Stochastic Block Transition Models for Dynamic Networks

There has been great interest in recent years on statistical models for dynamic networks. In this paper, I propose a stochastic block transition model (SBTM) for dynamic networks that is inspired by the well-known stochastic block model (SBM) for static networks and previous dynamic extensions of the SBM. Unlike most existing dynamic network models, it does not make a hidden Markov assumption on the edge-level dynamics, allowing the presence or absence of edges to directly influence future edge probabilities while retaining the interpretability of the SBM. I derive an approximate inference procedure for the SBTM and demonstrate that it is significantly better at reproducing durations of edges in real social network data.Comment: To appear in proceedings of AISTATS 201

NIR/Optical Selected Local Mergers --- Spatial Density and sSFR Enhancement

Mergers play important roles in triggering the most active objects in the universe, including (U)LIRGs and QSOs. However, whether they are also important for the total stellar mass build-up in galaxies in general is unclear and controversial. The answer to that question depends on the merger rate and the average strength of merger induced star formation. In this talk, I will review studies on spatial density and sSFR enhancement of local mergers found in NIR/optical selected pair samples. In line with the current literature on galaxy formation/evolution, special attention will be paid to the dependence of the local merger rate and of the sSFR enhancement on four fundamental observables: (1) stellar mass, (2) mass ratio, (3) separation, and (4) environment.Comment: A review talk; 8 pages; to appear on the Conference Proceedings for "Galaxy Mergers in an Evolving Universe", held in Hualien, Taiwan (October 2011

Personalized Degrees: Effects on Link Formation in Dynamic Networks from an Egocentric Perspective

Understanding mechanisms driving link formation in dynamic social networks is a long-standing problem that has implications to understanding social structure as well as link prediction and recommendation. Social networks exhibit a high degree of transitivity, which explains the successes of common neighbor-based methods for link prediction. In this paper, we examine mechanisms behind link formation from the perspective of an ego node. We introduce the notion of personalized degree for each neighbor node of the ego, which is the number of other neighbors a particular neighbor is connected to. From empirical analyses on four on-line social network datasets, we find that neighbors with higher personalized degree are more likely to lead to new link formations when they serve as common neighbors with other nodes, both in undirected and directed settings. This is complementary to the finding of Adamic and Adar that neighbor nodes with higher (global) degree are less likely to lead to new link formations. Furthermore, on directed networks, we find that personalized out-degree has a stronger effect on link formation than personalized in-degree, whereas global in-degree has a stronger effect than global out-degree. We validate our empirical findings through several link recommendation experiments and observe that incorporating both personalized and global degree into link recommendation greatly improves accuracy.Comment: To appear at the 10th International Workshop on Modeling Social Media co-located with the Web Conference 201

A Generalized Coupon Collector Problem

This paper provides analysis to a generalized version of the coupon collector problem, in which the collector gets $d$ distinct coupons each run and she chooses the one that she has the least so far. On the asymptotic case when the number of coupons $n$ goes to infinity, we show that on average $\frac{n\log n}{d} + \frac{n}{d}(m-1)\log\log{n}+O(mn)$ runs are needed to collect $m$ sets of coupons. An efficient exact algorithm is also developed for any finite case to compute the average needed runs exactly. Numerical examples are provided to verify our theoretical predictions.Comment: 20 pages, 6 figures, preprin