We present an efficient algorithm for learning mixed membership models when the number of variables $p$ is much larger than the number of hidden components $k$. This algorithm reduces the computational complexity of state-of-the-art tensor methods, which require decomposing an $O\left(p^3\right)$ tensor, to factorizing $O\left(p/k\right)$ sub-tensors each of size $O\left(k^3\right)$. In addition, we address the issue of negative entries in the empirical method of moments based estimators. We provide sufficient conditions under which our approach has provable guarantees. Our approach obtains competitive empirical results on both simulated and real data.
This paper considers the problem of modeling and estimating community memberships of nodes in a directed network where every row (column) node is associated with a vector determining its membership in each row (column) community. To model such directed network, we propose directed degree corrected mixed membership (DiDCMM) model by considering degree heterogeneity. DiDCMM is identifiable under popular conditions for mixed membership network when considering degree heterogeneity. Based on the cone structure inherent in the normalized version of the left singular vectors and the simplex structur…
University of Southern California（南加州大学）；University of Montreal（蒙特利尔大学）；University of Amsterdam（阿姆斯特丹大学）
We propose a stochastic gradient Markov chain Monte Carlo (SG-MCMC) algorithm for scalable inference in mixed-membership stochastic blockmodels (MMSB). Our algorithm is based on the stochastic gradient Riemannian Langevin sampler and achieves both faster speed and higher accuracy at every iteration than the current state-of-the-art algorithm based on stochastic variational inference. In addition we develop an approximation that can handle models that entertain a very large number of communities. The experimental results show that SG-MCMC strictly dominates competing algorithms in all cases.
Models for sequential data such as the recurrent neural network (RNN) often implicitly model a sequence as having a fixed time interval between observations and do not account for group-level effects when multiple sequences are observed. We propose a model for grouped sequential data based on the RNN that accounts for varying time intervals between observations in a sequence by learning a group-level base parameter to which each sequence can revert. Our approach is motivated by the mixed membership framework, and we show how it can be used for dynamic topic modeling in which the distribution o…
China University of Mining and Technology（中国矿业大学）；Nankai University（南开大学）
Community detection in network analysis is an attractive research area recently. Here, under the degree-corrected mixed membership (DCMM) model, we propose an efficient approach called mixed regularized spectral clustering (Mixed-RSC for short) based on the regularized Laplacian matrix. Mixed-RSC is designed based on an ideal cone structure of the variant for the eigen-decomposition of the population regularized Laplacian matrix. We show that the algorithm is asymptotically consistent under mild conditions by providing error bounds for the inferred membership vector of each node. As a byproduc…
University of California, Irvine（加州大学欧文分校）；University of Southern California（南加州大学）
Community detection in graphs has been extensively studied both in theory and in applications. However, detecting communities in hypergraphs is more challenging. In this paper, we propose a tensor decomposition approach for guaranteed learning of communities in a special class of hypergraphs modeling social tagging systems or folksonomies. A folksonomy is a tripartite 3-uniform hypergraph consisting of (user, tag, resource) hyperedges. We posit a probabilistic mixed membership community model, and prove that the tensor method consistently learns the communities under efficient sample complexit…
We propose a novel parameterized family of Mixed Membership Mallows Models (M4) to account for variability in pairwise comparisons generated by a heterogeneous population of noisy and inconsistent users. M4 models individual preferences as a user-specific probabilistic mixture of shared latent Mallows components. Our key algorithmic insight for estimation is to establish a statistical connection between M4 and topic models by viewing pairwise comparisons as words, and users as documents. This key insight leads us to explore Mallows components with a separable structure and leverage recent adva…
Disease phenotyping algorithms process observational clinical data to identify patients with specific diseases. Supervised phenotyping methods require significant quantities of expert-labeled data, while unsupervised methods may learn non-disease phenotypes. To address these limitations, we propose the Semi-Supervised Mixed Membership Model (SS3M) -- a probabilistic graphical model for learning disease phenotypes from clinical data with relatively few labels. We show SS3M can learn interpretable, disease-specific phenotypes which capture the clinical characteristics of the diseases specified b…
The mixed membership stochastic blockmodel (MMSB) is a popular framework for community detection and network generation. It learns a low-rank mixed membership representation for each node across communities by exploiting the underlying graph structure. MMSB assumes that the membership distributions of the nodes are independently drawn from a Dirichlet distribution, which limits its capability to model highly correlated graph structures that exist in real-world networks. In this paper, we present a flexible richly structured MMSB model, \textit{Struct-MMSB}, that uses a recently developed stati…
University of Alberta（阿尔伯塔大学）；University of New South Wales（新南威尔士大学）；University of Social Sciences, Poland（波兰社会科学大学）
