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Convex Analysisの二,三の進展について
徹 丸山
- Vol. 70, Iss: 1, pp 97-119
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The article was published on 1977-02-01 and is currently open access. It has received 5933 citations till now.read more
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References
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Optimal distributed online prediction using mini-batches
TL;DR: This work presents the distributed mini-batch algorithm, a method of converting many serial gradient-based online prediction algorithms into distributed algorithms that is asymptotically optimal for smooth convex loss functions and stochastic inputs and proves a regret bound for this method.
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A Douglas–Rachford Splitting Approach to Nonsmooth Convex Variational Signal Recovery
TL;DR: A decomposition method based on the Douglas-Rachford algorithm for monotone operator-splitting for signal recovery problems and applications to non-Gaussian image denoising in a tight frame are demonstrated.
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On elementary flux modes in biochemical reaction systems at steady state
TL;DR: It is shown that for systems in which all flux- have fixed signs, all elementary modes are given by the generating vectors of a convex cone and can, thus, be computed by an existing algorithm.
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High-dimensional generalized linear models and the lasso
TL;DR: In this paper, a nonasymptotic oracle inequality for the empirical risk minimizer with Lasso penalty with Lipschitz loss functions was proved for high-dimensional generalized linear models, where the penalty is based on the coefficients in the linear predictor, after normalization with the empirical norm.
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Optimum power allocation for parallel Gaussian channels with arbitrary input distributions
TL;DR: This paper gives the power allocation policy that maximizes the mutual information over parallel channels with arbitrary input distributions, and admits a graphical interpretation, referred to as mercury/waterfilling, which generalizes the waterfilling solution and allows retaining some of its intuition.