查询词典 Chebyshev inequality

Through above study, the theoretical analysis of the inherent fault tolerance of feed-forward neural networks has been extended from hard-limit activation functions to differentiable activation functions; 2. By using above method, fault tolerance of discrete Hopfield feedback neural networks have been also analyzed. It means that the above method can be applied not only for feed-forward neural networks but also for feedback neural networks; 3. For the feed-forward neural network with the Sigmoid activation function, Chebyshev Inequality method was presented.

这项研究将以前仅限于对硬限幅作用函数前向神经网络固有容错性能的理论分析推广到具有可微作用函数的前向神经网络； 2 针对离散型Hopfield反馈神经网络，利用上面提出的方法，对其同样进行了容错性分析，得出许多有用的结论和计算公式，说明上面提出的方法不仅适用于前向神经网络，同时也适用于反馈神经网络； 3 针对具有Sigmoid作用函数的前向神经网络提出了一种切比雪夫不等式法。

Markov's inequality and Chebyshev's inequality are very important in probabilistic theory.

Markov不等式和Chebyshev不等式是概率论中两个重要的不等式。

In addition, anomaly detection can be implemented by Chebyshev inequality in raw alert series, filtered alert series, frequency series of alerts. Then the capability of detecting specific security events can be improved.

另外还采用切比雪夫公式对告警时间序列、误告警去除后的时间序列、时频转换后的频域序列进行异常检测，提高了检测特定类型安全事件的能力。

Aiming at the problems of over-fitting and generalization for neural networks, the locally most entropic colored Gaussian joint input-output probability density function estimate is studied, and a new method by means of Chebyshev inequality is proposed to self-revise respectively according to every cluster.

针对神经网络的过拟合和泛化能力差的问题，研究了样本数据的输入输出混合概率密度函数的局部最大熵密度估计，提出了运用Chebyshev不等式的样本参数按类分批自校正方法，以此估计拉伸样本集，得到新的随机扩充训练集。

I. d. Bernoulli random variables. First, we can get the upper bound with order from Chebyshev inequality. Second, a better upper bound was gotten with the new inequalities, which can fasten the convergence rate.

并对服从两点分布的独立随机变量X1，X2，…，X进行研究，首先利用Chebyshev不等式得到随机变量偏离方差ES的上界，但它只有阶的收敛速度，然后利用新的不等式得到一个新的上界，它有更快的收敛速度，这在探讨收敛速度时有着重要的理论意义。

Moreover, with its help people can also evaluate the fault-tolerant performance of ANN. In this paper, Chebyshev Inequality method, as a kind of evaluating thought, was firstly concerned in the faulttolerance analysis of ANN; 4. The variation of faulty behaviors of ANNs during the course of learning was studied by taking the discrete Hopfield neural network and Hebb learning algorithm as examples.

这种方法首次将切比雪夫不等式引入人工神经网络容错性分析当中，从而提出了对人工神经网络容错性分析采用估算的思想； 4 以离散型Hopfield神经网络和Hebb学习算法为例，着重研究了在学习过程中人工神经网络故障性能的变化。

Given a finite training sample set, according to the proposal of establishing a Local Most Entropy probability density function to estimate the number of cluster a method for estimating 〓 is proposed, where a complicated method based on Maximum Likelihood Cross-Validation is replaced by Chebyshev inequality.

为改善BP算法的收敛速度慢、易陷入局部最小的问题，提出了带一类非线性特性动量项的变步长BP算法，构造了一个能自适应升降温的动量项非线性强度函数，在编程中又采用了有条件引入非线性特性动量项的措施，大大提高了搜索过程跳出局部极小、快速稳定收敛的能力。

Based on this thought, in this thesis, the alternation theorem is first extended to the Chebyshev approximation problems with inequality constraints, and then two algorithms are devised for designing linear phase FIR filters with inequality constraints in Chebyshev sense according to the extended theorem.

L.J.Karam和McClellan在文献[20]中把交错点组定理扩展到复数域，并提出了求解复系数FIR滤波器的复Remez算法，但由于此扩展定理只是一个充分条件，所以此算法不能保证得到最优解。在文献[23]中，他们对复Remez算法进行了完善，使其收敛到最优解。

Second, On the basis of analysis of density distribution of sequence points on the chaotic orbit of one-dimension chaotic mapping, a mutative interval chaotic optimization algorithm is presented in search for the solution optimums of the non-linear constrained problems with multi-variables and multi-peak values. With the objective function probability measurement approaching a limit 1, the convergence of the algorithm on the global optimal solution is proofed by aid of Chebyshev inequality.

二、基于一维混沌映射混沌点集的概率测度分析，提出了一种适于解决多变量多峰值非线性约束问题的新的混沌优化算法——变区间混沌优化算法，并应用切比雪夫不等式论证了算法依概率收敛于全局最优解。

In this paper, we generalized the reverse Shebyshev inequality and obtained the integral inequality of two vector function s, whose monotone of correspondence elements is reverse.

推广了反向Chebyshev不等式，得到了对应分量的单调性相反的连续向量函数的积分不等式和模的单调性相反的连续向量函数的积分不等式。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。