ABSTRACT
There are many contexts in which this assumption is unrealistic. For instance, if we take a photograph with a digital camera, we receive an n×m grid of pixel color values sampling the continuum of light coming into the camera lens. We might think of a photograph as a continuous function from image position (x, y) to color (r, g, b), but in reality we only know the image value at nm separated locations on the image plane. Similarly, in machine learning and statistics, often we only are given samples of a function at points where we collected data, and we must interpolate to have values elsewhere; in a medical setting we may monitor a patient’s response to different dosages of a drug but must predict what will happen at a dosage we have not tried explicitly.
