A rich class of network models associate each node with a low-dimensional latent coordinate that controls the propensity for connections to form. Models of this type are well established in the literature, where it is typical to assume that the underlying geometry is Euclidean. Recent work has explored the consequences of this choice and has motivated the study of models which rely on non-Euclidean latent geometries, with a primary focus on spherical and hyperbolic geometry. In this paper\footnote{This is the first version of this work. Any potential mistake belongs to the first author.}, we examine to what extent latent features can be inferred from the observable links in the network, considering network models which rely on spherical, hyperbolic and lattice geometries. For each geometry, we describe a latent network model, detail constraints on the latent coordinates which remove the well-known identifiability issues, and present schemes for Bayesian estimation. Thus, we develop a computational procedures to perform inference for network models in which the properties of the underlying geometry play a vital role. Furthermore, we access the validity of those models with real data applications.
相關內容
Networking：IFIP International Conferences on Networking。
Explanation：國際網(wang)絡會議。
Publisher：IFIP。
SIT：
In data analysis problems where we are not able to rely on distributional assumptions, what types of inference guarantees can still be obtained? Many popular methods, such as holdout methods, cross-validation methods, and conformal prediction, are able to provide distribution-free guarantees for predictive inference, but the problem of providing inference for the underlying regression function (for example, inference on the conditional mean $\mathbb{E}[Y|X]$) is more challenging. In the setting where the features $X$ are continuously distributed, recent work has established that any confidence interval for $\mathbb{E}[Y|X]$ must have non-vanishing width, even as sample size tends to infinity. At the other extreme, if $X$ takes only a small number of possible values, then inference on $\mathbb{E}[Y|X]$ is trivial to achieve. In this work, we study the problem in settings in between these two extremes. We find that there are several distinct regimes in between the finite setting and the continuous setting, where vanishing-width confidence intervals are achievable if and only if the effective support size of the distribution of $X$ is smaller than the square of the sample size.
Understanding the operation of biological and artificial networks remains a difficult and important challenge. To identify general principles, researchers are increasingly interested in surveying large collections of networks that are trained on, or biologically adapted to, similar tasks. A standardized set of analysis tools is now needed to identify how network-level covariates -- such as architecture, anatomical brain region, and model organism -- impact neural representations (hidden layer activations). Here, we provide a rigorous foundation for these analyses by defining a broad family of metric spaces that quantify representational dissimilarity. Using this framework we modify existing representational similarity measures based on canonical correlation analysis to satisfy the triangle inequality, formulate a novel metric that respects the inductive biases in convolutional layers, and identify approximate Euclidean embeddings that enable network representations to be incorporated into essentially any off-the-shelf machine learning method. We demonstrate these methods on large-scale datasets from biology (Allen Institute Brain Observatory) and deep learning (NAS-Bench-101). In doing so, we identify relationships between neural representations that are interpretable in terms of anatomical features and model performance.
The design of a metric between probability distributions is a longstanding problem motivated by numerous applications in Machine Learning. Focusing on continuous probability distributions on the Euclidean space $\mathbb{R}^d$, we introduce a novel pseudo-metric between probability distributions by leveraging the extension of univariate quantiles to multivariate spaces. Data depth is a nonparametric statistical tool that measures the centrality of any element $x\in\mathbb{R}^d$ with respect to (w.r.t.) a probability distribution or a data set. It is a natural median-oriented extension of the cumulative distribution function (cdf) to the multivariate case. Thus, its upper-level sets -- the depth-trimmed regions -- give rise to a definition of multivariate quantiles. The new pseudo-metric relies on the average of the Hausdorff distance between the depth-based quantile regions w.r.t. each distribution. Its good behavior w.r.t. major transformation groups, as well as its ability to factor out translations, are depicted. Robustness, an appealing feature of this pseudo-metric, is studied through the finite sample breakdown point. Moreover, we propose an efficient approximation method with linear time complexity w.r.t. the size of the data set and its dimension. The quality of this approximation as well as the performance of the proposed approach are illustrated in numerical experiments.
The autoregressive process is one of the fundamental and most important models that analyze a time series. Theoretical results and practical tools for fitting an autoregressive process with i.i.d. innovations are well-established. However, when the innovations are white noise but not i.i.d., those tools fail to generate a consistent confidence interval for the autoregressive coefficients. Focus on an autoregressive process with \textit{dependent} and \textit{non-stationary} innovations, this paper provides a consistent result and a Gaussian approximation theorem for the Yule-Walker estimator. Moreover, it introduces the second order wild bootstrap that constructs a consistent confidence interval for the estimator. Numerical experiments confirm the validity of the proposed algorithm with different kinds of white noise innovations. Meanwhile, the classical method(e.g., AR(Sieve) bootstrap) fails to generate a correct confidence interval when the innovations are dependent. According to Kreiss et al. \cite{10.1214/11-AOS900} and the Wold decomposition, assuming a real-life time series satisfies an autoregressive process is reasonable. However, innovations in that process are more likely to be white noises instead of i.i.d.. Therefore, our method should provide a practical tool that handles real-life problems.
