10,085 research outputs found
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
CoCoA: A General Framework for Communication-Efficient Distributed Optimization
The scale of modern datasets necessitates the development of efficient
distributed optimization methods for machine learning. We present a
general-purpose framework for distributed computing environments, CoCoA, that
has an efficient communication scheme and is applicable to a wide variety of
problems in machine learning and signal processing. We extend the framework to
cover general non-strongly-convex regularizers, including L1-regularized
problems like lasso, sparse logistic regression, and elastic net
regularization, and show how earlier work can be derived as a special case. We
provide convergence guarantees for the class of convex regularized loss
minimization objectives, leveraging a novel approach in handling
non-strongly-convex regularizers and non-smooth loss functions. The resulting
framework has markedly improved performance over state-of-the-art methods, as
we illustrate with an extensive set of experiments on real distributed
datasets
Regularizing Portfolio Optimization
The optimization of large portfolios displays an inherent instability to
estimation error. This poses a fundamental problem, because solutions that are
not stable under sample fluctuations may look optimal for a given sample, but
are, in effect, very far from optimal with respect to the average risk. In this
paper, we approach the problem from the point of view of statistical learning
theory. The occurrence of the instability is intimately related to over-fitting
which can be avoided using known regularization methods. We show how
regularized portfolio optimization with the expected shortfall as a risk
measure is related to support vector regression. The budget constraint dictates
a modification. We present the resulting optimization problem and discuss the
solution. The L2 norm of the weight vector is used as a regularizer, which
corresponds to a diversification "pressure". This means that diversification,
besides counteracting downward fluctuations in some assets by upward
fluctuations in others, is also crucial because it improves the stability of
the solution. The approach we provide here allows for the simultaneous
treatment of optimization and diversification in one framework that enables the
investor to trade-off between the two, depending on the size of the available
data set
L1-Regularized Distributed Optimization: A Communication-Efficient Primal-Dual Framework
Despite the importance of sparsity in many large-scale applications, there
are few methods for distributed optimization of sparsity-inducing objectives.
In this paper, we present a communication-efficient framework for
L1-regularized optimization in the distributed environment. By viewing
classical objectives in a more general primal-dual setting, we develop a new
class of methods that can be efficiently distributed and applied to common
sparsity-inducing models, such as Lasso, sparse logistic regression, and
elastic net-regularized problems. We provide theoretical convergence guarantees
for our framework, and demonstrate its efficiency and flexibility with a
thorough experimental comparison on Amazon EC2. Our proposed framework yields
speedups of up to 50x as compared to current state-of-the-art methods for
distributed L1-regularized optimization
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