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This paper deals with detecting change of distribution in multi-dimensional data sets. For a given baseline data set and a set of newly observed data points, we define a statistical test called the <i>density test</i> for deciding if the observed data points are sampled from the underlying distribution that produced the baseline data set. We define a test(More)
Given a spatial data set placed on an <i>n</i> x <i>n</i> grid, our goal is to find the rectangular regions within which subsets of the data set exhibit anomalous behavior. We develop algorithms that, given any user-supplied arbitrary likelihood function, conduct a likelihood ratio hypothesis test (LRT) over each rectangular region in the grid, rank all of(More)
— When anomaly detection software is used as a data analysis tool, finding the hardest-to-detect anomalies is not the most critical task. Rather, it is often more important to make sure that those anomalies that are reported to the user are in fact interesting. If too many unremarkable data points are returned to the user labeled as candidate anomalies, the(More)
Given a spatial dataset placed on an <i>n</i> &#215;<i>n</i> grid, our goal is to find the rectangular regions within which subsets of the dataset exhibit anomalous behavior. We develop algorithms that, given any user-supplied arbitrary likelihood function, conduct a likelihood ratio hypothesis test (LRT) over each rectangular region in the grid, rank all(More)
Classic mixture models assume that the prevalence of the various mixture components is fixed and does not vary over time. This presents problems for applications where the goal is to learn how complex data distributions evolve. We develop models and Bayesian learning algorithms for inferring the temporal trends of the components in a mixture model as a(More)
2008 1 c 2008 Laukik Vilas Chitnis 2 To my parents and teachers 3 ACKNOWLEDGMENTS First of all, let me express my sincere gratitude toward my advisers, Dr. Sanjay Ranka and Dr. Alin Dobra, for guiding me in this endeavor called doctoral research. I thank them for always nudging me in the right direction; beginning with helping me define my area of research.(More)
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