The Mixed-Membership Stochastic Blockmodel~(MMSB) is proposed as one of the state-of-the-art Bayesian relational methods suitable for learning the complex hidden structure underlying the network data. However, the current formulation of MMSB suffers from the following two issues: (1), the prior information~(e.g. entities' community structural information) can not be well embedded in the modelling; (2), community evolution can not be well described in the literature. Therefore, we propose a non-parametric fragmentation coagulation based Mixed Membership Stochastic Blockmodel (fcMMSB). Our model…
Inference and Visualization of Community Structure in Attributed Hypergraphs Using Mixed-Membership Stochastic Block Models
Graduate School of Systems Design, Tokyo Metropolitan University（东京 Metropolitan 大学系统设计研究生院）；Principles of Informatics Research Division, National Institute of Informatics（国家信息研究所信息原理研究部门）
We investigate the use of self-tracking data and unsupervised mixed-membership models to phenotype endometriosis. Endometriosis is a systemic, chronic condition of women in reproductive age and, at the same time, a highly enigmatic condition with no known biomarkers to monitor its progression and no established staging. We leverage data collected through a self-tracking app in an observational research study of over 2,800 women with endometriosis tracking their condition over a year and a half (456,900 observations overall). We extend a classical mixed-membership model to accommodate the idios…
Oregon State University（俄勒冈州立大学）；School of Electrical Engineering and Computer Science（电气工程与计算机科学学院）
This work considers clustering nodes of a largely incomplete graph. Under the problem setting, only a small amount of queries about the edges can be made, but the entire graph is not observable. This problem finds applications in large-scale data clustering using limited annotations, community detection under restricted survey resources, and graph topology inference under hidden/removed node interactions. Prior works tackled this problem from various perspectives, e.g., convex programming-based low-rank matrix completion and active query-based clique finding. Nonetheless, many existing methods…
Recent studies of cancer somatic mutation profiles seek to identify mutations for targeted therapy in personalized medicine. Analysis of profiles, however, is not trivial, as each profile is heterogeneous and there are multiple confounding factors that influence the cause-and-effect relationships between cancer genes such as cancer (sub)type, biological processes, total number of mutations, and non-linear mutation interactions. Moreover, cancer is biologically redundant, i.e., distinct mutations can result in the alteration of similar biological processes, so it is important to identify all po…
Last years have seen a regain of interest for the use of stochastic block modeling (SBM) in recommender systems. These models are seen as a flexible alternative to tensor decomposition techniques that are able to handle labeled data. Recent works proposed to tackle discrete recommendation problems via SBMs by considering larger contexts as input data and by adding second order interactions between contexts' related elements. In this work, we show that these models are all special cases of a single global framework: the Serialized Interacting Mixed membership Stochastic Block Model (SIMSBM). It…
University of Maryland, Baltimore County（马里兰大学巴尔的摩县分校）
Word embeddings improve the performance of NLP systems by revealing the hidden structural relationships between words. Despite their success in many applications, word embeddings have seen very little use in computational social science NLP tasks, presumably due to their reliance on big data, and to a lack of interpretability. I propose a probabilistic model-based word embedding method which can recover interpretable embeddings, without big data. The key insight is to leverage mixed membership modeling, in which global representations are shared, but individual entities (i.e. dictionary words)…
University of Bristol（布里斯托大学）；Heilbronn Institute for Mathematical Research（海尔布隆数学研究所）；University of Pittsburgh（匹兹堡大学）；North Carolina State University（北卡罗来纳州立大学）；Johns Hopkins University（约翰斯·霍普金斯大学）
Spectral embedding is a procedure which can be used to obtain vector representations of the nodes of a graph. This paper proposes a generalisation of the latent position network model known as the random dot product graph, to allow interpretation of those vector representations as latent position estimates. The generalisation is needed to model heterophilic connectivity (e.g., `opposites attract') and to cope with negative eigenvalues more generally. We show that, whether the adjacency or normalised Laplacian matrix is used, spectral embedding produces uniformly consistent latent position esti…
Universitat Rovira i Virgili（罗维拉-威尔吉利大学）；Institució Catalana de Recerca i Estudis Avançats (ICREA)（加泰罗尼亚研究与高级研究院）；Santa Fe Institute（圣塔菲研究所）
With ever-increasing amounts of online information available, modeling and predicting individual preferences-for books or articles, for example-is becoming more and more important. Good predictions enable us to improve advice to users, and obtain a better understanding of the socio-psychological processes that determine those preferences. We have developed a collaborative filtering model, with an associated scalable algorithm, that makes accurate predictions of individuals' preferences. Our approach is based on the explicit assumption that there are groups of individuals and of items, and that…
Nordita（北欧理论物理研究所）；Stockholm University（斯德哥尔摩大学）；KTH Royal Institute of Technology（瑞典皇家理工学院）；Johns Hopkins University（约翰斯·霍普金斯大学）；Harvard University（哈佛大学）
The Latent Dirichlet Allocation (LDA) model is a popular method for creating mixed-membership clusters. Despite having been originally developed for text analysis, LDA has been used for a wide range of other applications. We propose a new formulation for the LDA model which incorporates covariates. In this model, a negative binomial regression is embedded within LDA, enabling straight-forward interpretation of the regression coefficients and the analysis of the quantity of cluster-specific elements in each sampling units (instead of the analysis being focused on modeling the proportion of each…
