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
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.
References
More filters
Journal ArticleDOI
New Approach to the Stability of Chemical Reaction Networks: Piecewise Linear in Rates Lyapunov Functions
TL;DR: Piecewise-linear in rates Lyapunov functions are introduced for a class of chemical reaction networks (CRNs) and can be used to establish their asymptotic stability with respect to the corresponding stoichiometric compatibility class.
Journal ArticleDOI
Deriving constraints among argument sizes in logic programs
TL;DR: It is proved that every polycone has a uniquenormal form in this representation, and given an algorithm to produce it, which gives a decision procedure for the question of whether two sets of linear equations define the same polycone.
Journal ArticleDOI
When Does the Positive Semidefiniteness Constraint Help in Lifting Procedures
Michel X. Goemans,Levent Tunçel +1 more
TL;DR: It is proved that the procedure using the positive semidefiniteness constraint is not better than the one without it, in the worst case, according to LovAisz and Schrijver's procedures for 0-1 integer programming problems.
Journal ArticleDOI
$f$ -Divergence Estimation and Two-Sample Homogeneity Test Under Semiparametric Density-Ratio Models
TL;DR: This work derives an optimal estimator of f-divergence in the sense of the asymptotic variance in a semiparametric setting, and provides a statistic for two-sample homogeneity test based on the optimal estimators.
Journal ArticleDOI
A convex polynomial that is not sos-convex
Amir Ali Ahmadi,Pablo A. Parrilo +1 more
TL;DR: A negative answer to the question of whether sos-convexity is also a necessary condition for convexity of polynomials is given by presenting an explicit example of a trivariate homogeneous polynomial of degree eight that is convex but not sos.