61,424 research outputs found
A Taxonomy of Big Data for Optimal Predictive Machine Learning and Data Mining
Big data comes in various ways, types, shapes, forms and sizes. Indeed,
almost all areas of science, technology, medicine, public health, economics,
business, linguistics and social science are bombarded by ever increasing flows
of data begging to analyzed efficiently and effectively. In this paper, we
propose a rough idea of a possible taxonomy of big data, along with some of the
most commonly used tools for handling each particular category of bigness. The
dimensionality p of the input space and the sample size n are usually the main
ingredients in the characterization of data bigness. The specific statistical
machine learning technique used to handle a particular big data set will depend
on which category it falls in within the bigness taxonomy. Large p small n data
sets for instance require a different set of tools from the large n small p
variety. Among other tools, we discuss Preprocessing, Standardization,
Imputation, Projection, Regularization, Penalization, Compression, Reduction,
Selection, Kernelization, Hybridization, Parallelization, Aggregation,
Randomization, Replication, Sequentialization. Indeed, it is important to
emphasize right away that the so-called no free lunch theorem applies here, in
the sense that there is no universally superior method that outperforms all
other methods on all categories of bigness. It is also important to stress the
fact that simplicity in the sense of Ockham's razor non plurality principle of
parsimony tends to reign supreme when it comes to massive data. We conclude
with a comparison of the predictive performance of some of the most commonly
used methods on a few data sets.Comment: 18 pages, 2 figures 3 table
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
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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