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Stable improved softmax using constant normalisation

ELECTRONICS LETTERS 2017年第23期53卷 1504-1505页

作者： Lim, S. Lee, D. Kyung Hee Univ Dept Elect & Radio Engn Yongin 17104 South Korea Kyung Hee Univ Humanitas Coll Yongin 17104 South Korea

In deep learning architectures, rectified linear unit based functions are widely used as activation functions of hidden layers, and the softmax is used for the output layers. Two critical problems of the softmax are introduced, and an improved softmax method to resolve the problems is proposed. The proposed method minimises instability of the softmax while reducing its losses. Moreover, this method is straightforward so its computation complexity is low, but it is substantially reasonable and operates robustly. Therefore, the proposed method can replace the softmax functions.

关键词： learning (artificial intelligence) computational complexity transfer functions constant normalisation improved softmax method rectified linear unit based functions deep learning architectures activation functions hidden layers computation complexity

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Methods of Gauss-Jordan elimination to compute core inverse A(sic) and dual core inverse A(sic)

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LINEAR & MULTILINEAR ALGEBRA 2022年第12期70卷 2354-2366页

作者： Sheng, Xingping Xin, Dawei Southeast Univ Sch Math Nanjing 211189 Peoples R China Fuyang Normal Univ Sch Math & Stat Fuyang 236037 Anhui Peoples R China

In this paper, two formulas, which were studied by Wang and Liu (2015) and Ma and Li (2019), respectively, for the core inverse, are simplified. Then two methods for computing the core inverseand dual core inverseare investigated through Gauss-Jordan elimination on the two appropriate block partitioned matrices. The corresponding algorithms are also summarized. The computational complexities of the these two algorithms are analysed in detail. In the end, some numerical examples are presented to demonstrate the efficiency of the two algorithms.

关键词： Core inverse dual core inverse Gauss-Jordan elimination partitioned matrix computation complexity

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Comparing performance of algorithms for generating concept lattices

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JOURNAL OF EXPERIMENTAL & THEORETICAL ARTIFICIAL INTELLIGENCE 2002年第2期14卷 189-216页

作者： Kuznetsov, SO Obiedkov, SA All Russian Inst Sci & Tech Informat VINITI Moscow Russia Russian State Univ Humanities Moscow Russia

Recently concept lattices became widely used tools for intelligent data analysis. In this paper, several algorithms that generate the set of all formal concepts and diagram graphs of concept lattices are considered. Some modifications of well-known algorithms are proposed. Algorithmic complexity of the algorithms is studied both theoretically (in the worst case) and experimentally. Conditions of preferable use of some algorithms are given in terms of density/sparseness of underlying formal contexts. Principles of comparing practical performance of algorithms are discussed.

关键词： concept lattice algorithms computation complexity

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Kalman Filtering with Unknown Sensor Measurement Losses

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IFAC-PapersOnLine 2016年第22期49卷 315-320页

作者： Zhang, Jiaqi You, Keyou Department of Automation and Tsinghua National Laboratory for Information Science and Technology Tsinghua University Beijing100084 China

This work studies the state estimation problem of a networked linear system where a sensor and an estimator are connected via a lossy network. If the measurement loss is known to the estimator, the minimum variance estimate is easily computed by the intermittent Kalman filter (IKF). However, this does not hold for the case of unknown measurement losses, and we have to address the non-Gaussianity/non-linearity of the networked system. By exploiting the measurement loss process and the IKF, we design three recursive suboptimal filters for state estimation, i.e., BKF-I, BKF-II and RBPF. The BKF-I is based on the MAP estimator of the loss process and the BKF-II is derived by an estimate of the conditional loss probability. The RBPF is an effective sequential importance sampling algorithm by marginalizing out the loss process. A target tracking example is included to illustrate their effectiveness and shows the tradeoff between computation complexity and estimation accuracy of the proposed filters. © 2016

关键词： Kalman filters Importance sampling Linear systems State estimation Target tracking computation complexity Conditional loss probability Estimation problem Networked systems Particle filter Sensor measurements Sequential importance sampling Suboptimal filter

