random graphs often used in social science due to their elegance of definition and flexibility of expression.

Fitting the parameters of such models to data is quite challenging however, due to the complexity of the partition function and the need to count subgraphs.

W study a pseudolikelihood based on the large deviations theory for ERGMs developed by Chatterjee and Diaconis and investigate its performance under noisy subgraph count estimates.

The work in this project shows preliminary results that fitting algorithms based on this pseudolikelihood and Monte Carlo subgraph count estimators may be viable in low edge density graph regimes.