Presentations

Latent Space Mixture Models for Networks

Edoardo Airoldi and Eric Xing

Carnegie Mellon University

Projecting observed interactions onto a low-dimensional latent

space is a convenient way to visualize structure that possibly

underlies the data. Popular methods, however, tend to separate the

projection task from the quantitative analysis of the structure that

is possibly present in the latent space. For example, latent space

models project interactions onto a latent space by inverting some

function of data and latent positional elements, whereas stochastic

block models seek specific structural regularities in the form of

latent clusters and cluster-to-cluster connection patterns.

We develop a new methodology that integrates the task of

projecting data onto a latent space with that of seeking structure.

We explicitly posit a parametric version of the regularities we wish

to infer, e.g., soft clusters, as structural elements of the latent

space onto which we project that observed interactions. We present a

specific model that extends the latent space model of Hoff et al.

(2002) by positing a mixture of Gaussians in the latent space, and we

derive a convenient variational approximation to solve the Bayes

problem for this model.

Dynamic Contextual Friendship Networks

Anna Goldenberg and Alice Zheng

Carnegie Mellon University

We live in a society built upon the complex web of interpersonal

relationships. For decades, researchers have been fascinated with the

characterization of such social networks, examples of which include

academic research paper co-authorships, film actor co-star relationships,

and many more. With the recent rise of large online user communities, the

study of these networks seems more relevant than ever.

In this talk, we focus on developing a generative model of evolving social

networks. The social actors in our model have evolving distributions over

spheres of interaction, which we term "contexts." The model allows for

the birth and death of social ties and addition of new actors. We study

the robustness of our model by examining the statistical properties of

simulated networks in comparison to those of real networks. We conclude

with computational issues of parameter learning in this model.

Chain Graph Temporal Models of Social Networks

Stephen Hanneke

Carnegie Mellon university

We propose a family of markov statistical models for social network

evolution over time, which represents an extension of Exponential Random

Graph Models (ERGMs). Many of the methods and theorems for ERGMs are

readily adapted for this model, including MCMC maximum likelihood

estimation algorithms. We discuss example models of this type along with

empirical results for estimation and prediction tasks.

Optimization and differential games approaches for the analysis of social networks

Chung-Chien Hong, N. G. Medhin

North Carolina State University

We present two approaches to the study of social networks. The first method

is based on nonlinear programming and the second on differential games. In

the nonlinear programming approach we consider a social group where each

actor of the social group has limited statistical information on each of the

other actors. Each actor also has a set of preferred values and attributes.

Further, the likelihood of a link from one actor to another is likely to be

higher in the case of perceived reciprocity. A non-linear programming

problem is constructed to obtain a social matrix, where an entry of 1 in the ij-

th entry indicates the presence of a link from actor i to actor j, whereas an

entry of zero indicates the absence of a link. We also construct a probability

social matrix where the entries represent the probability of a link. The model

is made dynamic by varying the preferred values of each actor. Finally, we

study the movements of actors leading to the identification of cliques. In this

model, an actor need not know every member of the group. However, there is

an increasing probability to get acquainted with more actors as time passes.

The differential games approach starts with a dynamical model where the

players/actors have a set of strategies reflecting their values and preferences.

The differential game is studied to understand the social network and its

time evolution.

On Network Sampling and Inference of Network Structure: A Case

Study Using Trace route and the Internet

Eric Kolaczyk

Boston University

Empirical network measurements have been at the heart of a variety of

discoveries of both commonality and differences in network structure

across disciplines. Among other things, such discoveries have inspired a

keen interest in the development of generative network graph models that

can reproduce observed characteristics. However, recent work in a number

of fields in the past few years has found that the method by which such

measurements are obtained can have important implications on the extent to

which the observed characteristics accurately reflect those of the 'true'

underlying network. In this talk I will review some examples of such work

and discuss the problem of reliable estimation of certain network

characteristics. I will concentrate on the context of traceroute sampling

in the Internet and the challenge of attacking various `species' problems.

Dynamic Social Network Analysis using Latent Space Models

Purnamrita Sarkar

Carnegie Mellon University

This work explores two aspects of social network modeling. First, we

generalize a successful static model of relationships into a dynamic model

that accounts for friendships drifting over time. Second, we show how to

make it tractable to learn such models from data, even as the number of

entities n gets large. The generalized model associates each entity with a

point in p-dimensional Euclidian latent space. The points can move as time

progresses but large moves in latent space are improbable. Observed

links between entities are more likely if the entities are close in latent

space. We show how to make such a model tractable (sub-quadratic in the

number of entities) by the use of appropriate kernel function for

similarity in latent space; the use of low dimensional kd-trees; a new

efficient dynamic adaptation of multidimensional scaling for a first pass

of approximate projection of entities into latent space; and an efficient

conjugate gradient update rule for non-linear local optimization in which

amortized time per entity during an update is O(log n). We use both

synthetic and real-world data on upto 11,000 entities which indicate

linear scaling in computation time and improved performance over four

alternative approaches. We also illustrate the system operating on twelve

years of NIPS co-publication data.

Social Networks in Elephants

Eric Vance

Duke University

Wild female African elephants live in a matriarchal society and form

persistent family groups. However, within these groups the elephants

frequently split into subgroups in a process known as fission/fusion, and

these patterns of affiliation are not well understood. In this talk I use a

bilinear mixed effects model proposed by Peter Hoff (2005) to isolate several

key components of elephant social behavior. This model incorporates the key

notion of an unobserved latent social space to better describe the interactions

between elephants. The model is flexible enough to include predictors of

pairwise affiliation, such as kinships, which allows large-mammal ecologists

to test assumptions about elephant social structure, and to develop new

theories of why and how elephants interact.

Program

9:00-9:30     Alan Karr, NISS
9:30-9:45     Discussion
9:45-10:15    Purnamrita Sarkar, CMU
10:15-10:30   Discussion
10:30-11:00   Coffee
11:00-11:30   Edo Airoldi and Eric Xing, CMU
11:30-11:45   Discussion
11:45-1:00    Lunch
1:00-1:30     Negash Medhin, NC State
1:30-1:45     Discussion
1:45-2:15     Eric Kolaczyk, Boston University
2:15-2:30     Discussion
2:30-2:45     Coffee
2:45-3:15     Stephen Hanneke, CMU
3:15-3:30     Discussion
3:30-4:00     Eric Vance, Duke
4:00-4:15     Discussion
4:15-4:45     Goldenberg and Zheng, CMU
4:45-5:00     Discussion

Hotel Information

Holiday Inn Select 
PITTSBURGH @UNIV CTR (OAKLAND) 
100 LYTTON AVE
PITTSBURGH, PA 15213
  
Hotel Reservations:    1-888-HOLIDAY (888-465-4329)  
Hotel Front Desk:   1-412-6826200 
Hotel Fax:   1-412-6825745 
Email: [email protected]
Check-In Time: 3:00 PM
Check-Out Time: 12:00 PM

When making their reservations, guests should mention that they're part of the 
SAMSI group in order to get the CMU rate of $109.