Introduction to Machine Learning

Problem : Convert steps to distance.

Let us take a group of people from population, count their number of steps and convert it to distance. It can be likely done by :
                                         X = distance / no. of Steps

Let us assume that there is group of different people, so we take in consideration that it will be X1,X2,......,Xk. Let us assume the plot for the same is
                                 
                                 

Let us assume it is the estimate of the distribution in the population and we consider mean or the expected value as the solution to our problem. In X variable there is uncertainty because it is of different people.

The matrices that can be used to calculate dispersion are :
  • Variance
  • Standard Deviation
Reasons for dispersion according to problem can be :
  • depends on the individual on the basis like speed, height, Age etc.
  • depends on the way it is evaluated on the basis that Error associated with it or there could be noise in the measurement.
  • Any real world observation will have uncertainty with it.

Random Variable : It is a variable that has range and probability distribution associated with it where probability distribution is for all r belongs to R 
P(r) = x where x = [0,1] . Variables can be of two types : 
  • Categorical : It is the finite set.
Numerical : It has probability density function because of infinite set.

In machine learning, we have lot of data where we take data as sample and population is universe and through this we learn a process to mimic real world process. There is the function f to data and there is the function g which we learn and gives us  approximation to function f. Therefore, g approximates f for all x belongs to population.
                                           f(x) ~ g(x)
Sample  has to be representative of population. Sample should not be biased.

Uniform Random Sampling : When all the aspects of the object is included.

Machine learning happens on a sample but the function is desired to be applicable to the population, Therefore, it should be generalized and accurate. When we want to make databases we make data model for machine learning. For any process we find or learn function which is called generalization (induction).

When we find more cases similar to one we are going through is called case base reasoning. 

Sample of data is subset of population, where population is x1,x2,.....,xn that is set of random variables and q(x1,x2,.......,xn) is sample data. In general , from sample we want to learn function. We can add default to population where default can be 0 or 1.

Discriminative Model : It follows conditional probability where 
  P(default|x1,......,xn)

Generative Model : It follows joint probability distribution model where 
 P(x1,x2,......,xn,Y) / P(x1,x2,.....,xn) = P(Y|x1,x2,......,xn).

To learn function we need :
  • Data sample which is subset of population.
  • g which is the approximate function to f.
  • Search algorithm to find the function g(x).
  • Cost function to measure the goodness of the model.

Let us consider function is linear and functional form is :
        distance = m*no.of steps + c
where m,c are the parameters.

Cost function =(1/n)Σ(disti -f(stepi,m0c0))^2

Mathematically :

                β* = argβ min(1/n) Σyi - f(xi,β)

where β = m,c 
          yi = actual output value
           xi = predicted output value
       
  
 

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