Charles Weko

This paper proves identifiability of the hub model parameters and estimation consistency under mild conditions. Furthermore, this paper generalizes the hub model by introducing a model component that allows hubless groups in which individual nodes spontaneously appear independent of any other individual. We refer to this additional component as the null component. The new model bridges the gap between the hub model and the degenerate case of the mixture model – the Bernoulli product.

Analysis must clearly support decision-making and be easily consumable for busy Pentagon executives.

Do not mistake this to mean analysts have to “dumb down” their product. Instead, analysts have to grasp the intense cognitive demand Department of Defense executives experience. Analysts must limit the amount of unnecessary additional load they place on these executives.

In medical research, economics, and the social sciences data frequently appear as subsets of a set of objects. Over the past century a number of descriptive statistics have been developed to infer network structure from such data. However, these measures lack a generating mechanism that links the inferred network structure to the observed groups. To address this issue, we propose a model-based approach called the Hub Model which assumes that every observed group has a leader and that the leader… Show more

In medical research, economics, and the social sciences data frequently appear as subsets of a set of objects. Over the past century a number of descriptive statistics have been developed to infer network structure from such data. However, these measures lack a generating mechanism that links the inferred network structure to the observed groups. To address this issue, we propose a model-based approach called the Hub Model which assumes that every observed group has a leader and that the leader has brought together the other members of the group. The performance of Hub Models is demonstrated by simulation studies. We apply this model to the characters in a famous 18th century Chinese novel. Show less

Association indices have been a mainstay of social behaviour analysis for decades. However, researchers have long recognized that these indices can be biased under certain conditions. In this paper, I develop a process map of the steps necessary to transform social behaviour into estimates of association rates. This helps to distinguish the subject population's behaviour from the researcher's data collection protocol. By doing this, we can isolate the sources of bias. I also show that bias in… Show more

Association indices have been a mainstay of social behaviour analysis for decades. However, researchers have long recognized that these indices can be biased under certain conditions. In this paper, I develop a process map of the steps necessary to transform social behaviour into estimates of association rates. This helps to distinguish the subject population's behaviour from the researcher's data collection protocol. By doing this, we can isolate the sources of bias. I also show that bias in association indices is often a function of the true association rate. This means that while bias does not affect the ordering of associations, it can impact analysis in unpredictable ways. Performing network analysis with biased association indices can lead researchers to arrive at different conclusions than if they had used unbiased estimators. To simplify the mathematical task of deriving unbiased estimators, I introduce three properties of maximum likelihood estimators that allow one to treat association data as output from a multinomial distribution, then use the functional invariance property of maximum likelihood estimators to solve for estimators. I apply these properties to a selection of common data collection protocols to show that there is no single association index that is appropriate for all cases. Instead, each of the commonly used indices is unbiased under appropriate conditions. Furthermore, when it is possible that some of the individuals are not identified, I introduce some new unbiased estimators. I close with a discussion of nontraditional techniques of collecting data that provide an opportunity to increase the number of outputs from the data collection process. These techniques may ultimately make it possible to specify association behaviour more carefully by allowing for more parameters in the data generation process. Show less

Social network analysis presupposes that observed social behavior is influenced by an unobserved network. Traditional approaches to inferring the latent network use pairwise descriptive statistics that rely on a variety of measures of co-occurrence. While these techniques have proven useful in a wide range of applications, the literature does not describe the generating mechanism of the observed data from the network.
In a previous article, the authors presented a technique which used a… Show more

Social network analysis presupposes that observed social behavior is influenced by an unobserved network. Traditional approaches to inferring the latent network use pairwise descriptive statistics that rely on a variety of measures of co-occurrence. While these techniques have proven useful in a wide range of applications, the literature does not describe the generating mechanism of the observed data from the network.
In a previous article, the authors presented a technique which used a finite mixture model as the connection between the unobserved network and the observed social behavior. This model assumed that each group was the result of a star graph on a subset of the population. Thus, each group was the result of a leader who selected members of the population to be in the group. They called these hub models.
This approach treats the network values as parameters of a model. However, this leads to a general challenge in estimating parameters which must be addressed. For small datasets there can be far more parameters to estimate than there are observations. Under these conditions, the estimated network can be unstable.
In this article, we propose a solution which penalizes the number of nodes which can exert a leadership role. We implement this as a pseudo-Expectation Maximization algorithm.
We demonstrate this technique through a series of simulations which show that when the number of leaders is sparse, parameter estimation is improved. Further, we apply this technique to a dataset of animal behavior and an example of recommender systems. Show less

This dissertation defines stochastic models called Star Models for modeling group formation. Each observed group is assumed to have a single leader who has brought the group together. We derive maximum likelihood estimators for the model parameters. The parameter estimation of Star Models fits naturally into the framework of the Expectation-Maximization algorithm. The resulting parameters have an intuitive interpretation as the assertiveness of individual nodes and their popularity within the… Show more

This dissertation defines stochastic models called Star Models for modeling group formation. Each observed group is assumed to have a single leader who has brought the group together. We derive maximum likelihood estimators for the model parameters. The parameter estimation of Star Models fits naturally into the framework of the Expectation-Maximization algorithm. The resulting parameters have an intuitive interpretation as the assertiveness of individual nodes and their popularity within the population.

We apply the new methods to simulated data to compare our results with the existing methods. Additionally, we apply these techniques to the famous 18th century Chinese novel, Dream of the Red Chamber to demonstrate the superior performance of the Star Model.
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In the fall of 2010, United States Forces-Iraq (USF-I) drew down to 50,000 service members and began Operation NEW DAWN. In order to support the Bilateral Security Agreement between the United States and Iraq, U.S. planners had to reposture two million pieces of equipment and retrograde the remaining service members by 31 December 2011. The Retrograde from Iraq (RFI) study was conducted in support of a request from the USF-I Chief of Staff, Major General William Garrett. MG Garrett requested… Show more

In the fall of 2010, United States Forces-Iraq (USF-I) drew down to 50,000 service members and began Operation NEW DAWN. In order to support the Bilateral Security Agreement between the United States and Iraq, U.S. planners had to reposture two million pieces of equipment and retrograde the remaining service members by 31 December 2011. The Retrograde from Iraq (RFI) study was conducted in support of a request from the USF-I Chief of Staff, Major General William Garrett. MG Garrett requested support from the Center for Army Analysis (CAA) to assess USF-I's ability to achieve its reposture objectives. This effort included the closure of 92 bases. The RFI study provided forecasts on when all equipment would clear individual bases for base closure, when all equipment would leave Iraq, the level of utilization rates for various transportation resources, and the velocity of equipment as it departed. These analyses were conducted under varying transportation networks and planning factors. With the requirement to reposture more than two million pieces of equipment, these forecasts supported numerous key decision points with greatly enhanced information and reduced uncertainty. Show less

To bridge the cultural differences between the military and academics successfully, statisticians should be prepared to overcome objections and misconceptions as they arise.

Why the future of unmanned systems depends on making them smarter.

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December 2009.]

Professional Bulletin of United States Army Logistics