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检索条件"主题词=Randomized Algorithms"

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Tight Bounds for Asynchronous randomized Consensus 07

Tight Bounds for Asynchronous Randomized Consensus

引用

39th Annual ACM Symposium on Theory of Computing

作者： Attiya, Hagit Censor, Keren Technion Israel Inst Technol Dept Comp Sci IL-32000 Haifa Israel

ISBN: (纸本)9781595936318

A distributed consensus algorithm allows n processes to reach acommon decision value starting from individual inputs. Wait-free consensus, in which a process always terminates within a finite number of its own steps, is impossible in anasynchronous shared-memory system. However, consensus becomes solvable using randomization when a process only has to terminatewith probability 1. randomized consensus algorithms are typically evaluated by their total step complexity, which is the expected total number of steps taken by all *** work proves that the total step complexity of randomized consensus is Θ(n2) in an asynchronous shared memory systemusing multi-writer multi-reader registers. The bound is achieved by improving both the lower and the upper bounds for this *** addition to improving upon the best previously known result bya factor of log2 n, the lower bound features agreatly streamlined proof. Both goals are achieved through restricting attention to a set of layered executions andusing an isoperimetric inequality for analyzing their *** matching algorithm decreases the expected total step complexity by a log n factor, by leveraging themulti-writing capability of the shared registers. Its correctness proof is facilitated by viewing each execution of the algorithmas a stochastic process and applying Kolmogorov's inequality.

关键词： lower bound shared-memory distributed computing randomized algorithms isoperimetric inequality

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A randomized approach to switched nonlinear systems identification

A randomized approach to switched nonlinear systems identifi...

引用

18th IFAC Symposium on System Identification (SYSID)

作者： Bianchi, Federico Prandini, Maria Piroddi, Luigi Politecn Milan Dipartimento Elettron Informaz & Bioingn Milan Italy

This paper addresses the identification of Switched Nonlinear AutoRegressive eXogenous (SNARX) systems characterized as a collection of nonlinear dynamical systems (modes), each one described via a discrete time NARX model, indexed by a discrete-valued variable (switching signal). We propose a novel approach which, given a realization of the input/output signals collected from the system, jointly classifies the data attributing them to the different modes, and identifies the model structure and parameters for each mode. The involved optimization problem is partly combinatorial due to the data classification over modes and the model structure selection, and partly continuous due to the parameter estimation required to complete the identification of the dynamical models assigned to the different modes. A probabilistic framework is employed to address the problem, where Categorical and Bernoulli distributions are respectively used for the assignment of modes over time and for the structure selection of the NARX models describing the modes. A randomized procedure is then proposed to solve the problem, based on a sample-and-evaluate strategy that progressively refines the induced SNARX model probability distribution. The approach is tested on a numerical example taken from the literature, where it shows promising results. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： NARX model identification switched systems randomized algorithms

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randomized control design through probabilistic validation

Randomized control design through probabilistic validation

引用

American Control Conference (ACC)

作者： Alamo, T. Luque, A. Ramirez, D. R. Tempo, R. Univ Seville Dept Ingn Sistemas & Automat Escuela Super Ingenieros Camino Descubrimientos S-N Seville 41092 Spain Politecn Torino CNR IEIIT I-10129 Turin Italy

ISBN: (纸本)9781457710964;9781457710957

In this paper, we present a randomized strategy for design under uncertainty. The main contribution is to provide a general class of sequential algorithms which satisfy the required specifications using probabilistic validation. At each iteration of the sequential algorithm, a candidate solution is probabilistically validated by means of a set of randomly generated uncertainty samples. The idea of validation sets has been used in some randomized algorithms when a given candidate solution is classified as probabilistic solution when it satisfies all the constraints on the validation set. In this paper, we show the limitations of this strategy and present a more general setting where the candidate solution may violate the specifications for a reduced number of elements of the validation set. This generalized scheme exhibits some advantages, in particular in terms of obtaining a probabilistic solution.

关键词： Probabilistic robustness randomized algorithms uncertain systems

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randomized Computations in Domain Decomposition Methods

Randomized Computations in Domain Decomposition Methods

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IEEE International Symposium on Antennas and Propagation / USNC/URSI National North American Radio Science Meeting

作者： Wang, Wei Vouvakis, Marinos N. Univ Massachusetts Dept Elect & Comp Engn Amherst MA 01003 USA

ISBN: (纸本)9781479978151

An efficient and robust FETI-2 lambda domain decomposition method (DDM) framework for electromagnetic (EM) modeling is outlined. The proposed framework uses randomized algorithms to approximate the low-rank discrete Dirichlet-to-Neumann (DtN) map interations that arise in FETI-2 lambda. The resulting approach is also combined with effective and robust local and global DDM preconditioners. A realistic numerical example is given to verify the effectiveness, effieincy and robustness.

