Machine Learning: Lesson 1

Supervised Learning -> A set of training data (data that is given to be correct) is given and a program makes a prediction (extrapolation/interpolation). The prediction is a regression.

Unsupervised Learning -> A given data set consists of undetermined information. The goal is to create a program that will find a structure amongst the given data set. Structure can be a cluster. Clusters can be studied and programs can gather information about them that will allow data scientists to explore further.

Hypothesis Function -> $h_{\theta}(x)= \theta_0 + \theta_1\cdot x$ where h is the hypothesis function, $x$ is the input value for a given data set, and $\theta_0$ and $\theta_1$ are parameters that help compute the cost function. The hypothesis function describes a set of data using a regression so that supervised learning can be applied to such a set. Depending on the values substituted for the parameters, a minimum cost function can be calculated to find the best regression to fit any data set.

Cost Function -> is a univariate (or multivariate) function that takes a hypothesis function and a data set, returning a value that describes how well such a hypothesis function fit a given data set. Minimizing the cost function is a common task endowed upon data scientists so that supervised learning can be applied to a given data set.

Cost Function Formula -> $J_(\theta_1,\theta_2) = \frac{1}{2m}\sum_{i=0}^{N}(h_{\theta}(x^(i)) - y^(i))^2$

Where $m$ is the number of training data in a given data set and $i$ is the ith datum in a set of training data.

Gradient Descent Algorithm -> An algorithm that runs through a contour plot of a cost function with two or more parameters ($\left\{\theta_0,\theta_1,\theta_2,\dotsc,\theta_n\right\}$ and traverses the plot to find the local minimum. Depending on where the algorithm sets its starting point, a different minimum might be found.

Gradient Descent Algorithm Implementation -> /**Convergence is of type value returned by Cost Function, which ought to be the lowest point on a contour plot. If the current point is the smallest nearby, i.e. Cost Function is minimized, then end loop return the point of convergence.**/while(!convergence){for(int j = 1, j < n; j++){$\theta_j = \theta_j + \alpha \frac{\partial}{\partial \theta_j} J(\theta_0,\theta_1)$/**where $\alpha$ is the learning rate and $\frac{\partial}{\partial \theta_j}$ is the change in the position along the contour plot**/}}