31,247 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
Positive Definite Kernels in Machine Learning
This survey is an introduction to positive definite kernels and the set of
methods they have inspired in the machine learning literature, namely kernel
methods. We first discuss some properties of positive definite kernels as well
as reproducing kernel Hibert spaces, the natural extension of the set of
functions associated with a kernel defined
on a space . We discuss at length the construction of kernel
functions that take advantage of well-known statistical models. We provide an
overview of numerous data-analysis methods which take advantage of reproducing
kernel Hilbert spaces and discuss the idea of combining several kernels to
improve the performance on certain tasks. We also provide a short cookbook of
different kernels which are particularly useful for certain data-types such as
images, graphs or speech segments.Comment: draft. corrected a typo in figure
Support vector machine for functional data classification
In many applications, input data are sampled functions taking their values in
infinite dimensional spaces rather than standard vectors. This fact has complex
consequences on data analysis algorithms that motivate modifications of them.
In fact most of the traditional data analysis tools for regression,
classification and clustering have been adapted to functional inputs under the
general name of functional Data Analysis (FDA). In this paper, we investigate
the use of Support Vector Machines (SVMs) for functional data analysis and we
focus on the problem of curves discrimination. SVMs are large margin classifier
tools based on implicit non linear mappings of the considered data into high
dimensional spaces thanks to kernels. We show how to define simple kernels that
take into account the unctional nature of the data and lead to consistent
classification. Experiments conducted on real world data emphasize the benefit
of taking into account some functional aspects of the problems.Comment: 13 page
On a generalization of iterated and randomized rounding
We give a general method for rounding linear programs that combines the
commonly used iterated rounding and randomized rounding techniques. In
particular, we show that whenever iterated rounding can be applied to a problem
with some slack, there is a randomized procedure that returns an integral
solution that satisfies the guarantees of iterated rounding and also has
concentration properties. We use this to give new results for several classic
problems where iterated rounding has been useful
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