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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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Learning the Kernel Function via Regularization
TL;DR: It is shown that, although K may be an uncountable set, the optimal kernel is always obtained as a convex combination of at most m+2 basic kernels, where m is the number of data examples.
Posted Content
Incremental Gradient, Subgradient, and Proximal Methods for Convex Optimization: A Survey.
TL;DR: A unified algorithmic framework is introduced for incremental methods for minimizing a sum P m=1 fi(x) consisting of a large number of convex component functions fi, including the advantages offered by randomization in the selection of components.
Journal ArticleDOI
A Path Following Algorithm for the Graph Matching Problem
TL;DR: In this article, a convex-concave programming approach is proposed for the labeled weighted graph matching problem, which is obtained by rewriting the problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems.
Journal ArticleDOI
The worst additive noise under a covariance constraint
Suhas Diggavi,Thomas M. Cover +1 more
TL;DR: The problem becomes one of extremizing the mutual information over all noise processes with covariances satisfying the correlation constraints R/sub 0/,..., R/ sub p/ for high signal powers, the worst additive noise is Gauss-Markov of order p as expected.
Journal Article
Breaking the curse of dimensionality with convex neural networks
TL;DR: In this paper, the authors consider neural networks with a single hidden layer and non-decreasing positively homogeneous activation functions like the rectified linear units and provide a detailed theoretical analysis of their generalization performance, with a study of both the approximation and the estimation errors.
References
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Increasing Returns and Long-Run Growth
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Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers
TL;DR: It is argued that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas.
Pattern Recognition and Machine Learning
TL;DR: Probability distributions of linear models for regression and classification are given in this article, along with a discussion of combining models and combining models in the context of machine learning and classification.
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An Algorithm for Vector Quantizer Design
Y. Linde,A. Buzo,Robert M. Gray +2 more
TL;DR: An efficient and intuitive algorithm is presented for the design of vector quantizers based either on a known probabilistic model or on a long training sequence of data.