# What is the difference between Curve Fitting and Regression(Machine Learning)?

I know that Machine Learning regression algorithms try to find the function of the data. That is, if we have 1000 data points (x,y), to find a general continuous function that follows the trends of the data and which can provide estimated values y for other x that we do not know their actual value y.

But curve fitting doesn't do very similar thing? I mean, yes, we may have a function this time and not only those 1000 points, but it also tries to find a general continuous function that follows the trends of the data.

Therefore what is the most actual difference between the two? The algorithms that work for Regression in ML can't they be applied at curve fitting as well?

Update 28 Apr 14

I am reading this paper and it says that it uses Curve fitting and Regression techniques. What is actually their difference? What algorithms/techniques can be considered as Curve Fitting and what as Regression?

• I've looked through the paper you added. It concerns a curve-fitting/parameter estimator for each of several simple data models, with the aim of providing a visualization of the order of growth of algorithmic complexity with the size of input data. I'm unclear what your Question is, if it relates to this paper. – hardmath Apr 28 '14 at 22:37
• The link to that paper you asked about is broken. You'd be in the best position to fix the link with a new location for the paper (I think I was able to find it elsewhere on the Web, but it would be a chance to clear up any question you have about the paper per my previous Comment). – hardmath Dec 27 '17 at 14:14

## 1 Answer

Yes, curve fitting and "machine learning" regression both involving approximating data with functions. Various algorithms of "machine learning" could be applied to curve fitting, but in most cases these do not have the efficiency and accuracy of more general curve fitting algorithms, finding a choice of parameters for a mathematical model which gives "best fit" (variously defined) to a data set.

In curve fitting we are often interested in parameters for a mathematical model based on a theory of cause and effect underlying the data, which may include random or systematic errors.

An attraction of "machine learning" is to give machines a task of "discovering" information through data mining. E.g. machine learning algorithms might be applied to optical character recognition.

• I suggest a change in your subject line, to say "between curve-fitting and machine learning". This is motivated by a somewhat different sense of regression in statistics. Approximation theory is pervasive in analysis. – hardmath Mar 8 '14 at 14:38
• ooohhh!!! Thanks a lot hardmath. Didn't know that. I will change that now. I'll also accept your answer as best answer, as it is very helpful. I usually do that ~24hrs after I post the question. – K. Stasko Mar 8 '14 at 14:42
• Note that you can also change your Accepted Answer choice, in any case. – hardmath Mar 8 '14 at 14:53
• After a long time, Hi hardmath :) Is it possible to explain me a little more your answer, to fit the update I wrote at the question? – K. Stasko Apr 28 '14 at 19:06
• I'll take a look when I get off from work. – hardmath Apr 28 '14 at 19:35