
A Note on Posterior Probability Estimation for Classifiers
One of the central themes in the classification task is the estimation o...
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Conditional probability in Renyi spaces
In 1933 Kolmogorov constructed a general theory that defines the modern ...
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Markov Random Geometric Graph (MRGG): A Growth Model for Temporal Dynamic Networks
We introduce Markov Random Geometric Graphs (MRGGs), a growth model for ...
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Spectral clustering in the dynamic stochastic block model
In the present paper, we studied a Dynamic Stochastic Block Model (DSBM)...
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Deep LearningBased Image Kernel for Inductive Transfer
We propose a method to classify images from target classes with a small ...
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Stability and tail limits of transportbased quantile contours
We extend Robert McCann's treatment of the existence and uniqueness of a...
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Probabilistic Learning on Manifolds
This paper presents mathematical results in support of the methodology o...
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Cautious Active Clustering
We consider a set of points sampled from an unknown probability measure on a Euclidean space, each of which points belongs to one of the finitely many classes. We study the question of querying the class label at a very small number of judiciously chosen points so as to be able to attach the appropriate class label to every point in the set. Our approach is to consider the unknown probability measure as a convex combination of the conditional probabilities for each class. Our technique involves the use of a highly localized kernel constructed from Hermite polynomials, and use them to create a hierarchical estimate of the supports of the constituent probability measures. We do not need to make any assumptions on the nature of any of the probability measures nor know in advance the number of classes involved. We give theoretical guarantees measured by the Fscore for our classification scheme. Examples include classification in hyperspectral images, separation of distributions, and MNIST classification.
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