132,683 research outputs found
An Analysis of the Value of Information when Exploring Stochastic, Discrete Multi-Armed Bandits
In this paper, we propose an information-theoretic exploration strategy for
stochastic, discrete multi-armed bandits that achieves optimal regret. Our
strategy is based on the value of information criterion. This criterion
measures the trade-off between policy information and obtainable rewards. High
amounts of policy information are associated with exploration-dominant searches
of the space and yield high rewards. Low amounts of policy information favor
the exploitation of existing knowledge. Information, in this criterion, is
quantified by a parameter that can be varied during search. We demonstrate that
a simulated-annealing-like update of this parameter, with a sufficiently fast
cooling schedule, leads to an optimal regret that is logarithmic with respect
to the number of episodes.Comment: Entrop
Complexity regularization via localized random penalties
In this article, model selection via penalized empirical loss minimization in
nonparametric classification problems is studied. Data-dependent penalties are
constructed, which are based on estimates of the complexity of a small subclass
of each model class, containing only those functions with small empirical loss.
The penalties are novel since those considered in the literature are typically
based on the entire model class. Oracle inequalities using these penalties are
established, and the advantage of the new penalties over those based on the
complexity of the whole model class is demonstrated.Comment: Published by the Institute of Mathematical Statistics
(http://www.imstat.org) in the Annals of Statistics
(http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/00905360400000046
Block-diagonal covariance selection for high-dimensional Gaussian graphical models
Gaussian graphical models are widely utilized to infer and visualize networks
of dependencies between continuous variables. However, inferring the graph is
difficult when the sample size is small compared to the number of variables. To
reduce the number of parameters to estimate in the model, we propose a
non-asymptotic model selection procedure supported by strong theoretical
guarantees based on an oracle inequality and a minimax lower bound. The
covariance matrix of the model is approximated by a block-diagonal matrix. The
structure of this matrix is detected by thresholding the sample covariance
matrix, where the threshold is selected using the slope heuristic. Based on the
block-diagonal structure of the covariance matrix, the estimation problem is
divided into several independent problems: subsequently, the network of
dependencies between variables is inferred using the graphical lasso algorithm
in each block. The performance of the procedure is illustrated on simulated
data. An application to a real gene expression dataset with a limited sample
size is also presented: the dimension reduction allows attention to be
objectively focused on interactions among smaller subsets of genes, leading to
a more parsimonious and interpretable modular network.Comment: Accepted in JAS
Supersparse Linear Integer Models for Optimized Medical Scoring Systems
Scoring systems are linear classification models that only require users to
add, subtract and multiply a few small numbers in order to make a prediction.
These models are in widespread use by the medical community, but are difficult
to learn from data because they need to be accurate and sparse, have coprime
integer coefficients, and satisfy multiple operational constraints. We present
a new method for creating data-driven scoring systems called a Supersparse
Linear Integer Model (SLIM). SLIM scoring systems are built by solving an
integer program that directly encodes measures of accuracy (the 0-1 loss) and
sparsity (the -seminorm) while restricting coefficients to coprime
integers. SLIM can seamlessly incorporate a wide range of operational
constraints related to accuracy and sparsity, and can produce highly tailored
models without parameter tuning. We provide bounds on the testing and training
accuracy of SLIM scoring systems, and present a new data reduction technique
that can improve scalability by eliminating a portion of the training data
beforehand. Our paper includes results from a collaboration with the
Massachusetts General Hospital Sleep Laboratory, where SLIM was used to create
a highly tailored scoring system for sleep apnea screeningComment: This version reflects our findings on SLIM as of January 2016
(arXiv:1306.5860 and arXiv:1405.4047 are out-of-date). The final published
version of this articled is available at http://www.springerlink.co
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