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MAPE puts a heavier penalty on negative errors, < than on positive errors. [9] As a consequence, when MAPE is used to compare the accuracy of prediction methods it is biased in that it will systematically select a method whose forecasts are too low.
The earliest reference to a similar formula appears to be Armstrong (1985, p. 348), where it is called "adjusted MAPE" and is defined without the absolute values in the denominator. It was later discussed, modified, and re-proposed by Flores (1986).
When bootstrap aggregating is performed, two independent sets are created. One set, the bootstrap sample, is the data chosen to be "in-the-bag" by sampling with replacement.
Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
x erf x 1 − erf x; 0: 0: 1: 0.02: 0.022 564 575: 0.977 435 425: 0.04: 0.045 111 106: 0.954 888 894: 0.06: 0.067 621 594: 0.932 378 406: 0.08: 0.090 078 126: 0.909 ...
While the chosen value is an invalid result for this operation, it might be a valid input to followup operations. For example in Python str.find returns −1 if the substring is not found, [2] but −1 is a valid index (negative indices generally start from the end [3]).
Here x ≥ 0 means that each component of the vector x should be non-negative, and ‖·‖ 2 denotes the Euclidean norm. Non-negative least squares problems turn up as subproblems in matrix decomposition, e.g. in algorithms for PARAFAC [2] and non-negative matrix/tensor factorization. [3] [4] The latter can be considered a generalization of ...
Then the map : defined by () = (‖ ‖) is a smooth function that is positive on and vanishes off of . [1] For every , let = {| | : , …, =}, where this supremum is not equal to + (so is a non-negative real number) because () ¯ =, the partial derivatives all vanish (equal ) at any outside of , while on the compact set ¯, the values of each ...