Titlebook: Sublinear Computation Paradigm; Algorithmic Revoluti Naoki Katoh,Yuya Higashikawa,Yushi Uno Book‘‘‘‘‘‘‘‘ 2022 The Editor(s) (if applicable)

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Oracle-Based Primal-Dual Algorithms for Packing and Covering Semidefinite Programsnentially or even infinitely many) constraints. In this chapter, we give an overview of some of the techniques that can be used to solve this class of problems, focusing on multiplicative weight updates and logarithmic-potential methods.

esoteric

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Empirical Bayes Method for Boltzmann Machinesional problem by using the replica method and the Plefka expansion, which is quite simple and fast because it does not require any iterative procedures and gives reasonable estimates under certain conditions.

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What Is the Sublinear Computation Paradigm?e instance (input data). In other words, the running time is .(.), where . is the size of the instance. This century marks the start of the era of big data. In order to manage big data, polynomial-time algorithms, which are considered to be efficient, may sometimes be inadequate because they may req

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Property Testing on Graphs and Gamesresearch framework for constant-time algorithms. In property testing, an algorithm determines whether a given instance satisfies some predetermined property or is far from satisfying the property with high probability by reading a constant-sized part of the input. A property is said to be testable i

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Constant-Time Algorithms for Continuous Optimization Problemsand tensor decomposition, both of which have numerous applications in machine learning and data mining. The key component in our analysis is ., which was originally developed to study graphs analytically.

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Oracle-Based Primal-Dual Algorithms for Packing and Covering Semidefinite Programsently, several techniques have been proposed that utilize the particular structure of this class of problems in order to obtain more efficient algorithms than those offered by general SDP solvers. For certain applications, it may be necessary to deal with SDPs with a very large number of (e.g., expo

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Information Processing on Compressed Databols and therefore includes not only ordinary text but also a wide range of data, such as pixel sequences and time-series data. Over the past two decades, a variety of algorithms and their applications have been proposed for compressed information processing. In this survey, we mainly focus on two p