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Graph neural networks (GNNs) have emerged as a powerful tool for analyzing and learning from complex data structured as graphs, demonstrating remarkable effectiveness in various applications, such as social network analysis, recommendation systems, and drug discovery. However, despite their impressive performance, the fairness problem has increasingly gained attention as a crucial aspect to consider. Existing research in graph learning focuses on either group fairness or individual fairness. However, since each concept provides unique insights into fairness from distinct perspectives, integrating them into a fair graph neural network system is crucial. To the best of our knowledge, no study has yet to comprehensively tackle both individual and group fairness simultaneously. In this paper, we propose a new concept of individual fairness within groups and a novel framework named Fairness for Group and Individual (FairGI), which considers both group fairness and individual fairness within groups in the context of graph learning. FairGI employs the similarity matrix of individuals to achieve individual fairness within groups, while leveraging adversarial learning to address group fairness in terms of both Equal Opportunity and Statistical Parity. The experimental results demonstrate that our approach not only outperforms other state-of-the-art models in terms of group fairness and individual fairness within groups, but also exhibits excellent performance in population-level individual fairness, while maintaining comparable prediction accuracy., Comment: 16 pages, 3 figures

Text analysis is an interesting research area in data science and has various applications, such as in artificial intelligence, biomedical research, and engineering. We review popular methods for text analysis, ranging from topic modeling to the recent neural language models. In particular, we review Topic-SCORE, a statistical approach to topic modeling, and discuss how to use it to analyze MADStat - a dataset on statistical publications that we collected and cleaned. The application of Topic-SCORE and other methods on MADStat leads to interesting findings. For example, $11$ representative topics in statistics are identified. For each journal, the evolution of topic weights over time can be visualized, and these results are used to analyze the trends in statistical research. In particular, we propose a new statistical model for ranking the citation impacts of $11$ topics, and we also build a cross-topic citation graph to illustrate how research results on different topics spread to one another. The results on MADStat provide a data-driven picture of the statistical research in $1975$--$2015$, from a text analysis perspective.

We collected and cleaned a large data set on publications in statistics. The data set consists of the coauthor relationships and citation relationships of 83, 331 papers published in 36 representative journals in statistics, probability, and machine learning, spanning 41 years. The data set allows us to construct many different networks, and motivates a number of research problems about the research patterns and trends, research impacts, and network topology of the statistics community. In this paper we focus on (i) using the citation relationships to estimate the research interests of authors, and (ii) using the coauthor relationships to study the network topology. Using co-citation networks we constructed, we discover a "statistics triangle", reminiscent of the statistical philosophy triangle (Efron, 1998). We propose new approaches to constructing the "research map" of statisticians, as well as the "research trajectory" for a given author to visualize his/her research interest evolvement. Using co-authorship networks we constructed, we discover a multi-layer community tree and produce a Sankey diagram to visualize the author migrations in different sub-areas. We also propose several new metrics for research diversity of individual authors. We find that "Bayes", "Biostatistics", and "Nonparametric" are three primary areas in statistics. We also identify 15 sub-areas, each of which can be viewed as a weighted average of the primary areas, and identify several underlying reasons for the formation of co-authorship communities. We also find that the research interests of statisticians have evolved significantly in the 41-year time window we studied: some areas (e.g., biostatistics, high-dimensional data analysis, etc.) have become increasingly more popular., Comment: 61 pages, 16 figures

Graph, as an important data representation, is ubiquitous in many real world applications ranging from social network analysis to biology. How to correctly and effectively learn and extract information from graph is essential for a large number of machine learning tasks. Graph embedding is a way to transform and encode the data structure in high dimensional and non-Euclidean feature space to a low dimensional and structural space, which is easily exploited by other machine learning algorithms. We have witnessed a huge surge of such embedding methods, from statistical approaches to recent deep learning methods such as the graph convolutional networks (GCN). Deep learning approaches usually outperform the traditional methods in most graph learning benchmarks by building an end-to-end learning framework to optimize the loss function directly. However, most of the existing GCN methods can only perform convolution operations with node features, while ignoring the handy information in edge features, such as relations in knowledge graphs. To address this problem, we present CensNet, Convolution with Edge-Node Switching graph neural network, for learning tasks in graph-structured data with both node and edge features. CensNet is a general graph embedding framework, which embeds both nodes and edges to a latent feature space. By using line graph of the original undirected graph, the role of nodes and edges are switched, and two novel graph convolution operations are proposed for feature propagation. Experimental results on real-world academic citation networks and quantum chemistry graphs show that our approach achieves or matches the state-of-the-art performance in four graph learning tasks, including semi-supervised node classification, multi-task graph classification, graph regression, and link prediction., Comment: This manuscript has been accepted by the IEEE Transactions on Pattern Analysis and Machine Intelligence

