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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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Linear quantile mixed models
Marco Geraci,Matteo Bottai +1 more
TL;DR: Estimation strategies to reduce the computational burden and inefficiency associated with the Monte Carlo EM algorithm are discussed and a combination of Gaussian quadrature approximations and non-smooth optimization algorithms are presented.
Journal ArticleDOI
Asymptotically Optimal Importance Sampling and Stratification for Pricing Path‐Dependent Options
TL;DR: In this article, a variance reduction technique for Monte Carlo simulations of path-dependent options driven by high-dimensional Gaussian vectors is proposed, which combines importance sampling based on a change of drift with stratified sampling along a small number of key dimensions.
Journal ArticleDOI
Dictionary Learning for Sparse Approximations With the Majorization Method
TL;DR: A novel method for dictionary learning and extends the learning problem by introducing different constraints on the dictionary by using the majorization method, an optimization method that substitutes the original objective function with a surrogate function that is updated in each optimization step.
Journal ArticleDOI
Calculus of the Exponent of Kurdyka–Łojasiewicz Inequality and Its Applications to Linear Convergence of First-Order Methods
Guoyin Li,Ting Kei Pong +1 more
TL;DR: The Kurdyka–Łojasiewicz exponent is studied, an important quantity for analyzing the convergence rate of first-order methods, and various calculus rules are developed to deduce the KL exponent of new (possibly nonconvex and nonsmooth) functions formed from functions with known KL exponents.
Journal ArticleDOI
The Optimal Mechanism for Selling to a Budget-Constrained Buyer
Yeon-Koo Che,Ian Gale +1 more
TL;DR: This paper finds an optimal mechanism for selling an indivisible good to consumers who may be budget-constrained and consists of a continuum of lotteries indexed by the probability of comsumption and the entry fee.
References
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Deep Learning
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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.