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.

Outlier detection is an important task in statistical analyses. 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. This gives a way to investigate the underlying nature of outliers. This is also called understandability in the literature. Outlier detection has many applications including areas such as • Fraud detection • Medical and public health • Anomaly detection in text data • Fault detection (on critical systems) • Forensic science The MethodThe method can be described by the outlier test procedure below. Assume we are interested in whether or not a new observation z is an outlier in some data set D. First an interaction graph G is fitted to the variables in D; a decomposable undirected graph that describes the association structure between variables in D. If the assumption that z belongs to D is true, z should be included in D. Denote by D z the new data set including z. Finally the outlier model M is constructed using G and D z from which we can query the p-value, p, for the test about z belonging to D. If p is less than some chosen threshold (significance level), say 0.05, z is declared an outlier in D.

General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.-Users may download and print one copy of any publication from the public portal for the purpose of private study or research. -You may not further distribute the material or use it for any profit-making activity or commercial gain -You may freely distribute the URL identifying the publication in the public portal -

We propose Unity Smoothing (US) for handling inconsistencies between a Bayesian network model and new unseen observations. We show that prediction accuracy, using the junction tree algorithm with US is comparable to that of Laplace smoothing. Moreover, in applications were sparsity of the data structures is utilized, US outperforms Laplace smoothing in terms of memory usage. Furthermore, we detail how to avoid redundant calculations that must otherwise be performed during the message passing scheme in the junction tree algorithm which we refer to as Unity Propagation (UP).Experimental results shows that it is always faster to exploit UP on top of the Lauritzen-Spigelhalter message passing scheme for the junction tree algorithm.