20,167 research outputs found
Extreme Entropy Machines: Robust information theoretic classification
Most of the existing classification methods are aimed at minimization of
empirical risk (through some simple point-based error measured with loss
function) with added regularization. We propose to approach this problem in a
more information theoretic way by investigating applicability of entropy
measures as a classification model objective function. We focus on quadratic
Renyi's entropy and connected Cauchy-Schwarz Divergence which leads to the
construction of Extreme Entropy Machines (EEM).
The main contribution of this paper is proposing a model based on the
information theoretic concepts which on the one hand shows new, entropic
perspective on known linear classifiers and on the other leads to a
construction of very robust method competetitive with the state of the art
non-information theoretic ones (including Support Vector Machines and Extreme
Learning Machines).
Evaluation on numerous problems spanning from small, simple ones from UCI
repository to the large (hundreads of thousands of samples) extremely
unbalanced (up to 100:1 classes' ratios) datasets shows wide applicability of
the EEM in real life problems and that it scales well
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
Kernel methods in machine learning
We review machine learning methods employing positive definite kernels. These
methods formulate learning and estimation problems in a reproducing kernel
Hilbert space (RKHS) of functions defined on the data domain, expanded in terms
of a kernel. Working in linear spaces of function has the benefit of
facilitating the construction and analysis of learning algorithms while at the
same time allowing large classes of functions. The latter include nonlinear
functions as well as functions defined on nonvectorial data. We cover a wide
range of methods, ranging from binary classifiers to sophisticated methods for
estimation with structured data.Comment: Published in at http://dx.doi.org/10.1214/009053607000000677 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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