169 research outputs found
Online Community Detection by Spectral CUSUM
We present an online community change detection algorithm called spectral
CUSUM to detect the emergence of a community using a subspace projection
procedure based on a Gaussian model setting. Theoretical analysis is provided
to characterize the average run length (ARL) and expected detection delay
(EDD), as well as the asymptotic optimality. Simulation and real data examples
demonstrate the good performance of the proposed method
: Robust Principal Component Analysis for Exponential Family Distributions
Robust Principal Component Analysis (RPCA) is a widely used method for
recovering low-rank structure from data matrices corrupted by significant and
sparse outliers. These corruptions may arise from occlusions, malicious
tampering, or other causes for anomalies, and the joint identification of such
corruptions with low-rank background is critical for process monitoring and
diagnosis. However, existing RPCA methods and their extensions largely do not
account for the underlying probabilistic distribution for the data matrices,
which in many applications are known and can be highly non-Gaussian. We thus
propose a new method called Robust Principal Component Analysis for Exponential
Family distributions (), which can perform the desired
decomposition into low-rank and sparse matrices when such a distribution falls
within the exponential family. We present a novel alternating direction method
of multiplier optimization algorithm for efficient
decomposition. The effectiveness of is then demonstrated in
two applications: the first for steel sheet defect detection, and the second
for crime activity monitoring in the Atlanta metropolitan area
Convex Parameter Recovery for Interacting Marked Processes
We introduce a new general modeling approach for multivariate discrete event
data with categorical interacting marks, which we refer to as marked Bernoulli
processes. In the proposed model, the probability of an event of a specific
category to occur in a location may be influenced by past events at this and
other locations. We do not restrict interactions to be positive or decaying
over time as it is commonly adopted, allowing us to capture an arbitrary shape
of influence from historical events, locations, and events of different
categories. In our modeling, prior knowledge is incorporated by allowing
general convex constraints on model parameters. We develop two parameter
estimation procedures utilizing the constrained Least Squares (LS) and Maximum
Likelihood (ML) estimation, which are solved using variational inequalities
with monotone operators. We discuss different applications of our approach and
illustrate the performance of proposed recovery routines on synthetic examples
and a real-world police dataset
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