5,728 research outputs found
Linear Time Feature Selection for Regularized Least-Squares
We propose a novel algorithm for greedy forward feature selection for
regularized least-squares (RLS) regression and classification, also known as
the least-squares support vector machine or ridge regression. The algorithm,
which we call greedy RLS, starts from the empty feature set, and on each
iteration adds the feature whose addition provides the best leave-one-out
cross-validation performance. Our method is considerably faster than the
previously proposed ones, since its time complexity is linear in the number of
training examples, the number of features in the original data set, and the
desired size of the set of selected features. Therefore, as a side effect we
obtain a new training algorithm for learning sparse linear RLS predictors which
can be used for large scale learning. This speed is possible due to matrix
calculus based short-cuts for leave-one-out and feature addition. We
experimentally demonstrate the scalability of our algorithm and its ability to
find good quality feature sets.Comment: 17 pages, 15 figure
OCReP: An Optimally Conditioned Regularization for Pseudoinversion Based Neural Training
In this paper we consider the training of single hidden layer neural networks
by pseudoinversion, which, in spite of its popularity, is sometimes affected by
numerical instability issues. Regularization is known to be effective in such
cases, so that we introduce, in the framework of Tikhonov regularization, a
matricial reformulation of the problem which allows us to use the condition
number as a diagnostic tool for identification of instability. By imposing
well-conditioning requirements on the relevant matrices, our theoretical
analysis allows the identification of an optimal value for the regularization
parameter from the standpoint of stability. We compare with the value derived
by cross-validation for overfitting control and optimisation of the
generalization performance. We test our method for both regression and
classification tasks. The proposed method is quite effective in terms of
predictivity, often with some improvement on performance with respect to the
reference cases considered. This approach, due to analytical determination of
the regularization parameter, dramatically reduces the computational load
required by many other techniques.Comment: Published on Neural Network
Batch Policy Learning under Constraints
When learning policies for real-world domains, two important questions arise:
(i) how to efficiently use pre-collected off-policy, non-optimal behavior data;
and (ii) how to mediate among different competing objectives and constraints.
We thus study the problem of batch policy learning under multiple constraints,
and offer a systematic solution. We first propose a flexible meta-algorithm
that admits any batch reinforcement learning and online learning procedure as
subroutines. We then present a specific algorithmic instantiation and provide
performance guarantees for the main objective and all constraints. To certify
constraint satisfaction, we propose a new and simple method for off-policy
policy evaluation (OPE) and derive PAC-style bounds. Our algorithm achieves
strong empirical results in different domains, including in a challenging
problem of simulated car driving subject to multiple constraints such as lane
keeping and smooth driving. We also show experimentally that our OPE method
outperforms other popular OPE techniques on a standalone basis, especially in a
high-dimensional setting
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