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
Journal ArticleDOI
The plane with parallel coordinates
TL;DR: A new duality betweenbounded and unbounded convex sets and hstars (a generalization of hyperbolas) and between Convex Unions and Intersections is found and motivates some efficient ConveXity algorithms and other results inComputational Geometry.
Journal ArticleDOI
The Convex Geometry of Linear Inverse Problems
TL;DR: This paper provides a general framework to convert notions of simplicity into convex penalty functions, resulting in convex optimization solutions to linear, underdetermined inverse problems.
Journal ArticleDOI
A fast procedure for computing the distance between complex objects in three-dimensional space
TL;DR: An algorithm for computing the Euclidean distance between a pair of convex sets in R/sup m/ has special features which makes its application in a variety of robotics problems attractive.
Journal ArticleDOI
Sum capacity of the vector Gaussian broadcast channel and uplink-downlink duality
Pramod Viswanath,David Tse +1 more
TL;DR: The sum capacity of the vector Gaussian broadcast channel is characterized by showing that the existing inner bound of Marton and the existing upper bound of Sato are tight for this channel.
Journal ArticleDOI
Convexity, Classification, and Risk Bounds
TL;DR: A general quantitative relationship between the risk as assessed using the 0–1 loss and the riskAs assessed using any nonnegative surrogate loss function is provided, and it is shown that this relationship gives nontrivial upper bounds on excess risk under the weakest possible condition on the loss function.
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.