The Cauchy-Net Mixture Model for Clustering with Anomalous Data

We live in the data explosion era. The unprecedented amount of data offers a potential wealth of knowledge but also brings about concerns regarding ethical collection and usage. Mistakes stemming from anomalous data have the potential for severe, real-world consequences, such as when building prediction models for housing prices. To combat anomalies, we develop the Cauchy-Net Mixture Model (CNMM). The CNMM is a flexible Bayesian nonparametric tool that employs a mixture between a Dirichlet Process Mixture Model (DPMM) and a Cauchy distributed component, which we call the Cauchy-Net (CN). Each portion of the model offers benefits, as the DPMM eliminates the limitation of requiring a fixed number of a components and the CN captures observations that do not belong to the well-defined components by leveraging its heavy tails. Through isolating the anomalous observations in a single component, we simultaneously identify the observations in the net as warranting further inspection and prevent them from interfering with the formation of the remaining components. The result is a framework that allows for simultaneously clustering observations and making predictions in the face of the anomalous data. We demonstrate the usefulness of the CNMM in a variety of experimental situations and apply the model for predicting housing prices in Fairfax County, Virginia.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Statistics

Department dc:contributor.department

Statistics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2019

Author dc:creator

• Slifko, Matthew D.

Chair dc:contributor.committeechair

• Leman, Scotland C.

Committee members dc:contributor.committeemember

• Bieri, David Stephan
• Smith, Eric P.
• Ranganathan, Shyam

• Bayesian Nonparametrics
• Dirichlet Process Mixture Model
• Clustering
• Anomaly Detection

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:22011

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/93576