47,388 research outputs found
Using TPA to count linear extensions
A linear extension of a poset is a permutation of the elements of the set
that respects the partial order. Let denote the number of linear
extensions. It is a #P complete problem to determine exactly for an
arbitrary poset, and so randomized approximation algorithms that draw randomly
from the set of linear extensions are used. In this work, the set of linear
extensions is embedded in a larger state space with a continuous parameter ?.
The introduction of a continuous parameter allows for the use of a more
efficient method for approximating called TPA. Our primary result is
that it is possible to sample from this continuous embedding in time that as
fast or faster than the best known methods for sampling uniformly from linear
extensions. For a poset containing elements, this means we can approximate
to within a factor of with probability at least using an expected number of random bits and comparisons in the poset
which is at most Comment: 12 pages, 4 algorithm
Optimizing Ranking Models in an Online Setting
Online Learning to Rank (OLTR) methods optimize ranking models by directly
interacting with users, which allows them to be very efficient and responsive.
All OLTR methods introduced during the past decade have extended on the
original OLTR method: Dueling Bandit Gradient Descent (DBGD). Recently, a
fundamentally different approach was introduced with the Pairwise
Differentiable Gradient Descent (PDGD) algorithm. To date the only comparisons
of the two approaches are limited to simulations with cascading click models
and low levels of noise. The main outcome so far is that PDGD converges at
higher levels of performance and learns considerably faster than DBGD-based
methods. However, the PDGD algorithm assumes cascading user behavior,
potentially giving it an unfair advantage. Furthermore, the robustness of both
methods to high levels of noise has not been investigated. Therefore, it is
unclear whether the reported advantages of PDGD over DBGD generalize to
different experimental conditions. In this paper, we investigate whether the
previous conclusions about the PDGD and DBGD comparison generalize from ideal
to worst-case circumstances. We do so in two ways. First, we compare the
theoretical properties of PDGD and DBGD, by taking a critical look at
previously proven properties in the context of ranking. Second, we estimate an
upper and lower bound on the performance of methods by simulating both ideal
user behavior and extremely difficult behavior, i.e., almost-random
non-cascading user models. Our findings show that the theoretical bounds of
DBGD do not apply to any common ranking model and, furthermore, that the
performance of DBGD is substantially worse than PDGD in both ideal and
worst-case circumstances. These results reproduce previously published findings
about the relative performance of PDGD vs. DBGD and generalize them to
extremely noisy and non-cascading circumstances.Comment: European Conference on Information Retrieval (ECIR) 201
Classical sampling theorems in the context of multirate and polyphase digital filter bank structures
The recovery of a signal from so-called generalized samples is a problem of designing appropriate linear filters called reconstruction (or synthesis) filters. This relationship is reviewed and explored. Novel theorems for the subsampling of sequences are derived by direct use of the digital-filter-bank framework. These results are related to the theory of perfect reconstruction in maximally decimated digital-filter-bank systems. One of the theorems pertains to the subsampling of a sequence and its first few differences and its subsequent stable reconstruction at finite cost with no error. The reconstruction filters turn out to be multiplierless and of the FIR (finite impulse response) type. These ideas are extended to the case of two-dimensional signals by use of a Kronecker formalism. The subsampling of bandlimited sequences is also considered. A sequence x(n ) with a Fourier transform vanishes for |ω|⩾Lπ/M, where L and M are integers with L<M, can in principle be represented by reducing the data rate by the amount M/L. The digital polyphase framework is used as a convenient tool for the derivation as well as mechanization of the sampling theorem
Recursive Compressed Sensing
We introduce a recursive algorithm for performing compressed sensing on
streaming data. The approach consists of a) recursive encoding, where we sample
the input stream via overlapping windowing and make use of the previous
measurement in obtaining the next one, and b) recursive decoding, where the
signal estimate from the previous window is utilized in order to achieve faster
convergence in an iterative optimization scheme applied to decode the new one.
To remove estimation bias, a two-step estimation procedure is proposed
comprising support set detection and signal amplitude estimation. Estimation
accuracy is enhanced by a non-linear voting method and averaging estimates over
multiple windows. We analyze the computational complexity and estimation error,
and show that the normalized error variance asymptotically goes to zero for
sublinear sparsity. Our simulation results show speed up of an order of
magnitude over traditional CS, while obtaining significantly lower
reconstruction error under mild conditions on the signal magnitudes and the
noise level.Comment: Submitted to IEEE Transactions on Information Theor
Image formation in synthetic aperture radio telescopes
Next generation radio telescopes will be much larger, more sensitive, have
much larger observation bandwidth and will be capable of pointing multiple
beams simultaneously. Obtaining the sensitivity, resolution and dynamic range
supported by the receivers requires the development of new signal processing
techniques for array and atmospheric calibration as well as new imaging
techniques that are both more accurate and computationally efficient since data
volumes will be much larger. This paper provides a tutorial overview of
existing image formation techniques and outlines some of the future directions
needed for information extraction from future radio telescopes. We describe the
imaging process from measurement equation until deconvolution, both as a
Fourier inversion problem and as an array processing estimation problem. The
latter formulation enables the development of more advanced techniques based on
state of the art array processing. We demonstrate the techniques on simulated
and measured radio telescope data.Comment: 12 page
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