The Markov Chain Monte Carlo (MCMC) methods are popular when considering sampling from a high-dimensional random variable $\mathbf{x}$ with possibly unnormalised probability density $p$ and observed data $\mathbf{d}$. However, MCMC requires evaluating the posterior distribution $p(\mathbf{x}|\mathbf{d})$ of the proposed candidate $\mathbf{x}$ at each iteration when constructing the acceptance rate. This is costly when such evaluations are intractable. In this paper, we introduce a new non-Markovian sampling algorithm called Moving Target Monte Carlo (MTMC). The acceptance rate at $n$-th iteration is constructed using an iteratively updated approximation of the posterior distribution $a_n(\mathbf{x})$ instead of $p(\mathbf{x}|\mathbf{d})$. The true value of the posterior $p(\mathbf{x}|\mathbf{d})$ is only calculated if the candidate $\mathbf{x}$ is accepted. The approximation $a_n$ utilises these evaluations and converges to $p$ as $n \rightarrow \infty$. A proof of convergence and estimation of convergence rate in different situations are given.

We present Karate Club a Python framework combining more than 30 state-of-the-art graph mining algorithms which can solve unsupervised machine learning tasks. The primary goal of the package is to make community detection, node and whole graph embedding available to a wide audience of machine learning researchers and practitioners. We designed Karate Club with an emphasis on a consistent application interface, scalability, ease of use, sensible out of the box model behaviour, standardized dataset ingestion, and output generation. This paper discusses the design principles behind this framework with practical examples. We show Karate Club's efficiency with respect to learning performance on a wide range of real world clustering problems, classification tasks and support evidence with regards to its competitive speed.

The Fairness, Accountability, and Transparency in Machine Learning (FAT-ML) literature proposes a varied set of group fairness metrics to measure discrimination against socio-demographic groups that are characterized by a protected feature, such as gender or race. Such a system can be deemed as either fair or unfair depending on the choice of the metric. Several metrics have been proposed, some of them incompatible with each other. We present here a framework to navigate the tensions between various group-wise metrics and to study fairness in data-driven decision making without the constraint of choosing a single metric. We do so empirically, by observing that several of these metrics cluster together in two or three main clusters for the same groups and machine learning methods. In addition, we propose a robust way to visualize multidimensional fairness in two dimensions through a Principal Component Analysis (PCA) of the group fairness metrics. Experimental results on multiple datasets show that the PCA decomposition explains the variance between the metrics with one to three components.

Deep learning models on graphs have achieved remarkable performance in various graph analysis tasks, e.g., node classification, link prediction and graph clustering. However, they expose uncertainty and unreliability against the well-designed inputs, i.e., adversarial examples. Accordingly, various studies have emerged for both attack and defense addressed in different graph analysis tasks, leading to the arms race in graph adversarial learning. For instance, the attacker has poisoning and evasion attack, and the defense group correspondingly has preprocessing- and adversarial- based methods. Despite the booming works, there still lacks a unified problem definition and a comprehensive review. To bridge this gap, we investigate and summarize the existing works on graph adversarial learning tasks systemically. Specifically, we survey and unify the existing works w.r.t. attack and defense in graph analysis tasks, and give proper definitions and taxonomies at the same time. Besides, we emphasize the importance of related evaluation metrics, and investigate and summarize them comprehensively. Hopefully, our works can serve as a reference for the relevant researchers, thus providing assistance for their studies. More details of our works are available at https://github.com/gitgiter/Graph-Adversarial-Learning.

Machine learning using behavioral and text data can result in highly accurate prediction models, but these are often very difficult to interpret. Linear models require investigating thousands of coefficients, while the opaqueness of nonlinear models makes things even worse. Rule-extraction techniques have been proposed to combine the desired predictive behaviour of complex "black-box" models with explainability. However, rule-extraction in the context of ultra-high-dimensional and sparse data can be challenging, and has thus far received scant attention. Because of the sparsity and massive dimensionality, rule-extraction might fail in their primary explainability goal as the black-box model may need to be replaced by many rules, leaving the user again with an incomprehensible model. To address this problem, we develop and test a rule-extraction methodology based on higher-level, less-sparse "metafeatures". We empirically validate the quality of the rules in terms of fidelity, explanation stability and accuracy over a collection of data sets, and benchmark their performance against rules extracted using the original features. Our analysis points to key trade-offs between explainability, fidelity, accuracy, and stability that Machine Learning researchers and practitioners need to consider. Results indicate that the proposed metafeatures approach leads to better trade-offs between these, and is better able to mimic the black-box model. There is an average decrease of the loss in fidelity, accuracy, and stability from using metafeatures instead of the original fine-grained features by respectively 18.08%, 20.15% and 17.73%, all statistically significant at a 5% significance level. Metafeatures thus improve a key "cost of explainability", which we define as the loss in fidelity when replacing a black-box with an explainable model.

