2,220 research outputs found
JSKETCH: Sketching for Java
Sketch-based synthesis, epitomized by the SKETCH tool, lets developers
synthesize software starting from a partial program, also called a sketch or
template. This paper presents JSKETCH, a tool that brings sketch-based
synthesis to Java. JSKETCH's input is a partial Java program that may include
holes, which are unknown constants, expression generators, which range over
sets of expressions, and class generators, which are partial classes. JSKETCH
then translates the synthesis problem into a SKETCH problem; this translation
is complex because SKETCH is not object-oriented. Finally, JSKETCH synthesizes
an executable Java program by interpreting the output of SKETCH.Comment: This research was supported in part by NSF CCF-1139021, CCF- 1139056,
CCF-1161775, and the partnership between UMIACS and the Laboratory for
Telecommunication Science
Randomized Sketches of Convex Programs with Sharp Guarantees
Random projection (RP) is a classical technique for reducing storage and
computational costs. We analyze RP-based approximations of convex programs, in
which the original optimization problem is approximated by the solution of a
lower-dimensional problem. Such dimensionality reduction is essential in
computation-limited settings, since the complexity of general convex
programming can be quite high (e.g., cubic for quadratic programs, and
substantially higher for semidefinite programs). In addition to computational
savings, random projection is also useful for reducing memory usage, and has
useful properties for privacy-sensitive optimization. We prove that the
approximation ratio of this procedure can be bounded in terms of the geometry
of constraint set. For a broad class of random projections, including those
based on various sub-Gaussian distributions as well as randomized Hadamard and
Fourier transforms, the data matrix defining the cost function can be projected
down to the statistical dimension of the tangent cone of the constraints at the
original solution, which is often substantially smaller than the original
dimension. We illustrate consequences of our theory for various cases,
including unconstrained and -constrained least squares, support vector
machines, low-rank matrix estimation, and discuss implications on
privacy-sensitive optimization and some connections with de-noising and
compressed sensing
Max-sum diversity via convex programming
Diversity maximization is an important concept in information retrieval,
computational geometry and operations research. Usually, it is a variant of the
following problem: Given a ground set, constraints, and a function
that measures diversity of a subset, the task is to select a feasible subset
such that is maximized. The \emph{sum-dispersion} function , which is the sum of the pairwise distances in , is
in this context a prominent diversification measure. The corresponding
diversity maximization is the \emph{max-sum} or \emph{sum-sum diversification}.
Many recent results deal with the design of constant-factor approximation
algorithms of diversification problems involving sum-dispersion function under
a matroid constraint. In this paper, we present a PTAS for the max-sum
diversification problem under a matroid constraint for distances
of \emph{negative type}. Distances of negative type are, for
example, metric distances stemming from the and norm, as well
as the cosine or spherical, or Jaccard distance which are popular similarity
metrics in web and image search
Isometric sketching of any set via the Restricted Isometry Property
In this paper we show that for the purposes of dimensionality reduction
certain class of structured random matrices behave similarly to random Gaussian
matrices. This class includes several matrices for which matrix-vector multiply
can be computed in log-linear time, providing efficient dimensionality
reduction of general sets. In particular, we show that using such matrices any
set from high dimensions can be embedded into lower dimensions with near
optimal distortion. We obtain our results by connecting dimensionality
reduction of any set to dimensionality reduction of sparse vectors via a
chaining argument.Comment: 17 page
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