HyperAI超神经

WeightIt is a relative concept. For a certain indicator, weight refers to the importance of the indicator in the overall evaluation.

In the evaluation process, weights are used to measure the importance of different aspects of the evaluation object so as to differentiate the role of each evaluation factor in the overall evaluation. That is, an evaluation without an end point is not an objective evaluation.

The basic formula of weight

The basic formula for finding the right is

${p\mathop{{}}\nolimits_{{i}}\text{ }=\text{ }\frac{{ \mu \mathop{{}}\nolimits^{{2}}}}{{m\mathop{{}}\nolimits_{{i}}\mathop{{}}\nolimits^{{2}}}}\text{ }{ \left( {i\text{ }=\text{ }1,\text{ }2,\text{ }…} \right) }}$

Where ${ \mu }$ is an arbitrary constant and ${m\mathop{{}}\nolimits_{{i}}}$ is the mean square error.

It can be seen that the weight is inversely proportional to the square of the mean error, that is, the higher the precision, the greater the weight. When ${m\mathop{{}}\nolimits_{{i}}\text{ }=\text{ }\mu}$ , ${p\mathop{{}}\nolimits_{{i}}\text{ }=\text{ }1}$ , so it is the mean error of the observation with weight equal to 1. The weight equal to 1 is usually called unit weight, and the observation with weight 1 is unit weight observation. ${ \mu }$ is the mean error of the unit weight observation, which is referred to as unit weight mean error for short.

The proportional relationship between the weights of each observation can be written as:

${p\mathop{{}}\nolimits_{{1}}\text{ }:\text{ }p\mathop{{}}\nolimits_{{2}}\text{ }:\text{ }⸳⸳⸳\text{ }:\text{ }p\mathop{{}}\nolimits_{{n}}\text{ }=\text{ }\frac{{ \mu \mathop{{}}\nolimits^{{2}}}}{{m\mathop{{}}\nolimits_{{1}}\mathop{{}}\nolimits^{{2}}}}\text{ }:\text{ }\frac{{ \mu \mathop{{}}\nolimits^{{2}}}}{{m\mathop{{}}\nolimits_{{2}}\mathop{{}}\nolimits^{{2}}}}\text{ }:\text{ }⸳⸳⸳\text{ }:\text{ }\frac{{ \mu \mathop{{}}\nolimits^{{2}}}}{{m\mathop{{}}\nolimits_{{n}}\mathop{{}}\nolimits^{{2}}}}\text{ }=\text{ }\frac{{1}}{{m\mathop{{}}\nolimits_{{1}}\mathop{{}}\nolimits^{{2}}}}\text{ }:\text{ }\frac{{1}}{{m\mathop{{}}\nolimits_{{2}}\mathop{{}}\nolimits^{{2}}}}\text{ }:\text{ }⸳⸳⸳\text{ }:\text{ }\frac{{1}}{{m\mathop{{}}\nolimits_{{n}}\mathop{{}}\nolimits^{{2}}}}}$

It can be seen that the ratio of the weights of a set of observations is equal to the ratio of the reciprocals of their mean square errors.