Outlier detection in contingency tables using decomposable graphical models

Abstract

For high‐dimensional data, it is a tedious task to determine anomalies such as outliers. We present a novel outlier detection method for high‐dimensional contingency tables. We use the class of decomposable graphical models to model the relationship among the variables of interest, which can be depicted by an undirected graph called the interaction graph. Given an interaction graph, we derive a closed‐form expression of the likelihood ratio test (LRT) statistic and an exact distribution for efficient simulation of the test statistic. An observation is declared an outlier if it deviates significantly from the approximated distribution of the test statistic under the null hypothesis. We demonstrate the use of the LRT outlier detection framework on genetic data modeled by Chow–Liu trees.

Detecting Outliers in High-dimensional Data with Mixed Variable Types using Conditional Gaussian Regression Models

“…, for i ∈ I, which is the maximum likelihood estimates of ( 16) as also exploited in the outlier detection model given in [22].…”

“…The likelihood ratio for the pure discrete part, Q D := L( p; n)/L( q; n), was investigated by [22]: Given a RIP ordering…”

“…[15] gave the following definition: "an observation which deviates so much from the other observations in the data-set as to arouse suspicions that it was generated by a different mechanism". In [22], this definition, was adapted by specifying a statistical hypothesis of an outlier being distributed differently than all other observations for discrete data sets. In this paper, we extend this definition to capture outliers in data sets with variables of mixed types, i.e.…”

molic: An R package for multivariate outlier detection in contingency tables

“…In Lindskou et al (2019) the molic package was used to detect outliers in microhap data from the 1000 Genomes Project (The 1000 Genomes Project Consortium, 2015). This data contains DNA profiles from five different continental regions (CRs); Europe (EUR), America (AMR), East Asia (EAS), South Asia (SAS) and Africa (AFR).…”

“…An outlier is a case-specific unit since it may be interpreted as natural extreme noise in some applications, whereas in other applications it may be the most interesting observation. The molic package has been written to facilitate the novel outlier detection method in high-dimensional contingency tables (Lindskou, Eriksen, & Tvedebrink, 2019). In other words, the method works for data sets in which all variables are categorical, implying that they can only take on a finite set of values (also called levels).The software uses decomposable graphical models (DGMs), where the probability mass function can be associated with an interaction graph, from which conditional independences among the variables can be inferred.…”