23,434 research outputs found
A Regularized Method for Selecting Nested Groups of Relevant Genes from Microarray Data
Gene expression analysis aims at identifying the genes able to accurately
predict biological parameters like, for example, disease subtyping or
progression. While accurate prediction can be achieved by means of many
different techniques, gene identification, due to gene correlation and the
limited number of available samples, is a much more elusive problem. Small
changes in the expression values often produce different gene lists, and
solutions which are both sparse and stable are difficult to obtain. We propose
a two-stage regularization method able to learn linear models characterized by
a high prediction performance. By varying a suitable parameter these linear
models allow to trade sparsity for the inclusion of correlated genes and to
produce gene lists which are almost perfectly nested. Experimental results on
synthetic and microarray data confirm the interesting properties of the
proposed method and its potential as a starting point for further biological
investigationsComment: 17 pages, 8 Post-script figure
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 review of domain adaptation without target labels
Domain adaptation has become a prominent problem setting in machine learning
and related fields. This review asks the question: how can a classifier learn
from a source domain and generalize to a target domain? We present a
categorization of approaches, divided into, what we refer to as, sample-based,
feature-based and inference-based methods. Sample-based methods focus on
weighting individual observations during training based on their importance to
the target domain. Feature-based methods revolve around on mapping, projecting
and representing features such that a source classifier performs well on the
target domain and inference-based methods incorporate adaptation into the
parameter estimation procedure, for instance through constraints on the
optimization procedure. Additionally, we review a number of conditions that
allow for formulating bounds on the cross-domain generalization error. Our
categorization highlights recurring ideas and raises questions important to
further research.Comment: 20 pages, 5 figure
Large-scale Multi-label Text Classification - Revisiting Neural Networks
Neural networks have recently been proposed for multi-label classification
because they are able to capture and model label dependencies in the output
layer. In this work, we investigate limitations of BP-MLL, a neural network
(NN) architecture that aims at minimizing pairwise ranking error. Instead, we
propose to use a comparably simple NN approach with recently proposed learning
techniques for large-scale multi-label text classification tasks. In
particular, we show that BP-MLL's ranking loss minimization can be efficiently
and effectively replaced with the commonly used cross entropy error function,
and demonstrate that several advances in neural network training that have been
developed in the realm of deep learning can be effectively employed in this
setting. Our experimental results show that simple NN models equipped with
advanced techniques such as rectified linear units, dropout, and AdaGrad
perform as well as or even outperform state-of-the-art approaches on six
large-scale textual datasets with diverse characteristics.Comment: 16 pages, 4 figures, submitted to ECML 201
One-step estimator paths for concave regularization
The statistics literature of the past 15 years has established many favorable
properties for sparse diminishing-bias regularization: techniques which can
roughly be understood as providing estimation under penalty functions spanning
the range of concavity between and norms. However, lasso
-regularized estimation remains the standard tool for industrial `Big
Data' applications because of its minimal computational cost and the presence
of easy-to-apply rules for penalty selection. In response, this article
proposes a simple new algorithm framework that requires no more computation
than a lasso path: the path of one-step estimators (POSE) does penalized
regression estimation on a grid of decreasing penalties, but adapts
coefficient-specific weights to decrease as a function of the coefficient
estimated in the previous path step. This provides sparse diminishing-bias
regularization at no extra cost over the fastest lasso algorithms. Moreover,
our `gamma lasso' implementation of POSE is accompanied by a reliable heuristic
for the fit degrees of freedom, so that standard information criteria can be
applied in penalty selection. We also provide novel results on the distance
between weighted- and penalized predictors; this allows us to build
intuition about POSE and other diminishing-bias regularization schemes. The
methods and results are illustrated in extensive simulations and in application
of logistic regression to evaluating the performance of hockey players.Comment: Data and code are in the gamlr package for R. Supplemental appendix
is at https://github.com/TaddyLab/pose/raw/master/paper/supplemental.pd
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