An invitation to Bayesian nonparametrics

Hjort, Nils Lid; Holmes, Chris; Müller, Peter; Walker, Stephen G.

doi:10.1017/cbo9780511802478.001

Cited by 236 publications

(293 citation statements)

References 0 publications

Supporting

Mentioning

291

Contrasting

Unclassified

Order By: Relevance

“…We focused on a specific Bayesian model but we emphasize that this strategy can be used to accommodate many kinds of assumptions. For example, we can posit varying degree distributions to better capture the expected properties of real networks or use Bayesian nonparametric assumptions (45) to infer the number of communities within the analysis. In general, with the ideas presented here, we can use sophisticated statistical models to analyze massive real-world networks.…”

Section: Discussionmentioning

confidence: 99%

Efficient discovery of overlapping communities in massive networks

Gopalan

Blei

2013

Proc. Natl. Acad. Sci. U.S.A.

220

162

View full text Add to dashboard Cite

Detecting overlapping communities is essential to analyzing and exploring natural networks such as social networks, biological networks, and citation networks. However, most existing approaches do not scale to the size of networks that we regularly observe in the real world. In this paper, we develop a scalable approach to community detection that discovers overlapping communities in massive realworld networks. Our approach is based on a Bayesian model of networks that allows nodes to participate in multiple communities, and a corresponding algorithm that naturally interleaves subsampling from the network and updating an estimate of its communities. We demonstrate how we can discover the hidden community structure of several real-world networks, including 3.7 million US patents, 575,000 physics articles from the arXiv preprint server, and 875,000 connected Web pages from the Internet. Furthermore, we demonstrate on large simulated networks that our algorithm accurately discovers the true community structure. This paper opens the door to using sophisticated statistical models to analyze massive networks. Community detection is important for both exploring a network and predicting connections that are not yet observed. For example, by finding the communities in a large citation graph of scientific articles, we can make hypotheses about the fields and subfields that they contain. By finding communities in a large social network, we can more easily make predictions to individual members about who they might be friends with but are not yet connected to.In this paper, we develop an algorithm that discovers communities in modern real-world networks. The challenge is that real-world networks are massive-they can contain hundreds of thousands or even millions of nodes. We will examine a network of scientific articles that contains 575,000 articles, a network of connected Web pages that contains 875,000 pages, and a network of US patents that contains 3,700,000 patents. Most approaches to community detection cannot handle data at this scale.There are two fundamental difficulties to detecting communities in such networks. The first is that many existing community detection algorithms assume that each node belongs to a single community (1,(3)(4)(5)(6)(7)(14)(15)(16). In real-world networks, each node will likely belong to multiple communities and its connections will reflect these multiple memberships (2,(8)(9)(10)(11)(12)(13)17). For example, in a large social network, a member may be connected to coworkers, friends from school, and neighbors. We need algorithms that discover overlapping communities to capture the heterogeneity of each node's connections.The second difficulty is that existing algorithms are too slow. Many community detection algorithms iteratively analyze each pair of nodes, regardless of whether the nodes in the pair are connected in the network (5, 6, 10). Consequently, these algorithms run in time squared in the number of nodes, which makes analyzing massive networks computationally intractable. Other a...

show abstract

Section: Discussionmentioning

confidence: 99%

Efficient discovery of overlapping communities in massive networks

Gopalan

Blei

2013

Proc. Natl. Acad. Sci. U.S.A.

220

162

View full text Add to dashboard Cite

show abstract

“…In this article, we describe a richer class of stochastic processes known as combinatorial stochastic processes that provide a useful foundation for the design of flexible models for temporal segmentation. Combinatorial stochastic processes have been studied for several decades in probability theory (see, e.g., [9]), and they have begun to play a role in statistics as well, most notably in the area of Bayesian nonparametric statistics where they yield Bayesian approaches to clustering and survival analysis (see, e.g., [10]). The work that we present here extends these efforts into the time series domain.…”

mentioning

confidence: 99%

Bayesian Nonparametric Methods for Learning Markov Switching Processes

Fox

Sudderth

Jordan

et al. 2010

IEEE Signal Process. Mag.

View full text Add to dashboard Cite

Markov switching processes, such as the hidden Markov model (HMM) and switching linear dynamical system (SLDS), are often used to describe rich dynamical phenomena. They describe complex behavior via repeated returns to a set of simpler models: imagine a person alternating between walking, running, and jumping behaviors, or a stock index switching between regimes of high and low volatility.Classical approaches to identification and estimation of these models assume a fixed, pre-specified number of dynamical models. We instead examine Bayesian nonparametric approaches that define a prior on Markov switching processes with an unbounded number of potential model parameters (i.e., Markov modes). By leveraging stochastic processes such as the beta and Dirichlet process, these methods allow the data to drive the complexity of the learned model, while still permitting efficient inference algorithms.They also lead to generalizations which discover and model dynamical behaviors shared among multiple related time series. Index TermsBayesian nonparametric methods, hidden Markov model, Markov jump linear system, time series.

show abstract

“…This is done within the framework presented in the monographs by Ghosh and Ramamoorthi (2003) and Hjort et al (2010), which contain a good account of the recent developments in Bayesian non-parametrics; see also Walker (2004);Walker et al (2005). Before embarking on this topic in explicit terms, we make some general remarks concerning consistency in the Bayesian setting.…”

Section: Discussionmentioning

confidence: 99%

The current duration design for estimating the time to pregnancy distribution: a nonparametric Bayesian perspective

et al. 2015

View full text Add to dashboard Cite

This paper was inspired by the studies of Niels Keiding and co-authors on estimating the waiting time-to-pregnancy (TTP) distribution, and in particular on using the current duration design in that context. In this design, a cross-sectional sample of women is collected from those who are currently attempting to become pregnant, and then by recording from each the time she has been attempting. Our aim here is to study the identifiability and the estimation of the waiting time distribution on the basis of current duration data. The main difficulty in this stems from the fact that very short waiting times are only rarely selected into the sample of current durations, and this renders their estimation unstable. We introduce here a Bayesian method for this estimation problem, prove its asymptotic consistency, and compare the method to some variants of the non-parametric maximum likelihood estimators (NPMLE), which have been used previously in this context. The properties of the Bayesian estimation method are studied also empirically, using both simulated data and TTP data on current durations collected by Slama et al. (2012).

show abstract

An invitation to Bayesian nonparametrics

Cited by 236 publications

References 0 publications

Efficient discovery of overlapping communities in massive networks

Efficient discovery of overlapping communities in massive networks

Bayesian Nonparametric Methods for Learning Markov Switching Processes

The current duration design for estimating the time to pregnancy distribution: a nonparametric Bayesian perspective

Contact Info

Product

Resources

About