16,089 research outputs found
Automated design of robust discriminant analysis classifier for foot pressure lesions using kinematic data
In the recent years, the use of motion tracking systems for acquisition of functional biomechanical gait data, has received increasing interest due to the richness and accuracy of the measured kinematic information. However, costs frequently restrict the number of subjects employed, and this makes the dimensionality of the collected data far higher than the available samples. This paper applies discriminant analysis algorithms to the classification of patients with different types of foot lesions, in order to establish an association between foot motion and lesion formation. With primary attention to small sample size situations, we compare different types of Bayesian classifiers and evaluate their performance with various dimensionality reduction techniques for feature extraction, as well as search methods for selection of raw kinematic variables. Finally, we propose a novel integrated method which fine-tunes the classifier parameters and selects the most relevant kinematic variables simultaneously. Performance comparisons are using robust resampling techniques such as Bootstrapand k-fold cross-validation. Results from experimentations with lesion subjects suffering from pathological plantar hyperkeratosis, show that the proposed method can lead tocorrect classification rates with less than 10% of the original features
Statistical Significance of the Netflix Challenge
Inspired by the legacy of the Netflix contest, we provide an overview of what
has been learned---from our own efforts, and those of others---concerning the
problems of collaborative filtering and recommender systems. The data set
consists of about 100 million movie ratings (from 1 to 5 stars) involving some
480 thousand users and some 18 thousand movies; the associated ratings matrix
is about 99% sparse. The goal is to predict ratings that users will give to
movies; systems which can do this accurately have significant commercial
applications, particularly on the world wide web. We discuss, in some detail,
approaches to "baseline" modeling, singular value decomposition (SVD), as well
as kNN (nearest neighbor) and neural network models; temporal effects,
cross-validation issues, ensemble methods and other considerations are
discussed as well. We compare existing models in a search for new models, and
also discuss the mission-critical issues of penalization and parameter
shrinkage which arise when the dimensions of a parameter space reaches into the
millions. Although much work on such problems has been carried out by the
computer science and machine learning communities, our goal here is to address
a statistical audience, and to provide a primarily statistical treatment of the
lessons that have been learned from this remarkable set of data.Comment: Published in at http://dx.doi.org/10.1214/11-STS368 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A Comparative Review of Dimension Reduction Methods in Approximate Bayesian Computation
Approximate Bayesian computation (ABC) methods make use of comparisons
between simulated and observed summary statistics to overcome the problem of
computationally intractable likelihood functions. As the practical
implementation of ABC requires computations based on vectors of summary
statistics, rather than full data sets, a central question is how to derive
low-dimensional summary statistics from the observed data with minimal loss of
information. In this article we provide a comprehensive review and comparison
of the performance of the principal methods of dimension reduction proposed in
the ABC literature. The methods are split into three nonmutually exclusive
classes consisting of best subset selection methods, projection techniques and
regularization. In addition, we introduce two new methods of dimension
reduction. The first is a best subset selection method based on Akaike and
Bayesian information criteria, and the second uses ridge regression as a
regularization procedure. We illustrate the performance of these dimension
reduction techniques through the analysis of three challenging models and data
sets.Comment: Published in at http://dx.doi.org/10.1214/12-STS406 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Estimating High Dimensional Covariance Matrices and its Applications
Estimating covariance matrices is an important part of portfolio selection, risk management, and asset pricing. This paper reviews the recent development in estimating high dimensional covariance matrices, where the number of variables can be greater than the number of observations. The limitations of the sample covariance matrix are discussed. Several new approaches are presented, including the shrinkage method, the observable and latent factor method, the Bayesian approach, and the random matrix theory approach. For each method, the construction of covariance matrices is given. The relationships among these methods are discussed.Factor analysis, Principal components, Singular value decomposition, Random matrix theory, Empirical Bayes, Shrinkage method, Optimal portfolios, CAPM, APT, GMM
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