The aim of this work is to develop a fully-distributed algorithmic framework for training graph convolutional networks (GCNs). The proposed method is able to exploit the meaningful relational structure of the input data, which are collected by a set of agents that communicate over a sparse network topology. After formulating the centralized GCN training problem, we first show how to make inference in a distributed scenario where the underlying data graph is split among different agents. Then, we propose a distributed gradient descent procedure to solve the GCN training problem. The resulting model distributes computation along three lines: during inference, during back-propagation, and during optimization. Convergence to stationary solutions of the GCN training problem is also established under mild conditions. Finally, we propose an optimization criterion to design the communication topology between agents in order to match with the graph describing data relationships. A wide set of numerical results validate our proposal. To the best of our knowledge, this is the first work combining graph convolutional neural networks with distributed optimization.
Network embedding is the process of learning low-dimensional representations for nodes in a network, while preserving node features. Existing studies only leverage network structure information and focus on preserving structural features. However, nodes in real-world networks often have a rich set of attributes providing extra semantic information. It has been demonstrated that both structural and attribute features are important for network analysis tasks. To preserve both features, we investigate the problem of integrating structure and attribute information to perform network embedding and propose a Multimodal Deep Network Embedding (MDNE) method. MDNE captures the non-linear network structures and the complex interactions among structures and attributes, using a deep model consisting of multiple layers of non-linear functions. Since structures and attributes are two different types of information, a multimodal learning method is adopted to pre-process them and help the model to better capture the correlations between node structure and attribute information. We employ both structural proximity and attribute proximity in the loss function to preserve the respective features and the representations are obtained by minimizing the loss function. Results of extensive experiments on four real-world datasets show that the proposed method performs significantly better than baselines on a variety of tasks, which demonstrate the effectiveness and generality of our method.
Network embedding aims to learn a latent, low-dimensional vector representations of network nodes, effective in supporting various network analytic tasks. While prior arts on network embedding focus primarily on preserving network topology structure to learn node representations, recently proposed attributed network embedding algorithms attempt to integrate rich node content information with network topological structure for enhancing the quality of network embedding. In reality, networks often have sparse content, incomplete node attributes, as well as the discrepancy between node attribute feature space and network structure space, which severely deteriorates the performance of existing methods. In this paper, we propose a unified framework for attributed network embedding-attri2vec-that learns node embeddings by discovering a latent node attribute subspace via a network structure guided transformation performed on the original attribute space. The resultant latent subspace can respect network structure in a more consistent way towards learning high-quality node representations. We formulate an optimization problem which is solved by an efficient stochastic gradient descent algorithm, with linear time complexity to the number of nodes. We investigate a series of linear and non-linear transformations performed on node attributes and empirically validate their effectiveness on various types of networks. Another advantage of attri2vec is its ability to solve out-of-sample problems, where embeddings of new coming nodes can be inferred from their node attributes through the learned mapping function. Experiments on various types of networks confirm that attri2vec is superior to state-of-the-art baselines for node classification, node clustering, as well as out-of-sample link prediction tasks. The source code of this paper is available at //github.com/daokunzhang/attri2vec.
An attributed network enriches a pure network by encoding a part of widely accessible node auxiliary information into node attributes. Learning vector representation of each node a.k.a. Network Embedding (NE) for such an attributed network by considering both structure and attribute information has recently attracted considerable attention, since each node embedding is simply a unified low-dimension vector representation that makes downstream tasks e.g. link prediction more efficient and much easier to realize. Most of previous works have not considered the significant case of a network with incomplete structure information, which however, would often appear in our real-world scenarios e.g. the abnormal users in a social network who intentionally hide their friendships. And different networks obviously have different levels of incomplete structure information, which imposes more challenges to balance two sources of information. To tackle that, we propose a robust NE method called Attributed Biased Random Walks (ABRW) to employ attribute information for compensating incomplete structure information by using transition matrices. The experiments of link prediction and node classification tasks on real-world datasets confirm the robustness and effectiveness of our method to the different levels of the incomplete structure information.
Topic models have been widely explored as probabilistic generative models of documents. Traditional inference methods have sought closed-form derivations for updating the models, however as the expressiveness of these models grows, so does the difficulty of performing fast and accurate inference over their parameters. This paper presents alternative neural approaches to topic modelling by providing parameterisable distributions over topics which permit training by backpropagation in the framework of neural variational inference. In addition, with the help of a stick-breaking construction, we propose a recurrent network that is able to discover a notionally unbounded number of topics, analogous to Bayesian non-parametric topic models. Experimental results on the MXM Song Lyrics, 20NewsGroups and Reuters News datasets demonstrate the effectiveness and efficiency of these neural topic models.
The Everyday Sexism Project documents everyday examples of sexism reported by volunteer contributors from all around the world. It collected 100,000 entries in 13+ languages within the first 3 years of its existence. The content of reports in various languages submitted to Everyday Sexism is a valuable source of crowdsourced information with great potential for feminist and gender studies. In this paper, we take a computational approach to analyze the content of reports. We use topic-modelling techniques to extract emerging topics and concepts from the reports, and to map the semantic relations between those topics. The resulting picture closely resembles and adds to that arrived at through qualitative analysis, showing that this form of topic modeling could be useful for sifting through datasets that had not previously been subject to any analysis. More precisely, we come up with a map of topics for two different resolutions of our topic model and discuss the connection between the identified topics. In the low resolution picture, for instance, we found Public space/Street, Online, Work related/Office, Transport, School, Media harassment, and Domestic abuse. Among these, the strongest connection is between Public space/Street harassment and Domestic abuse and sexism in personal relationships.The strength of the relationships between topics illustrates the fluid and ubiquitous nature of sexism, with no single experience being unrelated to another.
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