253 research outputs found
Fast Network Community Detection with Profile-Pseudo Likelihood Methods
The stochastic block model is one of the most studied network models for
community detection. It is well-known that most algorithms proposed for fitting
the stochastic block model likelihood function cannot scale to large-scale
networks. One prominent work that overcomes this computational challenge is
Amini et al.(2013), which proposed a fast pseudo-likelihood approach for
fitting stochastic block models to large sparse networks. However, this
approach does not have convergence guarantee, and is not well suited for small-
or medium- scale networks. In this article, we propose a novel likelihood based
approach that decouples row and column labels in the likelihood function, which
enables a fast alternating maximization; the new method is computationally
efficient, performs well for both small and large scale networks, and has
provable convergence guarantee. We show that our method provides strongly
consistent estimates of the communities in a stochastic block model. As
demonstrated in simulation studies, the proposed method outperforms the
pseudo-likelihood approach in terms of both estimation accuracy and computation
efficiency, especially for large sparse networks. We further consider
extensions of our proposed method to handle networks with degree heterogeneity
and bipartite properties
Problems and Suggestions for Professional Course Teaching of Finance
Finance is one of the most popular majors in higher education, whose professional courses cover the theoretical basis and practical skills related to finance. Learning finance knowledge is the basic path for students to master finance related knowledge and carry out financial work. This paper analyzes the characteristics of finance courses, based on the example of Financial Engineering, identifies the problems in classroom teaching and proposes appropriate countermeasures
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