Target Function
See: Predictive Model, Function Approximation.
References
2020
- (Wikipedia, 2020) ⇒ https://en.wikipedia.org/wiki/Function_approximation Retrieved:2020-3-26.
- In general, a function approximation problem asks us to select a function among a well-defined classthat closely matches ("approximates") a target function in a task-specific way. The need for function approximations arises in many branchesof applied mathematics, and computer science in particular .
One can distinguish two major classes of function approximation problems:
First, for known target functions approximation theory is the branch of numerical analysis that investigates how certain known functions (for example, special functions) can be approximated by a specific class of functions (for example, polynomials or rational functions) that often have desirable properties (inexpensive computation, continuity, integral and limit values, etc.).
Second, the target function, call it g, may be unknown; instead of an explicit formula, only a set of points of the form (x, g(x)) is provided. Depending on the structure of the domain and codomain of g, several techniques for approximating g may be applicable. For example, if g is an operation on the real numbers, techniques of interpolation, extrapolation, regression analysis, and curve fitting can be used. If the codomain (range or target set) of g is a finite set, one is dealing with a classification problem instead.
To some extent, the different problems (regression, classification, fitness approximation) have received a unified treatment in statistical learning theory, where they are viewed as supervised learning problems.
- In general, a function approximation problem asks us to select a function among a well-defined classthat closely matches ("approximates") a target function in a task-specific way. The need for function approximations arises in many branchesof applied mathematics, and computer science in particular .
1997
- (Mitchell, 1997) ⇒ Tom M. Mitchell. (1997). “Machine Learning." McGraw-Hill.
- QUOTE: 1.2.2 Choosing the Target Function. The next design choice is to determin exasctly what type of knowledge will be learned and how this will be used by the performance program. ... Let us call this 'target function [math]\displaystyle{ V }[/math] and again use the notation [math]\displaystyle{ V }[/math] : [math]\displaystyle{ B }[/math] → R to denote that [math]\displaystyle{ V }[/math] maps any legal board state from the set [math]\displaystyle{ B }[/math] to some real value. We intend for this target function [math]\displaystyle{ V }[/math] to assign higher scores to better board states ... Thus, we have reduced the learning task in this case to the problem of discover an operational description of the ideal target function V. It may be very difficult in general to learn such an operational form of [math]\displaystyle{ V }[/math] perfectly. In fact we often expect learning algorithms to acquire only some approximation to the target function, and for this reason the process of learning the target function is often called function approximation. In the current discussion we will use the symbol V^ to refer to the function that is actually learned by our program, to distinguish it from the ideal target function V.
- QUOTE: The key point in the above paragraph is that a lazy learning has the option of (implicitly) representing the target function by a combination of many local approximations, whereas an eager learner must commit at training time to a single global approximation. The distinction between eager and lazy learning is thus related to the distinction between global and local approximations to the target function.