second-order statistics

二阶统计量是指在概率论和统计学中，对于一个随机变量X，其二阶矩是指E(X^2)，即X的平方的期望值。在机器学习中，二阶统计量通常指的是权重相关矩阵，它是一个矩阵，其中每个元素表示权重向量中两个不同维度之间的相关性。在对抗训练中，考虑权重的二阶统计可以提高模型的鲁棒性和泛化能力。具体来说，通过引入权重相关矩阵，可以放宽所有权重在统计上独立的不合理假设，从而更好地捕捉权重之间的相关性。此外，二阶统计量还可以用于计算空间区域内特征的二阶统计量，从而提高模型的识别能力。

相关问题

Next, the first order statistics of the no. 36 kernel and the second order statistics of the no. 28 kernel were calculated; these refer to the designs of the no. 13,751 and no. 13,768 features. The characteristics of the filter response were reflected in the two parameters. As the second order statistics of the no. 28 kernel show, the no. 107 filter response of the wild-type tumor was more internally complicated and had more texture information. As the first order statistics of the no. 36 kernel show, the no. 107 filter response of the mutation-bearing tumors had lower intensity and was more gathered around the no. 36 kernel (the no. 36 kernel had a mean value of −0.1352 and a variance of 0.0055). Thus, the prediction based on CNN features clearly provided good results. Indeed, the two types of tumors have significantly different responses in deep filter banks. 解释

这段文字进一步解释了第107个深度滤波器的响应特征。通过计算第36个内核的一阶统计量和第28个内核的二阶统计量，得到了特征13,751和13,768的设计。这两个特征中反映了滤波器响应的特征。通过第28个内核的二阶统计量可以看出，野生型肿瘤的第107个滤波器响应更加内部复杂，具有更多的纹理信息。而通过第36个内核的一阶统计量可以看出，携带IDH1基因突变的肿瘤的第107个滤波器响应强度较低，并且更集中在第36个内核周围（第36个内核的平均值为-0.1352，方差为0.0055）。因此，基于CNN特征的预测提供了良好的结果。实际上，这两种肿瘤在深度滤波器组中的响应有显著的差异。