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When using interpolation, the size of the lookup table can be reduced by using nonuniform sampling, which means that where the function is close to straight, we use few sample points, while where it changes value quickly we use more sample points to keep the approximation close to the real curve.
First, with a data sample of length n, the data analyst may run the regression over only q of the data points (with q < n), holding back the other n – q data points with the specific purpose of using them to compute the estimated model’s MSPE out of sample (i.e., not using data that were used in the model estimation process).
The bias–variance decomposition forms the conceptual basis for regression regularization methods such as LASSO and ridge regression.Regularization methods introduce bias into the regression solution that can reduce variance considerably relative to the ordinary least squares (OLS) solution.
For instance, if =, the true value of is approximately , but using the naive logarithmic formula in IEEE 754 binary64 arithmetic may give _, with only five out of sixteen digits correct and the remainder (underlined) all incorrect.
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