**Graph Laplacian Mixture Model**

Graph learning methods have recently been receiving increasing interest as means to infer structure in datasets. Most of the recent approaches focus on different relationships between a graph and data sample distributions, mostly in settings where all available relate to the same graph. This is, however, not always the case, as data is often available in mixed form, yielding the need for methods that are able to cope with mixture data and learn multiple graphs. We propose a novel generative model that explains a collection of distinct data naturally living on different graphs. We assume the mapping of data to graphs is not known and investigate the problem of jointly clustering a set of data and learning a graph for each of the clusters. Experiments in both synthetic and real-world datasets demonstrate promising performance both in terms of data clustering, as well as multiple graph inference from mixture data. … **Rocker Project**

Docker Containers for the R Environment. … **Descriptive Statistics**

Descriptive statistics is the discipline of quantitatively describing the main features of a collection of information, or the quantitative description itself. Descriptive statistics are distinguished from inferential statistics (or inductive statistics), in that descriptive statistics aim to summarize a sample, rather than use the data to learn about the population that the sample of data is thought to represent. This generally means that descriptive statistics, unlike inferential statistics, are not developed on the basis of probability theory. Even when a data analysis draws its main conclusions using inferential statistics, descriptive statistics are generally also presented. For example in a paper reporting on a study involving human subjects, there typically appears a table giving the overall sample size, sample sizes in important subgroups (e.g., for each treatment or exposure group), and demographic or clinical characteristics such as the average age, the proportion of subjects of each sex, and the proportion of subjects with related comorbidities. … **Hierarchical Attention Network (HAN)**

Knowledge Base (KB) completion, which aims to determine missing relation between entities, has raised increasing attention in recent years. Most existing methods either focus on the positional relationship between entity pair and single relation (1-hop path) in semantic space or concentrate on the joint probability of Random Walks on multi-hop paths among entities. However, they do not fully consider the intrinsic relationships of all the links among entities. By observing that the single relation and multi-hop paths between the same entity pair generally contain shared/similar semantic information, this paper proposes a novel method to capture the shared features between them as the basis for inferring missing relations. To capture the shared features jointly, we develop Hierarchical Attention Networks (HANs) to automatically encode the inputs into low-dimensional vectors, and exploit two partial parameter-shared components, one for feature source discrimination and the other for determining missing relations. By joint Adversarial Training (AT) the entire model, our method minimizes the classification error of missing relations, and ensures the source of shared features are difficult to discriminate in the meantime. The AT mechanism encourages our model to extract features that are both discriminative for missing relation prediction and shareable between single relation and multi-hop paths. We extensively evaluate our method on several large-scale KBs for relation completion. Experimental results show that our method consistently outperforms the baseline approaches. In addition, the hierarchical attention mechanism and the feature extractor in our model can be well interpreted and utilized in the related downstream tasks. …

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Apr 2022

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