5,812 research outputs found
Optimal exponential bounds for aggregation of estimators for the Kullback-Leibler loss
We study the problem of model selection type aggregation with respect to the
Kullback-Leibler divergence for various probabilistic models. Rather than
considering a convex combination of the initial estimators ,
our aggregation procedures rely on the convex combination of the logarithms of
these functions. The first method is designed for probability density
estimation as it gives an aggregate estimator that is also a proper density
function, whereas the second method concerns spectral density estimation and
has no such mass-conserving feature. We select the aggregation weights based on
a penalized maximum likelihood criterion. We give sharp oracle inequalities
that hold with high probability, with a remainder term that is decomposed into
a bias and a variance part. We also show the optimality of the remainder terms
by providing the corresponding lower bound results.Comment: 25 page
Kullback-Leibler aggregation and misspecified generalized linear models
In a regression setup with deterministic design, we study the pure
aggregation problem and introduce a natural extension from the Gaussian
distribution to distributions in the exponential family. While this extension
bears strong connections with generalized linear models, it does not require
identifiability of the parameter or even that the model on the systematic
component is true. It is shown that this problem can be solved by constrained
and/or penalized likelihood maximization and we derive sharp oracle
inequalities that hold both in expectation and with high probability. Finally
all the bounds are proved to be optimal in a minimax sense.Comment: Published in at http://dx.doi.org/10.1214/11-AOS961 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Probabilistic Framework for Sensor Management
A probabilistic sensor management framework is introduced, which maximizes the utility of sensor systems with many different sensing modalities by dynamically configuring the sensor system in the most beneficial way. For this purpose, techniques from stochastic control and Bayesian estimation are combined such that long-term effects of possible sensor configurations and stochastic uncertainties resulting from noisy measurements can be incorporated into the sensor management decisions
Local Risk Bounds for Statistical Aggregation
In the problem of aggregation, the aim is to combine a given class of base
predictors to achieve predictions nearly as accurate as the best one. In this
flexible framework, no assumption is made on the structure of the class or the
nature of the target. Aggregation has been studied in both sequential and
statistical contexts. Despite some important differences between the two
problems, the classical results in both cases feature the same global
complexity measure. In this paper, we revisit and tighten classical results in
the theory of aggregation in the statistical setting by replacing the global
complexity with a smaller, local one. Some of our proofs build on the PAC-Bayes
localization technique introduced by Catoni. Among other results, we prove
localized versions of the classical bound for the exponential weights estimator
due to Leung and Barron and deviation-optimal bounds for the Q-aggregation
estimator. These bounds improve over the results of Dai, Rigollet and Zhang for
fixed design regression and the results of Lecu\'e and Rigollet for random
design regression.Comment: 47 page
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