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Locality-sensitive hashing in function spaces
[article]
2020
arXiv
pre-print
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We discuss the problem of performing similarity search over function spaces. To perform search over such spaces in a reasonable amount of time, we use locality-sensitive hashing (LSH). We present two methods that allow LSH functions on R^N to be extended to L^p spaces: one using function approximation in an orthonormal basis, and another using (quasi-)Monte Carlo-style techniques. We use the presented hashing schemes to construct an LSH family for Wasserstein distance over one-dimensional, continuous probability distributions.
arXiv:2002.03909v1
fatcat:6jave56byzaidasogrlkboz5ja
Randomized Singular Value Projection
2013
Zenodo
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Publication in the conference proceedings of SampTA, Bremen, Germany, 2013
doi:10.5281/zenodo.54423
fatcat:jneyrww2ifaezpan6ckmw4bww4
Resolvability of Hamming Graphs
[article]
2019
arXiv
pre-print
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A subset of vertices in a graph is called resolving when the geodesic distances to those vertices uniquely distinguish every vertex in the graph. Here, we characterize the resolvability of Hamming graphs in terms of a constrained linear system and deduce a novel but straightforward characterization of resolvability for hypercubes. We propose an integer linear programming method to assess resolvability rapidly, and provide a more costly but definite method based on Gr\"obner bases to determine
arXiv:1907.05974v1
fatcat:ryybfnbklnhyhjqpqifap2swem
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... ether or not a set of vertices resolves an arbitrary Hamming graph. As proof of concept, we identify a resolving set of size 77 in the metric space of all octapeptides (i.e., proteins composed of eight amino acids) with respect to the Hamming distance; in particular, any octamer may be readily represented as a 77-dimensional real-vector. Representing k-mers as low-dimensional numerical vectors may enable new applications of machine learning algorithms to symbolic sequences.
Robust Partially-Compressed Least-Squares
[article]
2015
arXiv
pre-print
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Randomized matrix compression techniques, such as the Johnson-Lindenstrauss transform, have emerged as an effective and practical way for solving large-scale problems efficiently. With a focus on computational efficiency, however, forsaking solutions quality and accuracy becomes the trade-off. In this paper, we investigate compressed least-squares problems and propose new models and algorithms that address the issue of error and noise introduced by compression. While maintaining computational
arXiv:1510.04905v1
fatcat:eos2ks6qxvgohjoowr5vri3of4
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... ficiency, our models provide robust solutions that are more accurate--relative to solutions of uncompressed least-squares--than those of classical compressed variants. We introduce tools from robust optimization together with a form of partial compression to improve the error-time trade-offs of compressed least-squares solvers. We develop an efficient solution algorithm for our Robust Partially-Compressed (RPC) model based on a reduction to a one-dimensional search. We also derive the first approximation error bounds for Partially-Compressed least-squares solutions. Empirical results comparing numerous alternatives suggest that robust and partially compressed solutions are effectively insulated against aggressive randomized transforms.
Stochastic Subspace Descent
[article]
2019
arXiv
pre-print
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We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and machine learning problems. The basic algorithm projects the gradient onto a random subspace at each iteration, similar to coordinate descent but without restricting directional derivatives to be along the axes. This algorithm is previously known but
arXiv:1904.01145v2
fatcat:47lconmx3rbspho2uhdqaawc7e
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... provide new analysis. We also extend the popular SVRG method to this framework but without requiring that the objective function be written as a finite sum. We provide proofs of convergence for our methods under various convexity assumptions and show favorable results when compared to gradient descent and BFGS on non-convex problems from the machine learning and shape optimization literature. We also note that our analysis gives a proof that the iterates of SVRG and several other popular first-order stochastic methods, in their original formulation, converge almost surely to the optimum; to our knowledge, prior to this work the iterates of SVRG had only been known to converge in expectation.
URV Factorization with Random Orthogonal System Mixing
[article]
2017
arXiv
pre-print
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The unpivoted and pivoted Householder QR factorizations are ubiquitous in numerical linear algebra. A difficulty with pivoted Householder QR is the communication bottleneck introduced by pivoting. In this paper we propose using random orthogonal systems to quickly mix together the columns of a matrix before computing an unpivoted QR factorization. This method computes a URV factorization which forgoes expensive pivoted QR steps in exchange for mixing in advance, followed by a cheaper, unpivoted
arXiv:1703.02499v1
fatcat:xvnfdmphtvhw7eiuu3htim4xve
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... QR factorization. The mixing step typically reduces the variability of the column norms, and in certain experiments, allows us to compute an accurate factorization where a plain, unpivoted QR performs poorly. We experiment with linear least-squares, rank-revealing factorizations, and the QLP approximation, and conclude that our randomized URV factorization behaves comparably to a similar randomized rank-revealing URV factorization, but at a fraction of the computational cost. Our experiments provide evidence that our proposed factorization might be rank-revealing with high probability.
Five-dimensional supergravity in N = 1/2 superspace
2020
Journal of High Energy Physics
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We construct 5D, N = 1 supergravity in a 4D, N = 1 superspace with an extra bosonic coordinate. This represents four of the supersymmetries and the associated Poincaré symmetries manifestly. The remaining four supersymmetries and the rest of the Poincaré symmetries are represented linearly but not manifestly. In the linearized approximation, the action reduces to the known superspace result. As an application of the formalism, we discuss the construction of the 5D gravitational Chern-Simons invariant A ∧ R ∧ R in this superspace.
doi:10.1007/jhep03(2020)098
fatcat:l6fzz6nvs5at7aywmdclwirrva
Randomized Clustered Nystrom for Large-Scale Kernel Machines
[article]
2016
arXiv
pre-print
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., 2012; Golts and Elad, 2016; Pourkamali-Anaraki and Becker, 2016) . ...
