1,786 research outputs found
Minimum Density Hyperplanes
Associating distinct groups of objects (clusters) with contiguous regions of
high probability density (high-density clusters), is central to many
statistical and machine learning approaches to the classification of unlabelled
data. We propose a novel hyperplane classifier for clustering and
semi-supervised classification which is motivated by this objective. The
proposed minimum density hyperplane minimises the integral of the empirical
probability density function along it, thereby avoiding intersection with high
density clusters. We show that the minimum density and the maximum margin
hyperplanes are asymptotically equivalent, thus linking this approach to
maximum margin clustering and semi-supervised support vector classifiers. We
propose a projection pursuit formulation of the associated optimisation problem
which allows us to find minimum density hyperplanes efficiently in practice,
and evaluate its performance on a range of benchmark datasets. The proposed
approach is found to be very competitive with state of the art methods for
clustering and semi-supervised classification
Flexible covariance estimation in graphical Gaussian models
In this paper, we propose a class of Bayes estimators for the covariance
matrix of graphical Gaussian models Markov with respect to a decomposable graph
. Working with the family defined by Letac and Massam [Ann.
Statist. 35 (2007) 1278--1323] we derive closed-form expressions for Bayes
estimators under the entropy and squared-error losses. The family
includes the classical inverse of the hyper inverse Wishart but has many more
shape parameters, thus allowing for flexibility in differentially shrinking
various parts of the covariance matrix. Moreover, using this family avoids
recourse to MCMC, often infeasible in high-dimensional problems. We illustrate
the performance of our estimators through a collection of numerical examples
where we explore frequentist risk properties and the efficacy of graphs in the
estimation of high-dimensional covariance structures.Comment: Published in at http://dx.doi.org/10.1214/08-AOS619 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
The Power of Localization for Efficiently Learning Linear Separators with Noise
We introduce a new approach for designing computationally efficient learning
algorithms that are tolerant to noise, and demonstrate its effectiveness by
designing algorithms with improved noise tolerance guarantees for learning
linear separators.
We consider both the malicious noise model and the adversarial label noise
model. For malicious noise, where the adversary can corrupt both the label and
the features, we provide a polynomial-time algorithm for learning linear
separators in under isotropic log-concave distributions that can
tolerate a nearly information-theoretically optimal noise rate of . For the adversarial label noise model, where the
distribution over the feature vectors is unchanged, and the overall probability
of a noisy label is constrained to be at most , we also give a
polynomial-time algorithm for learning linear separators in under
isotropic log-concave distributions that can handle a noise rate of .
We show that, in the active learning model, our algorithms achieve a label
complexity whose dependence on the error parameter is
polylogarithmic. This provides the first polynomial-time active learning
algorithm for learning linear separators in the presence of malicious noise or
adversarial label noise.Comment: Contains improved label complexity analysis communicated to us by
Steve Hannek
TUNING A THREE-PHASE SEPARATOR LEVEL CONTROLLER VIA PARTICLE SWARM OPTIMIZATION (PSO) ALGORITHM
Three-Phase Separators are used to separate well crudes into three portions; water, oil, and gas. A suitable control system should be in place to ensure the optimum function of the Three-Phase Separator. The current PID tuning technique does not provide an optimum system response of the separator. Overshoot response, offset, steady-state error and system instability are some of the problems faced. Besides, the current method used is purely based on trial and error which is time consuming. There is room for improvement of the current PID tuning technique. An artificial intelligence (AI) PID tuning technique called Particle Swarm Optimization (PSO) is introduced to improve the system response of the Three-Phase Separator. The PSO algorithm mimics the behaviour of bird flocking and fish schooling striving for its global best position. In our case, the global best position is replaced with the optimized PID tuning parameters for the separator. The PSO algorithm has been used in several other applications such as the Brushless DC motor and in the Control Ball & Beam system. It has proven to be an effective tuning technique. Tuning of the Three-Phase Separator via PSO could prove to be an effective solution for Oil & Gas industries
Thermodynamics of Ion Separation by Electrosorption
We present a simple, top-down approach for the calculation of minimum energy
consumption of electrosorptive ion separation using variational form of the
(Gibbs) free energy. We focus and expand on the case of electrostatic
capacitive deionization (CDI), and the theoretical framework is independent of
details of the double-layer charge distribution and is applicable to any
thermodynamically consistent model, such as the Gouy-Chapman-Stern (GCS) and
modified Donnan (mD) models. We demonstrate that, under certain assumptions,
the minimum required electric work energy is indeed equivalent to the free
energy of separation. Using the theory, we define the thermodynamic efficiency
of CDI. We explore the thermodynamic efficiency of current experimental CDI
systems and show that these are currently very low, less than 1% for most
existing systems. We applied this knowledge and constructed and operated a CDI
cell to show that judicious selection of the materials, geometry, and process
parameters can be used to achieve a 9% thermodynamic efficiency (4.6 kT energy
per removed ion). This relatively high value is, to our knowledge, by far the
highest thermodynamic efficiency ever demonstrated for CDI. We hypothesize that
efficiency can be further improved by further reduction of CDI cell series
resistances and optimization of operational parameters
Parallel Graph Decompositions Using Random Shifts
We show an improved parallel algorithm for decomposing an undirected
unweighted graph into small diameter pieces with a small fraction of the edges
in between. These decompositions form critical subroutines in a number of graph
algorithms. Our algorithm builds upon the shifted shortest path approach
introduced in [Blelloch, Gupta, Koutis, Miller, Peng, Tangwongsan, SPAA 2011].
By combining various stages of the previous algorithm, we obtain a
significantly simpler algorithm with the same asymptotic guarantees as the best
sequential algorithm
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