# Value-Function Fitting Task

A Value-Function Fitting Task is a function creation task and that accepts a parametric function family and a training dataset and is required to produce a fitted function according to some fitness function.

**AKA:**Function Approximation.**Context:****Input:**a Numerically-Labeled Training Dataset; a Function Family; and an Objective Measure.**output:**a Fitted Function.- It can range from being a Univariate Function Fitting Task to being a Multivariate Function Fitting Task.
- It can range from being a Supervised Function Fitting Task to being an Unsupervised Function Fitting Task.
- It can range from being a Parametric Function Fitting Task to being a Non-Parametric Function Fitting Task.
- It can range from being a Manual Function Fitting Task to being an Automated Function Fitting Task.
- It can range from being a Linear Function Fitting Task to being a Non-Linear Function Fitting Task (such as polynomial fitting).
- It can be solved by a Function Fitting System (that implements a function fitting algorithm).
- It can support tasks such as: Interpolation, Extrapolation, ...

**Example(s):****Counter-Example(s):****See:**Metric Space Optimization, Numerical Approximation, Taylor Series, Numerical Analysis, Approximation Theory, Smoothing, Mollifier, Model-based Learning.

## References

### 2015

- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/function_approximation Retrieved:2015-6-14.
- The need for '
*function approximations arises in many branches of applied mathematics, and computer science in particular. In general, a function approximation problem asks us to select a function among a well-defined class that closely matches ("approximates") a target function in a task-specific way.*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. A related problem online time series approximation^{[1]}is to summarize the data in one-pass and construct an approximate representation that can support a variety of timeseries queries with bounds on worst-case error.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.

- The need for '

- ↑ Gandhi, Sorabh, Luca Foschini, and Subhash Suri. “Space-efficient online approximation of time series data: Streams, amnesia, and out-of-order." Data Engineering (ICDE), 2010 IEEE 26th International Conference on. IEEE, 2010.