Karate Club consists of state-of-the-art methods to do unsupervised learning on graph structured data. To put it simply it is a Swiss Army knife for small-scale graph mining research. First, it provides network embedding techniques at the node and graph level. Second, it includes a variety of overlapping and non-overlapping community detection methods. Implemented methods cover a wide range of network science (NetSci, Complenet), data mining (ICDM, CIKM, KDD), artificial intelligence (AAAI, IJCAI) and machine learning (NeurIPS, ICML, ICLR) conferences, workshops, and pieces from prominent journals.

Karate Club consists of state-of-the-art methods to do unsupervised learning on graph structured data. To put it simply it is a Swiss Army knife for small-scale graph mining research. First, it provides network embedding techniques at the node and graph level. Second, it includes a variety of overlapping and non-overlapping community detection methods. Implemented methods cover a wide range of network science (NetSci, Complenet), data mining (ICDM, CIKM, KDD), artificial intelligence (AAAI, IJCAI) and machine learning (NeurIPS, ICML, ICLR) conferences, workshops, and pieces from prominent journals.

The input to the \emph{sets-$k$-means} problem is an integer $k\geq 1$ and a set $\mathcal{P}=\{P_1,\cdots,P_n\}$ of sets in $\mathbb{R}^d$. The goal is to compute a set $C$ of $k$ centers (points) in $\mathbb{R}^d$ that minimizes the sum $\sum_{P\in \mathcal{P}} \min_{p\in P, c\in C}\left\| p-c \right\|^2$ of squared distances to these sets. An \emph{$\varepsilon$-core-set} for this problem is a weighted subset of $\mathcal{P}$ that approximates this sum up to $1\pm\varepsilon$ factor, for \emph{every} set $C$ of $k$ centers in $\mathbb{R}^d$. We prove that such a core-set of $O(\log^2{n})$ sets always exists, and can be computed in $O(n\log{n})$ time, for every input $\mathcal{P}$ and every fixed $d,k\geq 1$ and $\varepsilon \in (0,1)$. The result easily generalized for any metric space, distances to the power of $z>0$, and M-estimators that handle outliers. Applying an inefficient but optimal algorithm on this coreset allows us to obtain the first PTAS ($1+\varepsilon$ approximation) for the sets-$k$-means problem that takes time near linear in $n$. This is the first result even for sets-mean on the plane ($k=1$, $d=2$). Open source code and experimental results for document classification and facility locations are also provided.

Social media channels, such as Facebook, Twitter, and Instagram, have altered our world forever. People are now increasingly connected than ever and reveal a sort of digital persona. Although social media certainly has several remarkable features, the demerits are undeniable as well. Recent studies have indicated a correlation between high usage of social media sites and increased depression. The present study aims to exploit machine learning techniques for detecting a probable depressed Twitter user based on both, his/her network behavior and tweets. For this purpose, we trained and tested classifiers to distinguish whether a user is depressed or not using features extracted from his/ her activities in the network and tweets. The results showed that the more features are used, the higher are the accuracy and F-measure scores in detecting depressed users. This method is a data-driven, predictive approach for early detection of depression or other mental illnesses. This study's main contribution is the exploration part of the features and its impact on detecting the depression level.

In this paper, we propose a deep probabilistic multi-view model that is composed of a linear multi-view layer based on probabilistic canonical correlation analysis (CCA) description in the latent space together with deep generative networks as observation models. The network is designed to decompose the variations of all views into a shared latent representation and a set of view-specific components where the shared latent representation is intended to describe the common underlying sources of variation among the views. An efficient variational inference procedure is developed that approximates the posterior distributions of the latent probabilistic multi-view layer while taking into account the solution of probabilistic CCA. A generalization to models with arbitrary number of views is also proposed. The empirical studies confirm that the proposed deep generative multi-view model can successfully extend deep variational inference to multi-view learning while it efficiently integrates the relationship between multiple views to alleviate the difficulty of learning.