关键词： randomized algorithms decomposition Domain Robustness RANDOMISING Frameworks numerical example

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Scalable and Sustainable Deep Learning via randomized Hashing 17

Scalable and Sustainable Deep Learning via Randomized Hashin...

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23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD)

作者： Spring, Ryan Shrivastava, Anshumali Rice Univ Dept Comp Sci Houston TX 43017 USA

ISBN: (纸本)9781450348874

Current deep learning architectures are growing larger in order to learn from complex datasets. These architectures require giant matrix multiplication operations to train millions of parameters. Conversely, there is another growing trend to bring deep learning to low-power, embedded devices. The matrix operations, associated with the training and testing of deep networks, are very expensive from a computational and energy standpoint. We present a novel hashing-based technique to drastically reduce the amount of computation needed to train and test neural networks. Our approach combines two recent ideas, Adaptive Dropout and randomized Hashing for Maximum Inner Product Search (MIPS), to select the nodes with the highest activations efficiently. Our new algorithm for deep learning reduces the overall computational cost of the forward and backward propagation steps by operating on significantly fewer nodes. As a consequence, our algorithm uses only 5% of the total multiplications, while keeping within 1% of the accuracy of the original model on average. A unique property of the proposed hashing-based back-propagation is that the updates are always sparse. Due to the sparse gradient updates, our algorithm is ideally suited for asynchronous, parallel training, leading to near-linear speedup, as the number of cores increases. We demonstrate the scalability and sustainability (energy efficiency) of our proposed algorithm via rigorous experimental evaluations on several datasets.

关键词： Neural Networks Deep Learning Locality-Sensitive Hashing randomized algorithms Parallel Computing

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randomized self-assembly for approximate shapes

引用

35th International Colloquium on Automata, Languages and Programming

作者： Kao, Ming-Yang Schweller, Robert Northwestern Univ Dept Elect Engn & Comp Sci Evanston IL 60208 USA Univ Texas Pan Amer Dept Comp Sci Edinburg TX 78541 USA

ISBN: (纸本)9783540705741

In this paper we design tile self-assembly systems which assemble arbitrarily close approximations to target squares ,with arbitrarily high probability. This is in contrast to previous work which has only considered deterministic assemblies of a single shape. Our technique takes advantage of the ability to assign tile concentrations to each tile type of a self-assembly system. Such an assignment yields a probability distribution over the set of possible assembled shapes. We show that by considering the assembly of close approximations to target shapes with high probability;as opposed to exact deterministic assembly, we are able to achieve significant reductions in tile complexity. In fact,;we restrict ourselves to constant sized tile systems. encoding all information about the target shape into the tile concentration assignment. In practice;this offers a potentially useful tradeoff;as large libraries of particles may be infeasible or require substantial effort;to create;while the replication of existing particles to adjust relative concentration may be much easier. To illustrate our technique we focus on the assembly of n x n, squares;a special case class of shapes whose study has proven fruitful in the development of new self-assembly systems.

关键词： self-assembly randomized algorithms approximation algorithms

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randomized Distributed Decision

Randomized Distributed Decision

引用

26th International Symposium on Distributed Computing (DISC)

作者： Fraigniaud, Pierre Korman, Amos Parter, Merav Peleg, David CNRS F-75700 Paris France Weizmann Inst Sci Rehovot Israel

ISBN: (纸本)9783642336515

The paper tackles the power of randomization in the context of locality by analyzing the ability to "boost" the success probability of deciding a distributed language. The main outcome of this analysis is that the distributed computing setting contrasts significantly with the sequential one as far as randomization is concerned. Indeed, we prove that in some cases, the ability to increase the success probability for deciding distributed languages is rather limited. We focus on the notion of a (p q)-decider for a language r, which is a distributed randomized algorithm that accepts instances in L with probability at least p and rejects instances outside of L with probability at least q. It is known that every hereditary language that can be decided in t rounds by a (p, q)-decider, where p(2) + q > 1, can be decided deterministically in O(t) rounds. One of our results gives evidence supporting the conjecture that the above statement holds for all distributed languages and not only for hereditary ones, by proving the conjecture for the restricted case of path topologies. For the range below the aforementioned threshold, namely, p(2)+ q < 1, we study the class Bk(t) (for k E N* U {cc}) of all languages decidable in at most t rounds by a (p,q)-decider, where pl+i + q > 1. Since every language is decidable (in zero rounds) by a (p q)-decider satisfying p + q = 1, the hierarchy Bk provides a spectrum of complexity classes between determinism (k = 1, under the above conjecture) and complete randomization (k = co). We prove that all these classes are separated, in a strong sense: for every integer k > 1, there exists a language L satisfying L E Bk+i (0) but L Bk(t) for any t = o(n). In addition, we show that B(t) does not contain all languages, for any t = o(n). In other words, we obtain the hierarchy B1 (t) c B2 (t) C C B,o(t) C All. Finally, we show that if the inputs can be restricted in certain ways, then the ability to boost the success probability becomes almost null, an

