4,416 research outputs found
Recursive Aggregation of Estimators by Mirror Descent Algorithm with Averaging
We consider a recursive algorithm to construct an aggregated estimator from a
finite number of base decision rules in the classification problem. The
estimator approximately minimizes a convex risk functional under the
l1-constraint. It is defined by a stochastic version of the mirror descent
algorithm (i.e., of the method which performs gradient descent in the dual
space) with an additional averaging. The main result of the paper is an upper
bound for the expected accuracy of the proposed estimator. This bound is of the
order with an explicit and small constant factor, where
is the dimension of the problem and stands for the sample size. A similar
bound is proved for a more general setting that covers, in particular, the
regression model with squared loss.Comment: 29 pages; mai 200
L2 Boosting on generalized Hoeffding decomposition for dependent variables. Application to Sensitivity Analysis
This paper is dedicated to the study of an estimator of the generalized
Hoeffding decomposition. We build such an estimator using an empirical
Gram-Schmidt approach and derive a consistency rate in a large dimensional
settings.
Then, we apply a greedy algorithm with these previous estimators to
Sensitivity Analysis. We also establish the consistency of this -boosting up to sparsity assumptions on the signal to analyse. We end the
paper with numerical experiments, which demonstrates the low computational cost
of our method as well as its efficiency on standard benchmark of Sensitivity
Analysis.Comment: 48 pages, 7 Figure
Optimization by gradient boosting
Gradient boosting is a state-of-the-art prediction technique that
sequentially produces a model in the form of linear combinations of simple
predictors---typically decision trees---by solving an infinite-dimensional
convex optimization problem. We provide in the present paper a thorough
analysis of two widespread versions of gradient boosting, and introduce a
general framework for studying these algorithms from the point of view of
functional optimization. We prove their convergence as the number of iterations
tends to infinity and highlight the importance of having a strongly convex risk
functional to minimize. We also present a reasonable statistical context
ensuring consistency properties of the boosting predictors as the sample size
grows. In our approach, the optimization procedures are run forever (that is,
without resorting to an early stopping strategy), and statistical
regularization is basically achieved via an appropriate penalization of
the loss and strong convexity arguments
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