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A pseudo genetic algorithm

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NEURAL COMPUTING & APPLICATIONS 2010年第1期19卷 77-83页

作者： Chen, Qijian Zhong, Yuanchang Zhang, Xiaohong Chongqing Univ Coll Commun Engn Chongqing 630044 Peoples R China Chongqing Univ Coll Software Engn Chongqing 630044 Peoples R China

Random individual initialization tends to generate too many eccentric and homogeneous individuals which cause slow and premature convergence. It needs many operations (selection strategy, incest prevention and mutation) to fix, which consume too much computation and lose many good genes. The proposed complementary-parent strategy initializes every other pair of parents with dynamically or statically complementary chromosomes (such as 010101aEuro broken vertical bar 0101 and 101010aEuro broken vertical bar 1010). Crossover of every generation is only performed between the offspring from the same parents, during which the parents are completely replaced by their own children. Higher population diversity is got without gene lost at all, by which search ability is enhanced. Incest prevention, selection strategies and mutation are unnecessary and consequently cancelled (so it is named pseudo genetic algorithm). As indicated by the simulation results, the speed of elitist search is accelerated greatly and computation complexity is reduced by half.

关键词： Pseudo genetic algorithm Complementaryparent strategy Dynamically complementary parents Statically complementary parents Population diversity Search ability computation complexity Homogeneous individuals

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Model aggregation for doubly divided data with large size and large dimension

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computationAL STATISTICS 2023年第1期38卷 509-529页

作者： He, Baihua Liu, Yanyan Yin, Guosheng Wu, Yuanshan Wuhan Univ Sch Math & Stat Wuhan 430072 Hubei Peoples R China Univ Hong Kong Dept Stat & Actuarial Sci Pokfulam Rd Hong Kong Peoples R China Zhongnan Univ Econ & Law Sch Stat & Math Wuhan 430073 Hubei Peoples R China

Massive data are often featured with high dimensionality as well as large sample size, which typically cannot be stored in a single machine and thus make both analysis and prediction challenging. We propose a distributed gridding model aggregation (DGMA) approach to predicting the conditional mean of a response variable, which overcomes the storage limitation of a single machine and the curse of high dimensionality. Specifically, on each local machine that stores partial data of relatively moderate sample size, we develop the model aggregation approach by splitting predictors wherein a greedy algorithm is developed. To obtain the optimal weights across all local machines, we further design a distributed and communication-efficient algorithm. Our procedure effectively distributes the workload and dramatically reduces the communication cost. Extensive numerical experiments are carried out on both simulated and real datasets to demonstrate the feasibility of the DGMA method.

关键词： Communication efficiency computation complexity Distributed algorithm Greedy algorithm High dimension One-shot approach Prediction Storage ability

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EFFICIENT PARALLEL ALGORITHMS CAN BE MADE ROBUST

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DISTRIBUTED COMPUTING 1992年第4期5卷 201-217页

作者： KANELLAKIS, PC SHVARTSMAN, AA DIGITAL EQUIPMENT CORP HUDSONMA 01749

The efficient parallel algorithms proposed for many fundamental problems, such as list ranking, integer sorting and computing preorder numberings on trees, are very sensitive to processor failures. The requirement of efficiency (commonly formalized using Parallel-time x Processors as a cost measure) has led to the design of highly tuned PRAM algorithms which, given the additional constraint of simple processor failures, unfortunately become inefficient or even incorrect. We propose a new notion of robustness, that combines efficiency with fault tolerance. For the common case of fail-stop errors, we develop a general and easy to implement technique to make robust many efficient parallel algorithms, e.g., algorithms for all the problems listed above. More specifically, for any dynamic pattern of fail-stop errors on a CRCW PRAM with at least one surviving processor, our method increases the original algorithm cost by at most a log2 multiplicative factor. Our technique is based on a robust solution of the problem of Write-All, i.e., using P processors, write 1's in all locations of an N-sized array. In addition we show that at least a log/log log multiplicative overhead will be incurred for certain patterns of failures by any algorithm that implements robust solutions to Write-All with P = N. However, by exploiting parallel slackness, we obtain an optimal cost algorithm when P less-than-or-equal-to N/log2 N - log N log log N.

