Machine Learning - Simplified

 Polynomial Curve Fitting Polynomial curve fitting is a statistical technique used to model a relationship between a dependent variable and one or more independent variables using a polynomial equation . This approach is particularly useful when the relationship between the variables is non-linear and cannot be adequately described by a simple linear model. Example Create a dataset with one independent variable x and a dependent variable denoted by sin(2πx). x 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 sin(2 πx ) 0 0.5878 0.9511 0.9511 0.5878 0 -0.5878 -0.9511 -0.9511 -0.5878 0   x   1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 sin(2 πx ) ...

  Consider the following dataset: Training Dataset A person named Aldo Enjoys sport under the given conditions. Concept The concept to learn is when does a person Aldo enjoy sports. The answer is Boolean : Yes – enjoys sport or No – doesn’t enjoy sport. Hypothesis Space The actual space in which we search is huge. So let us restrict to a hypothesis representation of the search space with only the attributes in the training dataset. The easiest way to represent is by taking the conjunction of all the attributes. That is, <sunny, warm, normal, strong, warm, same, yes> is a hypothesis represented by <x,c(x)>. Here c(x) is ‘yes’. We say that if it is, Sunny and warm and normal and strong and warm and same, then Aldo enjoys sports. Notations We assume the following notations as before: 0 – most specific and implies that the attribute should have no value. Attribute name – the given attributes in the table. Eg. sunny ? – the most generic where ...