Nam H. Lee

Labeled cortical mantle distance maps of the cingulate quantify differences between dementia of the Alzheimer type and healthy aging

The cingulate gyri in 37 subjects with and without early dementia of the Alzheimer type (DAT) were studied by using MRI at 1.0 mm3 isotropic resolution. Groups were segregated into young controls (n = 10), age-matched normal controls (n = 10), very mild DAT (n = 8), and mild DAT (n = 9). By using automated Bayesian segmentation of the cortex and gray matter/white matter (GM/WM) isosurface generation, tissue compartments were labeled into gray, white, and cerebrospinal fluid as a function of distance from the GM/WM isosurface. Cortical mantle distance maps are generated profiling the GM volume and cortical mantle distribution as a function of distance from the cortical surface. Probabilistic tests based on generalizations of Wilcoxon–Mann–Whitney tests were applied to quantify cortical mantle distribution changes with normal and abnormal aging. We find no significant change between young controls and healthy aging as measured by the GM volume and cortical mantle distribution as a function of distance in both anterior and posterior regions of the cingulate. Significant progression of GM loss is seen in the very mild DAT and mild DAT groups in all areas of the cingulate. Posterior regions show both GM volume loss as well as significant cortical mantle distribution decrease with the onset of mild DAT. The “shape of the cortical mantle” as measured by the cortical mantle distance profiles manifests a pronounced increase in variability with mild DAT.

Attribute Fusion in a Latent Process Model for Time Series of Graphs

Hypothesis testing on time series of attributed graphs has applications in diverse areas, e.g., social network analysis (wherein vertices represent individual actors or organizations), connectome inference (wherein vertices are neurons or brain regions) and text processing (wherein vertices represent authors or documents). We consider the problem of anomaly/change point detection given the latent process model for time series of graphs with categorical attributes on the edges presented in [N. H. Lee and C. E. Priebe, “A latent process model for time series of attributed random graphs,” Statist. Inference Stoch. Process., vol. 14, pp. 231–253, 2011]. Various attributed graph invariants are considered, and their power for detection as a function of a linear fusion parameter is presented. Our main result is that inferential performance in mathematically tractable first-order and second-order approximation models does provide guidance for methodological choices applicable to the exact (realistic but intractable) model. Furthermore, to the extent that the exact model is realistic, we may tentatively conclude that approximation model investigations have some bearing on real data applications.

Attribute fusion in a latent process model for time series of graphs

We consider anomaly/change point detection given a time series of graphs with categorical attributes on the edges. Various attributed graph invariants are considered, and their power for detection as a function of a linear fusion parameter is presented.

A Model Selection Approach for Clustering a Multinomial Sequence with Non-Negative Factorization

We consider a problem of clustering a sequence of multinomial observations by way of a model selection criterion. We propose a form of a penalty term for the model selection procedure. Our approach subsumes both the conventional AIC and BIC criteria but also extends the conventional criteria in a way that it can be applicable also to a sequence of sparse multinomial observations, where even within a same cluster, the number of multinomial trials may be different for different observations. In addition, as a preliminary estimation step to maximum likelihood estimation, and more generally, to maximum Lq estimation, we propose to use reduced rank projection in combination with non-negative factorization. We motivate our approach by showing that our model selection criterion and preliminary estimation step yield consistent estimates under simplifying assumptions. We also illustrate our approach through numerical experiments using real and simulated data.

An Implied Latent Position Process for Doubly Stochastic Messaging Activities

This paper studies the problem of identifying an inhomogeneous interaction structure amongst social agents. We construct the social network by a random graph and model the messaging activities via a multi-channel self-exciting point process. We design a methodology that divides the agents into two disjoint groups so that members within each group are considered to be of similar attributes. Our methodology and algorithm are useful for investigating and detecting abnormal activities within a network. We provide numerical illustrations based on a large email dataset from Enron. KeywordsSocial network; Multiple self-exciting point processes; Hypothesis testing; Risk mitigation. In this paper, we propose a model to estimate and analyze the structure of messaging activities in a social network. This is motivated by the recent proliferation of mobile technology, along with spread of blogs, social networking site, and media-sharing technology. For classification, detection, tracking and other practical purposes, robust statistical analysis as well as a good understanding of the data structure are essential. In this paper, we consider a collection of messaging data, made public by the Federal Energy Regulatory Commission in 2003, that contains highly accurate information about the time at which each message was exchanged. We introduce a meaningful way to reduce messaging data to a random graph and explore its possible application to a community detection problem. A simple and popular existing method to achieve this is to “pairwise threshold”, where for each pair of agents, an edge between vertex i and vertex j is formed if the number of messaging events between them exceeds a certain threshold. Such graphs are often thought to reveal a structure of an underlying social dynamic, motivating several successful models for a social network with sub-communities, and many tools for detecting a community with a particular graph theoretic and statistical properties have been proposed (Goldenberg et al. 2010, Kolaczyk 2009). On the other hand, some recent research (De Choudhury et al. 2010), has documented that changing the thresholds in the reduction procedure can produce dramatically different graphs, resulting in vastly dissimilar communities. This issue has motivated the work such as Heard et al. (2010) and Perry and Wolfe (2010). In both studies, as a remedy, the messaging events are modeled by way of point processes. In Heard et al. (2010), a piecewise-constant interaction rate is considered, while in Perry and Wolfe (2010) a Cox multiplicative intensity model is used with covariates that depend on the history of the process. Our approach is to model the dynamic network via n lowdimensional latent processes. One challenge to overcome is to estimate the intensity processes. Given an estimate of the intensity processes, we propose a novel embedding methodology to facilitate inference. Based on our methodology, we can produce a random graph with a particular probabilistic structure that could be very useful for the purpose of community detection. I. MESSAGING EVENTS LABELED WITH LINEARLY-ORDERED RISK LEVELS We consider a network of n vertices, and denote V = {1, . . . , n}. For ` ∈ N, we denote by τ`, {i`, j`} and k`, respectively, the occurrence time, the messaging pair and the risk level of the `-th message. Collectively, d` = (τ`, {i`, j`}, k`) represents the `-th messaging event. We require that τ` k2. For each (undirected) pair ij of the vertices and t ∈ [0, T ], we denote by Nij,k(t) the number of (undirected) messaging events on the topic k. between vertex i and vertex j during [0, t]. For each t ∈ [0, T ], let Dk(t) be the collection of all communication messaging events by time t on topic label k, i.e., Dk(t) = { (τk,`, {ik,`, jk,`}, k) : ` = 1, . . . , ∑