Open Access
Convex Analysisの二,三の進展について
徹 丸山
- Vol. 70, Iss: 1, pp 97-119
Reads0
Chats0
About:
The article was published on 1977-02-01 and is currently open access. It has received 5933 citations till now.read more
Citations
More filters
Book ChapterDOI
Ellipsoidal Techniques for Reachability Analysis
TL;DR: The proposed techniques, combined with calculation of external and internal approximations for intersections of ellipsoids, provide an approach to reachability problems for hybrid systems.
Journal ArticleDOI
Dual Stochastic Dominance and Related Mean-Risk Models
TL;DR: By exploiting duality relations of convex analysis, the quantile model of stochastic dominance for general distributions is developed and it is shown that several models using quantiles and tail characteristics of the distribution are in harmony with the stoChastic dominance relation.
Posted Content
Structured Variable Selection with Sparsity-Inducing Norms
TL;DR: In this paper, the authors consider the empirical risk minimization problem for linear supervised learning, with regularization by structured sparsityinducing norms, defined as sums of Euclidean norms on certain subsets of variables.
Journal ArticleDOI
Game theory, maximum entropy, minimum discrepancy and robust Bayesian decision theory
Peter Grünwald,A. Philip Dawid +1 more
TL;DR: In this article, the authors show that the problem of maximizing entropy and minimizing a related discrepancy or divergence between distributions can be viewed as dual problems, with the solution to each providing that to the other.
Journal ArticleDOI
A new class of upper bounds on the log partition function
TL;DR: A new class of upper bounds on the log partition function of a Markov random field (MRF) is introduced, based on concepts from convex duality and information geometry, and the Legendre mapping between exponential and mean parameters is exploited.
References
More filters
Book
Deep Learning
TL;DR: Deep learning as mentioned in this paper is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts, and it is used in many applications such as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames.
Journal ArticleDOI
Increasing Returns and Long-Run Growth
TL;DR: In this paper, the authors present a fully specified model of long-run growth in which knowledge is assumed to be an input in production that has increasing marginal productivity, which is essentially a competitive equilibrium model with endogenous technological change.
Book
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.
Journal ArticleDOI
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.