Box-constrained optimization for minimax supervised learning
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The optimization procedure for computing the discrete boxconstrained minimax classifier is presented, and a projected subgradient algorithm which computes the prior maximizing this concave multivariate piecewise affine function over a polyhedral domain is considered.Abstract:
In this paper, we present the optimization procedure for computing the discrete boxconstrained minimax classifier introduced in [1, 2]. Our approach processes discrete or beforehand discretized features. A box-constrained region defines some bounds for each class proportion independently. The box-constrained minimax classifier is obtained from the computation of the least favorable prior which maximizes the minimum empirical risk of error over the box-constrained region. After studying the discrete empirical Bayes risk over the probabilistic simplex, we consider a projected subgradient algorithm which computes the prior maximizing this concave multivariate piecewise affine function over a polyhedral domain. The convergence of our algorithm is established.read more
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Discrete Box-Constrained Minimax Classifier for Uncertain and Imbalanced Class Proportions
TL;DR: A novel box-constrained minimax classifier is developed which takes into account some constraints on the priors to control the risk maximization and tends to equalize the class-conditional risks while being not too pessimistic.
References
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Scikit-learn: Machine Learning in Python
Fabian Pedregosa,Gaël Varoquaux,Alexandre Gramfort,Vincent Michel,Bertrand Thirion,Olivier Grisel,Mathieu Blondel,Peter Prettenhofer,Ron Weiss,Vincent Dubourg,Jake Vanderplas,Alexandre Passos,David Cournapeau,Matthieu Brucher,Matthieu Perrot,Edouard Duchesnay +15 more
TL;DR: Scikit-learn is a Python module integrating a wide range of state-of-the-art machine learning algorithms for medium-scale supervised and unsupervised problems, focusing on bringing machine learning to non-specialists using a general-purpose high-level language.
Posted Content
Scikit-learn: Machine Learning in Python
Fabian Pedregosa,Gaël Varoquaux,Alexandre Gramfort,Vincent Michel,Bertrand Thirion,Olivier Grisel,Mathieu Blondel,Andreas Müller,Joel Nothman,Gilles Louppe,Peter Prettenhofer,Ron Weiss,Vincent Dubourg,Jake Vanderplas,Alexandre Passos,David Cournapeau,Matthieu Brucher,Matthieu Perrot,Edouard Duchesnay +18 more
TL;DR: Scikit-learn as mentioned in this paper is a Python module integrating a wide range of state-of-the-art machine learning algorithms for medium-scale supervised and unsupervised problems.
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Malay Ghosh,James O. Berger +1 more
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Statistical Decision Theory and Bayesian Analysis
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TL;DR: How the abstract learning theory established conditions for generalization which are more general than those discussed in classical statistical paradigms are demonstrated and how the understanding of these conditions inspired new algorithmic approaches to function estimation problems are demonstrated.