关键词： Local distributed algorithms local decision randomized algorithms

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Verifiable Computation for randomized Algorithm 17th

Verifiable Computation for Randomized Algorithm

引用

17th International Conference on Cryptology in India (INDOCRYPT)

作者： Liu, Muhua Wu, Ying Xue, Rui Chinese Acad Sci Inst Informat Engn State Key Lab Informat Secur Beijing 100093 Peoples R China Univ Chinese Acad Sci Beijing 100049 Peoples R China

ISBN: (纸本)9783319498904;9783319498898

Verifiable computation enables a computationally weak client to delegate the difficult computation to a more powerful cloud server. When the client receives the returned result, it can verify the correctness of the result. As a new computing model, it has been widely studied. But, the previous works on verifiable computation was restricted to the case where the target function was deterministic. In this paper, we present a novel definition for verifiable computation supporting randomized algorithms, which allows a resource constrained client to outsource the computation of a randomized algorithm to an untrusted server. We consider a new setting where the random string, as the random input of the randomized algorithm, is generated by the cloud server. In our security definition, it must guarantee that the server can not tamper with the randomness which means that the generated string is indistinguishable with a truly random string. Our construction is based on indistinguishability obfuscation, constrained verifiable random function and functional pseudorandom function.

关键词： Verifiable computation randomized algorithms Indistinguishability obfuscation

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randomized Nystrom Features for Fast Regression: An Error Analysis 8th

Randomized Nystrom Features for Fast Regression: An Error An...

引用

8th International Conference on Algebraic Informatics (CAI)

作者： Trokicic, Aleksandar Todorovic, Branimir Univ Nis Fac Sci & Math Nish Serbia

ISBN: (纸本)9783030213633;9783030213626

We consider the problem of fast approximate kernel regression. Since kernels can map input features into the infinite dimensional space, kernel trick is used to make the algorithms tractable. However on large data set time complexity of O(n(2)) is prohibitive. Therefore, various approximation methods are employed, such as randomization. A Nystrom method (based on a random selection of columns) is usually employed. Main advantage of this algorithm is its time complexity which is reduced to O(nm(2) + m(3)). Space complexity is also reduced to O(nm) because it does not require the computation of the entire matrix. An arbitrary number m << n represents both the size of a random subset of an input set and the dimension of random feature vectors. A Nystrom method can be extended with the randomized SVD so that l (where l > m) randomly selected columns of a kernel matrix without replacement are used for a construction of m-dimensional random feature vectors while keeping time complexity linear in n. Approximated matrix computed in this way is a better approximation than the matrix computed via the Nystrom method. We will prove here that the expected error of the approximated kernel predictor derived via this method is approximately the same in expectation as the error of the error of kernel predictor. Furthermore, we will empirically show that using the l randomly selected columns of a kernel matrix for a construction of m-dimensional random feature vectors produces smaller error on a regression problem, than using m randomly selected columns.

关键词： Kernel methods Nystrom method randomized algorithms Random features Regression

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randomized Iterative Methods for Matrix Approximation 1

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7th International Conference on Machine Learning, Optimization, and Data Science (LOD) / 1st Symposium on Artificial Intelligence and Neuroscience (ACAIN)

作者： Azzam, Joy Ong, Benjamin W. Struthers, Allan A. Michigan Technol Univ Dept Math Sci Houghton MI 49931 USA

ISBN: (数字)9783030954703

ISBN: (纸本)9783030954703;9783030954697

Standard tools to update approximations to a matrix A (for example, Quasi-Newton Hessian approximations in optimization) incorporate computationally expensive one-sided samples AV. This article develops randomized algorithms to efficiently approximate A by iteratively incorporating cheaper two-sided samples U-inverted perpendicular AV. Theoretical convergence rates are proved and realized in numerical experiments. A heuristic accelerated variant is developed and shown to be competitive with existing methods based on one-sided samples.

关键词： Matrix approximation randomized algorithms Two-sided samples Quasi-Newton

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