Duality in Graphical Models

Graphical models have proven to be powerful tools for representing high-dimensional systems of random variables. One example of such a model is the undirected graph, in which lack of an edge represents conditional independence between two random variables given the rest. Another example is the bidirected graph, in which absence of edges encodes pairwise marginal independence. Both of these classes of graphical models have been extensively studied, and while they are considered to be dual to one another, except in a few instances this duality has not been thoroughly investigated. In this paper, we demonstrate how duality between undirected and bidirected models can be used to transport results for one class of graphical models to the dual model in a transparent manner. We proceed to apply this technique to extend previously existing results as well as to prove new ones, in three important domains. First, we discuss the pairwise and global Markov properties for undirected and bidirected models, using the pseudographoid and reverse-pseudographoid rules which are weaker conditions than the typically used intersection and composition rules. Second, we investigate these pseudographoid and reverse pseudographoid rules in the context of probability distributions, using the concept of duality in the process. Duality allows us to quickly relate them to the more familiar intersection and composition properties. Third and finally, we apply the dualization method to understand the implications of faithfulness, which in turn leads to a more general form of an existing result

Exploring Dimensionality Reduction Effects in Mixed Reality for Analyzing Tinnitus Patient Data

In the context of big data analytics, gaining insights into high-dimensional data sets can be properly achieved, inter alia, by the use of visual analytics. Current developments in the field of immersive analytics, mainly driven by the improvements of smart glasses and virtual reality headsets, are one enabler to enhance user-friendly and interactive ways for data analytics. Along this trend, more and more fields in the medical domain crave for this type of technology to analyze medical data in a new way. In this work, a mixed-reality prototype is presented that shall help tinnitus researchers and clinicians to analyze patient data more efficiently. In particular, the prototype simplifies the analysis on a high-dimensional real-world tinnitus patient data set by the use of dimensionality reduction effects. The latter is represented by resulting clusters, which are identified through the density of particles, while information loss is denoted as the remaining covered variance. Technically, the graphical interface of the prototype includes a correlation coefficient graph, a plot for the information loss, and a 3D particle system. Furthermore, the prototype provides a voice recognition feature to select or deselect relevant data variables by its users. Moreover, based on a machine learning library, the prototype aims at reducing the computational resources on the used smart glasses. Finally, in practical sessions, we demonstrated the prototype to clinicians and they reported that such a tool may be very helpful to analyze patient data on one hand. On the other, such system is welcome to educate unexperienced clinicians in a better way. Altogether, the presented tool may constitute a promising direction for the medical as well as other domains

Dimensionality Reduction and Subspace Clustering in Mixed Reality for Condition Monitoring of High-Dimensional Production Data

Visual analytics are becoming more and more important in the light of big data and related scenarios. Along this trend, the field of immersive analytics has been variously furthered as it is able to provide sophisticated visual data analytics on one hand, while preserving user-friendliness on the other. Furthermore, recent hardware developments like smart glasses, as well as achievements in virtual-reality applications, have fanned immersive analytic solutions. Notably, such solutions can be very effective when they are applied to high-dimensional data sets. Taking this advantage into account, the work at hand applies immersive analytics to a high-dimensional production data set in order to improve the digital support of daily work tasks. More specifically, a mixed-reality implementation is presented that shall support manufactures as well as data scientists to comprehensively analyze machine data. As a particular goal, the prototype shall simplify the analysis of manufacturing data through the usage of dimensionality reduction effects. Therefore, five aspects are mainly reported in this paper. First, it is shown how dimensionality reduction effects can be represented by clusters. Second, it is presented how the resulting information loss of the reduction is addressed. Third, the graphical interface of the developed prototype is illustrated as it provides a (1) correlation coefficient graph, a (2) plot for the information loss, and a (3) 3D particle system. In addition, an implemented voice recognition feature of the prototype is shown, which was considered as being promising to select or deselect data variables users are interested in when analyzing the data. Fourth, based on a machine learning library, it is shown how the prototype reduces computational resources by the use of smart glasses. The main idea is based on a recommendation approach as well as the use of subspace clustering. Fifth, results from a practical setting are presented, in which the prototype was shown to domain experts. The latter reported that such a tool is actually helpful to analyze machine data on a daily basis. Moreover, it was reported that such system can be used to educate machine operators more properly. As a general outcome of this work, the presented approach may constitute a helpful solution for the industry as well as other domains like medicine