Carey E. Priebe

Scan Statistics on Enron Graphs

We introduce a theory of scan statistics on graphs and apply the ideas to the problem of anomaly detection in a time series of Enron email graphs.

COMPARATIVE EVALUATION OF PATTERN RECOGNITION TECHNIQUES FOR DETECTION OF MICROCALCIFICATIONS IN MAMMOGRAPHY

Computer-assisted detection of microcalcifications in mammographic images will likely require a multistage algorithm that includes segmentation of possible microcalcifications, pattern recognition techniques to classify the segmented objects, a method to determine if a cluster of calcifications exists, and possibly a method to determine the probability of malignancy. This paper focuses on the first three of these stages, and especially on the classification of segmented local bright spots as either calcification or noncalcification. Seven classifiers (linear and quadratic classifiers, binary decision trees, a standard backpropagation network, 2 dynamic neural networks, and a K-nearest neighbor) are compared. In addition, a postprocessing step is performed on objects identified as calcifications by the classifiers to determine if any clusters of microcalcifications exist. A database of digitized film mammograms is used for training and testing. Detection accuracy of individual and clustered microcalcificat...

A Consistent Adjacency Spectral Embedding for Stochastic Blockmodel Graphs

We present a method to estimate block membership of nodes in a random graph generated by a stochastic blockmodel. We use an embedding procedure motivated by the random dot product graph model, a particular example of the latent position model. The embedding associates each node with a vector; these vectors are clustered via minimization of a square error criterion. We prove that this method is consistent for assigning nodes to blocks, as only a negligible number of nodes will be misassigned. We prove consistency of the method for directed and undirected graphs. The consistent block assignment makes possible consistent parameter estimation for a stochastic blockmodel. We extend the result in the setting where the number of blocks grows slowly with the number of nodes. Our method is also computationally feasible even for very large graphs. We compare our method with Laplacian spectral clustering through analysis of simulated data and a graph derived from Wikipedia documents.

RANDOM FORESTS FOR PHOTOMETRIC REDSHIFTS

The main challenge today in photometric redshift estimation is not in the accuracy but in understanding the uncertainties. We introduce an empirical method based on Random Forests to address these issues. The training algorithm builds a set of optimal decision trees on subsets of the available spectroscopic sample, which provide independent constraints on the redshift of each galaxy. The combined forest estimates have intriguing statistical properties, notable among which are Gaussian errors. We demonstrate the power of our approach on multi-color measurements of the Sloan Digital Sky Survey.

Adaptive mixture density estimation

Abstract A recursive, nonparametric method is developed for performing density estimation derived from mixture models, kernel estimation and stochastic approximation. The asymptotic performance of the method, dubbed “adaptive mixtures” (Priebe and Marchette, Pattern Recognition24, 1197–1209 (1991)) for its data-driven development of a mixture model approximation to the true density, is investigated using the method of sieves. Simulations are included indicating convergence properties for some simple examples.

The application of fractal analysis to mammographic tissue classification

As a first step in determining the efficacy of using computers to assist in diagnosis of medical images, an investigation has been conducted which utilizes the patterns, or textures, in the images. To be of value, any computer scheme must be able to recognize and differentiate the various patterns. An obvious example of this in mammography is the recognition of tumorous tissue and non-malignant abnormal tissue from normal parenchymal tissue. We have developed a pattern recognition technique which uses features derived from the fractal nature of the image. Further, we are able to develop mathematical models which can be used to differentiate and classify the many tissue types. Based on a limited number of cases of digitized mammograms, our computer algorithms have been able to distinguish tumorous from healthy tissue and to distinguish among various parenchymal tissue patterns. These preliminary results indicate that discrimination based on the fractal nature of images may well represent a viable approach to utilizing computers to assist in diagnosis.

CONSISTENT ADJACENCY-SPECTRAL PARTITIONING FOR THE STOCHASTIC BLOCK MODEL WHEN THE MODEL PARAMETERS ARE UNKNOWN ∗

For random graphs distributed according to a stochastic block model, we consider the inferential task of partioning vertices into blocks using spectral techniques. Spectral partioning using the normalized Laplacian and the adjacency matrix have both been shown to be consistent as the number of vertices tend to infinity. Importantly, both procedures require that the number of blocks and the rank of the communication probability matrix are known, even as the rest of the parameters may be unknown. In this article, we prove that the (suitably modified) adjacency-spectral partitioning procedure, requiring only an upper bound on the rank of the communication probability matrix, is consistent. Indeed, this result demonstrates a robustness to model mis-specification; an overestimate of the rank may impose a moderate performance penalty, but the procedure is still consistent. Furthermore, we extend this procedure to the setting where adjacencies may have multiple modalities and we allow for either directed or undirected graphs.

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.

The complete connectome of a learning and memory centre in an insect brain

Associating stimuli with positive or negative reinforcement is essential for survival, but a complete wiring diagram of a higher-order circuit supporting associative memory has not been previously available. Here we reconstruct one such circuit at synaptic resolution, the Drosophila larval mushroom body. We find that most Kenyon cells integrate random combinations of inputs but that a subset receives stereotyped inputs from single projection neurons. This organization maximizes performance of a model output neuron on a stimulus discrimination task. We also report a novel canonical circuit in each mushroom body compartment with previously unidentified connections: reciprocal Kenyon cell to modulatory neuron connections, modulatory neuron to output neuron connections, and a surprisingly high number of recurrent connections between Kenyon cells. Stereotyped connections found between output neurons could enhance the selection of learned behaviours. The complete circuit map of the mushroom body should guide future functional studies of this learning and memory centre.

Classification Using Class Cover Catch Digraphs

class cover catch digraphs based on proximity between training observations. Performance comparisons are presented on synthetic and real examples versus k-nearest neighbors, Fishers linear discriminant and support vector machines. We demonstrate that the proposed semiparametric classifier has performance approaching that of the optimal parametric classifier in cases for which the optimal is available for comparison.