What is the difference between regression and classification, when we try to generate output for a training data set $x$?
[Math] the difference between regression and classification
machine learningregression
Related Solutions
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.
IMHO, the "actual meaning" is not a mathematical question. I.e., if you understand the technical aspects of the changes in the coefficients, then anything else is just kind of philosophy. Namely, in a classical regression analysis you assume that the "real" underlying model that explains a poverty rate ($Y$) is the GDP ($X$) that is given by $Y = \beta_0 +\beta_1X+\epsilon$. I.e., there is some linear function with a noise term $\epsilon$, where the assumptions on the noise term determines the best estimating procedure of $\beta_0$ and $\beta_1$. In this case $Y$ is called dependent variable, whilst $X$ is independent. So, you can say that you are assuming that the poverty rate depends on the GDP level. Hence, by controlling the GDP you can alter the poverty rate. While in $X = \beta_0 +\beta_1Y+\epsilon$, your reasoning is reversed. I.e., your underlying question is "how poverty rate effects the GDP?". In both ways you are essentially estimating a linear correlation between $X$ and $Y$. The only difference is in the way you post the question and how you interpret the results.
Best Answer
Regression: the output variable takes continuous values.
Classification: the output variable takes class labels.