Name
Abstract | ||
|---|---|---|
In discovery with real data, one is always working with approximations. Even without noise, one computes over a finite set
of unequally spaced numbers, approximating one’s values with this set. With noise, the values are even more uncertain. Along
with the ambiguity of the exact values of numbers, there exists Occam’s razor to prefer simpler equations. That is, if a straight
line will explain the data, then that is generally thought preferable to equations of higher power. It should be noted that
this preference is a choice, however, and does not always work [8]. The preference needs to be codified to be automated, but codifying simplicity is not straightforward [8]. Finally, there needs to be a quantitative way to measure the goodness of an equation after it is chosen. Function finding
is numeric induction, so there can never be certainty. But assigning a value to the inductive support provides a way to compare
results across tasks. Thus dis- covery of functional forms can be divided into three tasks: 1_ choosing a search technique
to find the set of best equations within the limitations of finite precision arithmetic and noise; 2_ choosing from among
the best equations based on some criteria that encodes preference; and 3_ choosing a metric for the inductive support of the
found equation
|
Year | DOI | Venue |
|---|---|---|
2000 | 10.1007/3-540-44418-1_21 | Discovery Science |
Keywords | Field | DocType |
functional form | Line (geometry),Discrete mathematics,Linear equation,Finite set,Existential quantification,Computer science,Quadratic equation,Algorithm,occam,Analytic geometry,Ambiguity,Calculus | Conference |
ISBN | Citations | PageRank |
3-540-41352-9 | 1 | 0.38 |
References | Authors | |
0 | 1 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Judith Ellen Devaney | 1 | 11 | 3.45 |