29,382 research outputs found
Improving and extending the testing of distributions for shape-restricted properties
Distribution testing deals with what information can be deduced about an unknown distribution over ,
where the algorithm is only allowed to obtain a relatively small number of independent samples from the distribution. In the extended conditional sampling model, the algorithm is also allowed to obtain samples from the restriction of the original distribution on subsets of .
In 2015, Canonne, Diakonikolas, Gouleakis and Rubinfeld unified several previous results, and showed that for any property of distributions satisfying a ``decomposability'' criterion, there exists an algorithm (in the basic model) that can distinguish with high probability distributions satisfying the property from distributions that are far from it in the variation distance.
We present here a more efficient yet simpler algorithm for the basic model, as well as very efficient algorithms for the conditional model, which until now was not investigated under the umbrella of decomposable properties. Additionally, we provide an algorithm for the conditional model that handles a much larger class of properties.
Our core mechanism is an algorithm for efficiently producing an interval-partition of that satisfies a ``fine-grain'' quality. We show that with such a partition at hand we can avoid the search for the ``correct'' partition of
Asymptotics of the discrete log-concave maximum likelihood estimator and related applications
The assumption of log-concavity is a flexible and appealing nonparametric
shape constraint in distribution modelling. In this work, we study the
log-concave maximum likelihood estimator (MLE) of a probability mass function
(pmf). We show that the MLE is strongly consistent and derive its pointwise
asymptotic theory under both the well- and misspecified setting. Our asymptotic
results are used to calculate confidence intervals for the true log-concave
pmf. Both the MLE and the associated confidence intervals may be easily
computed using the R package logcondiscr. We illustrate our theoretical results
using recent data from the H1N1 pandemic in Ontario, Canada.Comment: 21 pages, 7 Figure
Computational polarimetric microwave imaging
We propose a polarimetric microwave imaging technique that exploits recent
advances in computational imaging. We utilize a frequency-diverse cavity-backed
metasurface, allowing us to demonstrate high-resolution polarimetric imaging
using a single transceiver and frequency sweep over the operational microwave
bandwidth. The frequency-diverse metasurface imager greatly simplifies the
system architecture compared with active arrays and other conventional
microwave imaging approaches. We further develop the theoretical framework for
computational polarimetric imaging and validate the approach experimentally
using a multi-modal leaky cavity. The scalar approximation for the interaction
between the radiated waves and the target---often applied in microwave
computational imaging schemes---is thus extended to retrieve the susceptibility
tensors, and hence providing additional information about the targets.
Computational polarimetry has relevance for existing systems in the field that
extract polarimetric imagery, and particular for ground observation. A growing
number of short-range microwave imaging applications can also notably benefit
from computational polarimetry, particularly for imaging objects that are
difficult to reconstruct when assuming scalar estimations.Comment: 17 pages, 15 figure
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