The problem of approximating a function from its samples for an incompletely determined model (for example, if a system of approximating functions is not completely known) is discussed and some properties of the approximation are found. The case with defects in the samples in the form of contamination or missing data is considered. The problem of how to select the functions to be used in the model is studied under different conditions. Some qualitative effects caused by defects in the samples are ascertained. This is only a summary of a paper to be published in full elsewhere.