Autoencoders for strategic decision support

In the majority of executive domains, a notion of normality is involved in most strategic decisions. However, few data-driven tools that support strategic decision-making are available. We introduce and extend the use of autoencoders to provide strategically relevant granular feedback. A first experiment indicates that experts are inconsistent in their decision making, highlighting the need for strategic decision support. Furthermore, using two large industry-provided human resources datasets, the proposed solution is evaluated in terms of ranking accuracy, synergy with human experts, and dimension-level feedback. This three-point scheme is validated using (a) synthetic data, (b) the perspective of data quality, (c) blind expert validation, and (d) transparent expert evaluation. Our study confirms several principal weaknesses of human decision-making and stresses the importance of synergy between a model and humans. Moreover, unsupervised learning and in particular the autoencoder are shown to be valuable tools for strategic decision-making

Wisdom of the Contexts: Active Ensemble Learning for Contextual Anomaly Detection

In contextual anomaly detection (CAD), an object is only considered anomalous within a specific context. Most existing methods for CAD use a single context based on a set of user-specified contextual features. However, identifying the right context can be very challenging in practice, especially in datasets, with a large number of attributes. Furthermore, in real-world systems, there might be multiple anomalies that occur in different contexts and, therefore, require a combination of several "useful" contexts to unveil them. In this work, we leverage active learning and ensembles to effectively detect complex contextual anomalies in situations where the true contextual and behavioral attributes are unknown. We propose a novel approach, called WisCon (Wisdom of the Contexts), that automatically creates contexts from the feature set. Our method constructs an ensemble of multiple contexts, with varying importance scores, based on the assumption that not all useful contexts are equally so. Experiments show that WisCon significantly outperforms existing baselines in different categories (i.e., active classifiers, unsupervised contextual and non-contextual anomaly detectors, and supervised classifiers) on seven datasets. Furthermore, the results support our initial hypothesis that there is no single perfect context that successfully uncovers all kinds of contextual anomalies, and leveraging the "wisdom" of multiple contexts is necessary.Comment: Submitted to IEEE TKD

Spectral Theory of Sparse Non-Hermitian Random Matrices

Sparse non-Hermitian random matrices arise in the study of disordered physical systems with asymmetric local interactions, and have applications ranging from neural networks to ecosystem dynamics. The spectral characteristics of these matrices provide crucial information on system stability and susceptibility, however, their study is greatly complicated by the twin challenges of a lack of symmetry and a sparse interaction structure. In this review we provide a concise and systematic introduction to the main tools and results in this field. We show how the spectra of sparse non-Hermitian matrices can be computed via an analogy with infinite dimensional operators obeying certain recursion relations. With reference to three illustrative examples --- adjacency matrices of regular oriented graphs, adjacency matrices of oriented Erd\H{o}s-R\'{e}nyi graphs, and adjacency matrices of weighted oriented Erd\H{o}s-R\'{e}nyi graphs --- we demonstrate the use of these methods to obtain both analytic and numerical results for the spectrum, the spectral distribution, the location of outlier eigenvalues, and the statistical properties of eigenvectors.Comment: 60 pages, 10 figure

Metrics for Graph Comparison: A Practitioner's Guide

Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and comparison of structures such as modular communities, rich clubs, hubs, and trees in data in these fields yields insight into the generative mechanisms and functional properties of the graph. Often, two graphs are compared via a pairwise distance measure, with a small distance indicating structural similarity and vice versa. Common choices include spectral distances (also known as $\lambda$ distances) and distances based on node affinities. However, there has of yet been no comparative study of the efficacy of these distance measures in discerning between common graph topologies and different structural scales. In this work, we compare commonly used graph metrics and distance measures, and demonstrate their ability to discern between common topological features found in both random graph models and empirical datasets. We put forward a multi-scale picture of graph structure, in which the effect of global and local structure upon the distance measures is considered. We make recommendations on the applicability of different distance measures to empirical graph data problem based on this multi-scale view. Finally, we introduce the Python library NetComp which implements the graph distances used in this work