关键词： PARALLEL computation FAULT TOLERANCE computation complexity LOWER BOUNDS ROBUST ALGORITHMS

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DPSynthesizer: Differentially Private Data Synthesizer for Privacy Preserving Data Sharing

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PROCEEDINGS OF THE VLDB ENDOWMENT 2014年第13期7卷 1677-1680页

作者： Li, Haoran Xiong, Li Zhang, Lifan Jiang, Xiaoqian Emory Univ Math & Comp Sci Dept Atlanta GA 30322 USA Univ Calif San Diego Biomed Informat Div La Jolla CA USA

Differential privacy has recently emerged in private statistical data release as one of the strongest privacy guarantees. Releasing synthetic data that mimic original data with differential privacy provides a promising way for privacy preserving data sharing and analytics while providing a rigorous privacy guarantee. However, to this date there is no open-source tools that allow users to generate differentially private synthetic data, in particular, for high dimensional and large domain data. Most of the existing techniques that generate differentially private histograms or synthetic data only work well for single dimensional or low-dimensional histograms. They become problematic for high dimensional and large domain data due to increased perturbation error and computation complexity. We propose DPSynthesizer, a toolkit for differentially private data synthesization. The core of DPSynthesizer is DPCopula designed for high dimensional and large-domain data. DPCopula computes a differentially private copula function from which synthetic data can be sampled. Copula functions are used to describe the dependence between multivariate random vectors and allow us to build the multivariate joint distribution using one-dimensional marginal distributions. DP Synthesizer also implements a set of state-of-the-art methods for building differentially private histograms, suitable for low-dimensional data, from which synthetic data can be generated. We will demonstrate the system using DPCopula as well as other methods with various data sets and show the feasibility, utility, and efficiency of various methods.

关键词： Data privacy Graphic methods computation complexity Differential privacies Joint distributions Marginal distribution Perturbation error Privacy preserving State of the art methods Statistical datas

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Improved Semi-supervised Clustering Algorithm Based on Affinity Propagation

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Journal of Donghua University(English Edition) 2015年第1期32卷 125-131页

作者：金冉刘瑞娟李晔锋寇春海 College of Information Science and Technology Donghua University College of Computer Science and Technology Zhejiang Wanli University College of Science Donghua University

A clustering algorithm for semi-supervised affinity propagation based on layered combination is proposed in this paper in light of existing flaws. To improve accuracy of the algorithm,it introduces the idea of layered combination, divides an affinity propagation clustering( APC) process into several hierarchies evenly,draws samples from data of each hierarchy according to weight,and executes semi-supervised learning through construction of pairwise constraints and use of submanifold label mapping,weighting and combining clustering results of all hierarchies by combined promotion. It is shown by theoretical analysis and experimental result that clustering accuracy and computation complexity of the semi-supervised affinity propagation clustering algorithm based on layered combination( SAP-LC algorithm) have been greatly improved.

关键词： semi-supervised clustering affinity propagation(AP) layered combination computation complexity combined promotion

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On the efficiency of solving Boolean polynomial systems with the characteristic set method

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JOURNAL OF SYMBOLIC computation 2021年 103卷 66-94页

作者： Huang, Zhenyu Sun, Yao Lin, Dongdai Chinese Acad Sci Inst Informat Engn SKLOIS Beijing 100093 Peoples R China

An improved characteristic set algorithm for solving Boolean polynomial systems is proposed. This algorithm is based on the idea of converting all the polynomials into monic ones by zero decomposition, and using additions to obtain pseudo-remainders. Three important techniques are applied in the algorithm. The first one is eliminating variables by new generated linear polynomials. The second one is optimizing the strategy of choosing polynomial for zero decomposition. The third one is to compute add-remainders to eliminate the leading variable of new generated monic polynomials. By analyzing the depth of the zero decomposition tree, we present some complexity bounds of this algorithm, which are lower than the complexity bounds of previous characteristic set algorithms. Extensive experimental results show that this new algorithm is more efficient than previous characteristic set algorithms for solving Boolean polynomial systems. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Boolean polynomial system Characteristic set method computation complexity Zero decomposition Cryptanalysis

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