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The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others.
It is a measure used to evaluate the performance of regression or forecasting models. It is a variant of MAPE in which the mean absolute percent errors is treated as a weighted arithmetic mean. Most commonly the absolute percent errors are weighted by the actuals (e.g. in case of sales forecasting, errors are weighted by sales volume). [3]
The idea of the kernel average smoother is the following. For each data point X 0 , choose a constant distance size λ (kernel radius, or window width for p = 1 dimension), and compute a weighted average for all data points that are closer than λ {\displaystyle \lambda } to X 0 (the closer to X 0 points get higher weights).
Cost-weighted fractions incorrect could compare expected costs of misclassification for different methods. The diagnostic odds ratio (DOR) can be a more useful overall metric, which can be defined directly as (TP×TN)/(FP×FN) = (TP/FN)/(FP/TN), or indirectly as a ratio of ratio of ratios (ratio of likelihood ratios, which are themselves ratios ...
According to David Salsburg, the algorithms used in kernel regression were independently developed and used in fuzzy systems: "Coming up with almost exactly the same computer algorithm, fuzzy systems and kernel density-based regressions appear to have been developed completely independently of one another."
For both classification and regression, a useful technique can be to assign weights to the contributions of the neighbors, so that nearer neighbors contribute more to the average than distant ones. For example, a common weighting scheme consists of giving each neighbor a weight of 1/ d , where d is the distance to the neighbor.
A weighted average, or weighted mean, is an average in which some data points count more heavily than others in that they are given more weight in the calculation. [6] For example, the arithmetic mean of 3 {\displaystyle 3} and 5 {\displaystyle 5} is 3 + 5 2 = 4 {\displaystyle {\frac {3+5}{2}}=4} , or equivalently 3 ⋅ 1 2 + 5 ⋅ 1 2 = 4 ...
GWA (general weighted average; similar to GPA) is a representation (often numerical) of the overall scholastic standing of students used for evaluation. GWA is based on the grades in all subjects taken at a particular level including subjects taken outside of the curriculum.