Saurabh Paul

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Let X be a data matrix of rank ρ, representing n points in d-dimensional space. The linear support vector machine constructs a hyperplane separator that maximizes the 1norm soft margin. We develop a new oblivious dimension reduction technique which is precomputed and can be applied to any input matrix X. We prove that, with high probability, the margin and(More)
Let <b>X</b> be a data matrix of rank &rho;, whose rows represent <i>n</i> points in <i>d</i>-dimensional space. The linear support vector machine constructs a hyperplane separator that maximizes the 1-norm soft margin. We develop a new oblivious dimension reduction technique that is precomputed and can be applied to any input matrix <b>X</b>. We prove(More)
We give two provably accurate featureselection techniques for the linear SVM. The algorithms run in deterministic and randomized time respectively. Our algorithms can be used in an unsupervised or supervised setting. The supervised approach is based on sampling features from support vectors. We prove that the margin in the feature space is preserved to(More)
We introduce a deterministic sampling based feature selection technique for regularized least squares classification. The method is unsupervised and gives worst-case guarantees of the generalization power of the classification function after feature selection with respect to the classification function obtained using all features. We perform experiments on(More)
Canonical Correlation Analysis (CCA) is a technique that finds how "similar" are the subspaces that are spanned by the columns of two different matrices <b>A</b> &#941;&#8476;(of size <sup><i>m-x-n</i></sup>) and <b>B</b> &#941;&#8476;(of size <sup><i>m-x-l</i></sup>). CCA measures similarity by means of the cosines of the so-called principal angles between(More)
We introduce single-set spectral sparsification as a deterministic sampling-based feature selection technique for regularized least-squares classification, which is the classification analog to ridge regression. The method is unsupervised and gives worst-case guarantees of the generalization power of the classification function after feature selection with(More)
Title of dissertation: MULTI-BAND BOSE-HUBBARD MODELS AND EFFECTIVE THREE-BODY INTERACTIONS Saurabh Paul, Doctor of Philosophy, 2016 Dissertation directed by: Professor Eite Tiesinga Joint Quantum Institute Department of Physics University of Maryland, College Park Experiments with ultracold atoms in optical lattice have become a versatile testing ground to(More)
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