The n rows of L represent the virtual samples or mapped data points (Zhang et al., 2012; Golts and Elad, 2016; Pourkamali-Anaraki and Becker, 2016) . ...
arXiv:1612.06470v1
fatcat:7qanrgmcijdaxas6bmizyhecia
One-Pass Sparsified Gaussian Mixtures
[article]
2019
arXiv
pre-print
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We present a one-pass sparsified Gaussian mixture model (SGMM). Given N data points in P dimensions, X, the model fits K Gaussian distributions to X and (softly) classifies each point to these clusters. After paying an up-front cost of O(NPlog P) to precondition the data, we subsample Q entries of each data point and discard the full P-dimensional data. SGMM operates in O(KNQ) time per iteration for diagonal or spherical covariances, independent of P, while estimating the model parameters in
arXiv:1903.04056v2
fatcat:acciwyqqevh27mgphy52shu64i
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... full P-dimensional space, making it one-pass and hence suitable for streaming data. We derive the maximum likelihood estimators for the parameters in the sparsified regime, demonstrate clustering on synthetic and real data, and show that SGMM is faster than GMM while preserving accuracy.
Theory of versatile fidelity estimation with confidence
[article]
2021
arXiv
pre-print
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Estimating the fidelity with a target state is important in quantum information tasks. Many fidelity estimation techniques present a suitable measurement scheme to perform the estimation. In contrast, we present techniques that allow the experimentalist to choose a convenient measurement setting. Our primary focus lies on a method that constructs an estimator with nearly minimax optimal confidence interval for any specified measurement setting. We demonstrate, through a combination of
arXiv:2112.07947v1
fatcat:nyrcotknyjaa3a573alc63xdmu
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... l and numerical results, various desirable properties for the method: robustness against experimental imperfections, competitive sample complexity, and accurate estimates in practice. We compare this method with Maximum Likelihood Estimation and the associated Profile Likelihood method, a Semi-Definite Programming based approach, as well as a popular direct fidelity estimation technique.
Five-dimensional Supergravity in N = 1/2 Superspace
[article]
2020
arXiv
pre-print
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We construct 5D, N = 1 supergravity in a 4D, N = 1 superspace with an extra bosonic coordinate. This represents four of the supersymmetries and the associated Poincaré symmetries manifestly. The remaining four supersymmetries and the rest of the Poincaré symmetries are represented linearly but not manifestly. In the linearized approximation, the action reduces to the known superspace result. As an application of the formalism, we construct the ∫ A∧ R∧ R invariant in this superspace.
arXiv:1909.09208v2
fatcat:kdurtu4ezzerjlyqqog5amumem
Theoretical Stellar Evolution
[chapter]
2002
Allen's Astrophysical Quantities
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BINARY STAR EVOLUTION by Stephen A. Becker The previous sections of this chapter have dealt with the evolutionary behavior of single stars. ...
Cox and Stephen A. ...
doi:10.1007/978-1-4612-1186-0_20
fatcat:j5efwzx3zrapdopigxsi2hu2d4
Penalized basis models for very large spatial datasets
[article]
2019
arXiv
pre-print
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Many modern spatial models express the stochastic variation component as a basis expansion with random coefficients. Low rank models, approximate spectral decompositions, multiresolution representations, stochastic partial differential equations and empirical orthogonal functions all fall within this basic framework. Given a particular basis, stochastic dependence relies on flexible modeling of the coefficients. Under a Gaussianity assumption, we propose a graphical model family for the
arXiv:1902.06877v1
fatcat:bz6vvw7perdq7bptuu7lsgl2ey
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... ic coefficients by parameterizing the precision matrix. Sparsity in the precision matrix is encouraged using a penalized likelihood framework. Computations follow from a majorization-minimization approach, a byproduct of which is a connection to the graphical lasso. The result is a flexible nonstationary spatial model that is adaptable to very large datasets. We apply the model to two large and heterogeneous spatial datasets in statistical climatology and recover physically sensible graphical structures. Moreover, the model performs competitively against the popular LatticeKrig model in predictive cross-validation, but substantially improves the Akaike information criterion score.
Liver Toxicity in Epidemiological Cohorts
2004
Clinical Infectious Diseases
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Hepatotoxicity has been demonstrated to be associated with antiretroviral therapy. Previous studies have included small numbers of patients and, thus, were unable to produce adequate statistical comparisons. I review data analyses from the Amsterdam, CHORUS, ICONA and Target studies (5133 patients), which were conducted by a number of investigators. There were differences between the cohorts with respect to the incidence of viral hepatitis and definitions of hepatotoxicity used. However, in all
doi:10.1086/381447
pmid:14986275
fatcat:mmyvreal55fhrhtay67pwp6yoq
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... cohorts, hepatotoxicity in human immunodeficiency virus type 1-infected patients was significantly associated with coinfection with viral hepatitis. In 3 cohorts, elevated baseline alanine aminotransferase levels predicted subsequent hepatotoxicity. Overall, there was a low incidence of long-term hepatotoxicity in these cohorts and no consistent association between a particular drug or drug class. Nevirapine use within the first 12 weeks after initiation of therapy with this drug and ritonavir use are associated with increased risk of antiretroviral-associated hepatotoxicity.
A variational approach to stable principal component pursuit
[article]
2014
arXiv
pre-print
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All three programs also use versions of PROPACK from Becker & Candès (2008) ; Larsen (1998) to compute partial SVDs. ...
arXiv:1406.1089v1
fatcat:cnp6vbu5zbfhfafvwyigz3sp34
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