Community detection in large social networks is affected by degree heterogeneity of nodes. The D-SCORE algorithm for directed networks was introduced to reduce this effect by taking the element-wise ratios of the singular vectors of the adjacency matrix before clustering. Meaningful results were obtained for the statistician citation network, but rigorous analysis on its performance was missing. First, this paper establishes theoretical guarantee for this algorithm and its variants for the directed degree-corrected block model (Directed-DCBM). Second, this paper provides significant improvements for the original D-SCORE algorithms by attaching the nodes outside of the community cores using the information of the original network instead of the singular vectors., Comment: Journal of Machine Learning Research 2020, to appear

We have collected and cleaned two network data sets: Coauthorship and Citation networks for statisticians. The data sets are based on all research papers published in four of the top journals in statistics from $2003$ to the first half of $2012$. We analyze the data sets from many different perspectives, focusing on (a) centrality, (b) community structures, and (c) productivity, patterns and trends. For (a), we have identified the most prolific/collaborative/highly cited authors. We have also identified a handful of "hot" papers, suggesting "Variable Selection" as one of the "hot" areas. For (b), we have identified about $15$ meaningful communities or research groups, including large-size ones such as "Spatial Statistics", "Large-Scale Multiple Testing", "Variable Selection" as well as small-size ones such as "Dimensional Reduction", "Objective Bayes", "Quantile Regression", and "Theoretical Machine Learning". For (c), we find that over the 10-year period, both the average number of papers per author and the fraction of self citations have been decreasing, but the proportion of distant citations has been increasing. These suggest that the statistics community has become increasingly more collaborative, competitive, and globalized. Our findings shed light on research habits, trends, and topological patterns of statisticians. The data sets provide a fertile ground for future researches on or related to social networks of statisticians.

In the high dimensional regression analysis when the number of predictors is much larger than the sample size, an important question is to select the important variable which are relevant to the response variable of interest. Variable selection and the multiple testing are both tools to address this issue. However, there is little discussion on the connection of these two areas. When the signal strength is strong enough such that the selection consistency is achievable, it seems to be unnecessary to control the false discovery rate. In this paper, we consider the regime where the signals are both rare and weak such that the selection consistency is not achievable and propose a method which controls the false discovery rate asymptotically. It is theoretically shown that the false non-discovery rate of the proposed method converges to zero at the optimal rate. Numerical results are provided to demonstrate the advantage of the proposed method., Comment: 26 pages

We consider testing for presence of a signal in Gaussian white noise with intensity 1/sqrt(n), when the alternatives are given by smoothness ellipsoids with an L2-ball of (squared) radius rho removed. It is known that, for a fixed Sobolev type ellipsoid of smoothness beta and size M, a rho which is of order n to the power -4 beta/(4 beta+1)} is the critical separation rate, in the sense that the minimax error of second kind over alpha-tests stays asymptotically between 0 and 1 strictly (Ingster, 1982). In addition, Ermakov (1990) found the sharp asymptotics of the minimax error of second kind at the separation rate. For adaptation over both beta and M in that context, it is known that a loglog-penalty over the separation rate for rho is necessary for a nonzero asymptotic power. Here, following an example in nonparametric estimation related to the Pinsker constant, we investigate the adaptation problem over the ellipsoid size M only, for fixed smoothness degree beta. It is established that the sharp risk asymptotics can be replicated in that adaptive setting, if rho tends to zero slower than the separation rate. The penalty for adaptation here turns out to be a sequence tending to infinity arbitrarily slowly.

Consider a linear model $Y=X\beta+z$, $z\sim N(0,I_n)$. Here, $X=X_{n,p}$, where both $p$ and $n$ are large, but $p>n$. We model the rows of $X$ as i.i.d. samples from $N(0,\frac{1}{n}\Omega)$, where $\Omega$ is a $p\times p$ correlation matrix, which is unknown to us but is presumably sparse. The vector $\beta$ is also unknown but has relatively few nonzero coordinates, and we are interested in identifying these nonzeros. We propose the Univariate Penalization Screeing (UPS) for variable selection. This is a screen and clean method where we screen with univariate thresholding and clean with penalized MLE. It has two important properties: sure screening and separable after screening. These properties enable us to reduce the original regression problem to many small-size regression problems that can be fitted separately. The UPS is effective both in theory and in computation., Comment: Published in at http://dx.doi.org/10.1214/11-AOS947 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)