From the available database, we have some inputs x (i) and corresponding to these inputs, there are outputs y(i). There is some correlation made between inputs and outputs which is also known as algorithm. To put this simple through example, let’s say user throughput is varying linearly with SINR in 5G. So, there is some correlation made basis the available data (collected in RAN controller from O-DU/O-CU) and this correlation/algorithm derived is – Throughput = θ0​ *SINR+ θ1​. There are two constant values (θ0​ and θ1​) which when combined with any new input SINR value x(n) it gives throughput y(n) as an output accurately (almost). Above linear equation (algorithm) is a model. This is an example of very simple model (algorithm). It could be complicated with multiple variables and constant values.

To establish notation for future use, we’ll use x^{(i)}x(i) to denote the “input” variables (living area in this example), also called input features, and y^{(i)}y(i) to denote the “output” or target variable that we are trying to predict (price). A pair (x^{(i)} , y^{(i)} )(x(i),y(i)) is called a training example, and the dataset that we’ll be using to learn—a list of m training examples (x(i),y(i));i=1,…,m—is called a training set. Note that the superscript “(i)” in the notation is simply an index into the training set and has nothing to do with exponentiation. We will also use X to denote the space of input values, and Y to denote the space of output values.

To describe the supervised learning problem slightly more formally, our goal is, given a training set, to learn a function h : X → Y so that h(x) is a “good” predictor for the corresponding value of y. For historical reasons, this function h is called a hypothesis. Seen pictorially, the process is therefore like this:

When the target variable that we’re trying to predict is continuous, such as in housing example, we call the learning problem a regression problem. When y can take on only a small number of discrete values (such as if, given the living area, we wanted to predict if a dwelling is a house or an apartment, say), we call it a classification problem.

How model is tuned –

Above model once made initially, it needs to be trained time to time to predict outcome better. That means there would be more accuracy and less error (less difference between predicted value and actual value). This error is defined by a term cost function.

Cost Function

We can measure the accuracy of our hypothesis function by using a cost function (J). This takes an average difference (a fancier version of an average) of all the results of the hypothesis(h) with inputs from x’s and the actual output y’s. i=1,…,m—is a training set (so there are m number of inputs or outputs)

To break it apart, it is half of mean square of difference between predicated and actual value.

This function is otherwise called the “Squared error function”, or “Mean squared error”.

To make this cost function minimum (closer to zero), there is another function known as Gradient Descent, which plays a major role in tuning cost function.

Gradient Descent

So, we have our hypothesis function and we have a way of measuring how well it fits into the data. Now we need to estimate the parameters in the hypothesis function. That’s where gradient descent comes in.

Imagine that we graph our hypothesis function based on its fields​ (actually we are graphing the cost function as a function of the parameter estimates). We are not graphing x and y itself, but the parameter range of our hypothesis function and the cost resulting from selecting a particular set of parameters.

We put θ0​ on the x axis and θ1​ on the y axis, with the cost function on the vertical z axis. The points on our graph will be the result of the cost function using our hypothesis with those specific theta parameters. The graph below depicts such a setup.

We will know that we have succeeded when our cost function is at the very bottom of the pits in our graph, i.e. when its value is the minimum. The red arrows show the minimum points in the graph.

The way we do this is by taking the derivative (the tangential line to a function) of our cost function. The slope of the tangent is the derivative at that point and it will give us a direction to move towards. We make steps down the cost function in the direction with the steepest descent. The size of each step is determined by the parameter α, which is called the learning rate. This step size (or learning rate) needs to be accurate.

For example, the distance between each ‘star’ in the graph above represents a step determined by our parameter α. A smaller α would result in a smaller step and a larger α results in a larger step. The direction in which the step is taken is determined by the partial derivative of J(θ0, θ1​). Depending on where one starts on the graph, one could end up at different points. The image above shows us two different starting points that end up in two different places.