随机权分布对极限学习机性能影响的实验研究

极限学习机是一种训练单隐含层前馈神经网络的算法,它随机初始化输入层的权值和隐含层结点的偏置,用分析的方法确定输出层的权值。极限学习机具有学习速度快、泛化能力强的特点。很多研究都用服从[-1,1]区间均匀分布的随机数初始化输入层权值和隐含层结点的偏置,但没有对这种随机初始化合理性的研究。用实验的方法对这一问题进行了研究,分别研究了随机权服从均匀分布、高斯分布和指数分布对极限学习机性能的影响。研究发现随机权的分布对极限学习机的性能的确有影响,对于不同的问题或不同的数据集,服从[-1,1]区间均匀分布的随机权不一定是最优的选择。研究结论对从事极限学习机研究的人员具有一定的借鉴作用。

方差估计的随机加权分布的渐近展开——非独立同分布情形

设X_1,…,X_n是一组独立的随机变量序列,设EX_i=0,VarZ_i=μ_2,i=1,2,…,n,其中μ_2是待估参数。当X_i,i=1,2,…n给定后,分别用D_n=sum from i=1 to n (V_i(X_i-X)~2)-(1/n) sum from i=1 to n (X_i-X)~2及U_n=sum from i=1 to n (V_i(X_i-sum from i=1 to n V_iX_i)~2)-(1/n) sum from i=1 to n (X_i-X)~2两种形式的随机加权分布来逼近T_n=(1/n)sum from i=1 to n (X_i-X)~2-μ_2的分布,这里(V_1,…,V_n)是服从Dirichlet分布D(4,…,4)的随机向量。若记F_n是T_n/(VarT_n^(1/2))的分布,F_n~*,G_n~*分别是给定X_1,…,X_n条件下,D_n/(Var~*D_n^(1/2))和U_n/(Var~*U_n^(1/2))的条件分布。Var~*是关于X_1,…,X_n的条件方差。则在一定的条件下,对几乎所有的样本序列X_1,…,X_n (i)lim n^(1/2)(n→∞) sup |F_n~*(y)-F_n(y)|=0 (-∞<y<∞) (ii)lim n^(1/2)(n→∞) sup |G_n~*(y)-F_n(y)|=0 (-∞<y<∞)

RANDOM WEIGHTING METHOD FOR CENSORED REGRESSION MODEL

Rao and Zhao (1992) used random weighting method to derive the approximate distribution of the M-estimator in linear regression model.In this paper we extend the result to the censored regression model (or censored “Tobit” model).

Strong Convergence for Weighted Sums of Negatively Associated Arrays

Let {Xni} be an array of rowwise negatively associated random variables and Tnk=k∑i=1 i^a Xni for a ≥ -1, Snk =∑｜i｜≤k Ф（i/nη）1/nη Xni for η∈（0,1],where Ф is some function. The author studies necessary and sufficient conditions of ∞∑n=1 AnP（max 1≤k≤n｜Tnk｜〉εBn）〈∞ and ∞∑n=1 CnP（max 0≤k≤mn｜Snk｜〉εDn）〈∞ for all ε 〉 0, where An, Bn, Cn and Dn are some positive constants, mn ∈ N with mn /nη →∞. The results of Lanzinger and Stadtmfiller in 2003 are extended from the i.i.d, case to the case of the negatively associated, not necessarily identically distributed random variables. Also, the result of Pruss in 2003 on independent variables reduces to a special case of the present paper; furthermore, the necessity part of his result is complemented.

Weighted Scaling in Non-growth Random Networks

We propose a weighted model to explain the self-organizing formation of scale-free phenomenon in nongrowth random networks. In this model, we use multiple-edges to represent the connections between vertices and define the weight of a multiple-edge as the total weights of all single-edges within it and the strength of a vertex as the sum of weights for those multiple-edges attached to it. The network evolves according to a vertex strength preferential selection mechanism. During the evolution process, the network always holds its totM number of vertices and its total number of single-edges constantly. We show analytically and numerically that a network will form steady scale-free distributions with our model. The results show that a weighted non-growth random network can evolve into scMe-free state. It is interesting that the network also obtains the character of an exponential edge weight distribution. Namely, coexistence of scale-free distribution and exponential distribution emerges.