MCODE: Multivariate Conditional Outlier Detection

arXiv.org Machine Learning

Outlier detection aims to identify unusual data instances that deviate from expected patterns. The outlier detection is particularly challenging when outliers are context dependent and when they are defined by unusual combinations of multiple outcome variable values. In this paper, we develop and study a new conditional outlier detection approach for multivariate outcome spaces that works by (1) transforming the conditional detection to the outlier detection problem in a new (unconditional) space and (2) defining outlier scores by analyzing the data in the new space. Our approach relies on the classifier chain decomposition of the multi-dimensional classification problem that lets us transform the output space into a probability vector, one probability for each dimension of the output space. Outlier scores applied to these transformed vectors are then used to detect the outliers. Experiments on multiple multi-dimensional classification problems with the different outlier injection rates show that our methodology is robust and able to successfully identify outliers when outliers are either sparse (manifested in one or very few dimensions) or dense (affecting multiple dimensions).


Data Imputation through the Identification of Local Anomalies

arXiv.org Machine Learning

We introduce a comprehensive and statistical framework in a model free setting for a complete treatment of localized data corruptions due to severe noise sources, e.g., an occluder in the case of a visual recording. Within this framework, we propose i) a novel algorithm to efficiently separate, i.e., detect and localize, possible corruptions from a given suspicious data instance and ii) a Maximum A Posteriori (MAP) estimator to impute the corrupted data. As a generalization to Euclidean distance, we also propose a novel distance measure, which is based on the ranked deviations among the data attributes and empirically shown to be superior in separating the corruptions. Our algorithm first splits the suspicious instance into parts through a binary partitioning tree in the space of data attributes and iteratively tests those parts to detect local anomalies using the nominal statistics extracted from an uncorrupted (clean) reference data set. Once each part is labeled as anomalous vs normal, the corresponding binary patterns over this tree that characterize corruptions are identified and the affected attributes are imputed. Under a certain conditional independency structure assumed for the binary patterns, we analytically show that the false alarm rate of the introduced algorithm in detecting the corruptions is independent of the data and can be directly set without any parameter tuning. The proposed framework is tested over several well-known machine learning data sets with synthetically generated corruptions; and experimentally shown to produce remarkable improvements in terms of classification purposes with strong corruption separation capabilities. Our experiments also indicate that the proposed algorithms outperform the typical approaches and are robust to varying training phase conditions.


A Proposal for Statistical Outlier Detection in Relational Structures

AAAI Conferences

This paper extends unsupervised statistical outlier detection to the case of relational data. For nonrelational data, where each individual is characterized by a feature vector, a common approach starts with learning a generative statistical model for the population. The model assigns a likelihood measure for the feature vector that characterizes the individual; the lower the feature vector likelihood, the more anomalous the individual. A difference between relational and nonrelational data is that an individual is characterized not only by a list of attributes, but also by its links and by attributes of the individuals linked to it. We refer to a relational structure that specifies this information for a specific individual as the individual's database. Our proposal is to use the likelihood assigned by a generative model to the individual's database as the anomaly score for the individual; the lower the model likelihood, the more anomalous the individual. As a novel validation method, we compare the model likelihood with metrics of individual success. An empirical evaluation reveals a surprising finding in soccer and movie data: We observe in the data a strong correlation between the likelihood and success metrics.


Bayesian Learning of Clique Tree Structure

arXiv.org Machine Learning

The problem of categorical data analysis in high dimensions is considered. A discussion of the fundamental difficulties of probability modeling is provided, and a solution to the derivation of high dimensional probability distributions based on Bayesian learning of clique tree decomposition is presented. The main contributions of this paper are an automated determination of the optimal clique tree structure for probability modeling, the resulting derived probability distribution, and a corresponding unified approach to clustering and anomaly detection based on the probability distribution.