This article simulates on a computer what could have happened with measurements that we might have taken but actually did not, given what happened with the measurements that we did in fact make.
This article extends an earlier paper, "Cumulative deviation of a subpopulation from the full population," to assessing directly deviation between two subpopulations whose scores are all distinct. The previous paper is preferable when apposite.
Graphs of cumulative differences and associated variants of the Kolmogorov-Smirnov and Kuiper statistics help gauge calibration or subpopulation deviation without making any particular tradeoff between resolution and statistical confidence (unlike the traditional reliability diagrams and calibration plots).
This article introduces secure multiparty computations for privacy-preserving machine-learning using solely standard floating-point arithmetic, with carefully controlled leakage of information less than the loss of accuracy due to roundoff, all backed by rigorous mathematical proofs of worst-case bounds on information loss and numerical stability in finite-precision arithmetic.
This article is strange, yet representative of the curious, idiosyncratic tasks that pay the bills in industry, which often require knowledgeable, special-purpose solutions.
This article defines an easy-to-use metric of success or figure of merit for classification in which the classes come endowed with a hierarchical taxonomy.
This article constructs matrix decompositions which leverage simultaneously a single data set's intrinsic low-rank structure as well as low-rank structure in the data's interaction with another data set.
This article describes an implementation for Spark of principal component analysis, singular value decomposition, and low-rank approximation.
This article points out that a few iterations of alternating least squares provably suffice to produce nearly optimal spectral- and Frobenius-norm accuracies of low-rank approximations.
This article develops a classification stage specifically for use with supervised learning in scale-equivariant convolutional networks.
This article embeds multiwavelet absolute values in parametric families of complex-valued convnets.
This article points out that the Euclidean distance is underutilized in modern statistics.
This article works out some asymptotic distributions associated with the article, "Some deficiencies of χ2 and classical exact tests of significance," available above.
This article can help accelerate interior-point methods for convex optimization, such as linear programming.
This article modifies and supplements tests of the Kolmogorov-Smirnov type (including Kuiper's).
This article simplifies the precomputations required for computing fast spherical harmonic transforms, complementing the approach taken in the article, "Fast algorithms for spherical harmonic expansions, II," available below.
This article is now out-of-date; instead, please see Nathan Halko's, Per-Gunnar Martinsson's, and Joel Tropp's SIAM Review paper.
This article provides a generally preferable alternative to the classical pivoted "QR" decomposition algorithms (such as Gram-Schmidt or Householder) for the low-rank approximation of arbitrary matrices. Constructing a low-rank approximation is the core step in computing several of the greatest singular values and corresponding singular vectors of a matrix.
This article provides an algorithm for linear least-squares regression. When the regression is highly overdetermined, the algorithm is more efficient than the classical methods based on "QR" decompositions.
This article provides efficient algorithms for computing spherical harmonic transforms, largely superseding our first article on the subject, "Fast algorithms for spherical harmonic expansions."
This article surveys algorithms for the compression of matrices.
This article provides details regarding the survey, "Randomized algorithms for the low-rank approximation of matrices," available above. "A randomized algorithm for the decomposition of matrices" is almost identical to our (better-known) technical report, "A randomized algorithm for the approximation of matrices," from 2006.
This article reviews the fact that numerically stable formulae exist for interpolating any linear combination of n bounded functions using the values of the linear combination at a certain collection of n points in the domain of the functions. The article also provides references to algorithms which determine these stable formulae at reasonably small computational expense.
This article is now largely (but not entirely) superseded by the paper, "Fast algorithms for spherical harmonic expansions, II," available above.