Interpolation and extrapolation

(22nd-May-2020)

• For cases in which there is a natural interpretation of "between," such as where the prediction is about time or space, interpolation involves making a prediction between cases for which there are data. Extrapolation involves making a prediction that goes beyond the seen examples. Extrapolation is usually much more inaccurate than interpolation. For example, in ancient astronomy, the Ptolemaic system and heliocentric system of Copernicus made detailed models of the movement of solar system in terms of epicycles (cycles within cycles). The parameters for the models could be made to fit the data very well and they were very good at interpolation; however, the models were very poor at extrapolation. As another example, it is often easy to predict a stock price on a certain day given data about the prices on the days before and the days after that day. It is very difficult to predict the price that a stock will be tomorrow, and it would be very profitable to be able to do so. An agent must be careful if its test cases mostly involve interpolating between data points, but the learned model is used for extrapolation.