Introduction to Machine Learning(Part-4)

Training Data is the subset of population, where population can be of n variables x1,x2,........,xn. Let us discuss it by example , assume we are taking to factors to differentiate individuals that is Eye color and Hair color. Eye color can be Blue,Green  and Brown. Hair color can be Black, red, blond and grey. So the total combinations we will be working be 3*4 = 12

Here, we can make prediction of function by Joint Probability Distribution.We assume that eye color and hair color does not tell us much about the individuals.Let us add an attribute Milk allergy which has binary values Yes(y) or No(N), now the combinations on which we can work will be 3*4*2 = 24.

If we add an another attribute income which is continuous then the combinations to learn is  3*4*2*∞ = ∞. So , there are two ways by which we can learn this problem:

  • Discretize / Bucket : In this we divide the attribute income in interval like: k maps to [1,100k] ,[100k,500k,.......]
  • Probability Density Function : Here we apply mixture of gaussians for the P(income). This is a parametric model where the overall parameters will be 2k+k-1.


2k+k-1 because in mixture of gaussian they have different mean and standard deviation  and input is also the mixture to it.
 Here, according to above diagram 
     p(X) = 5Σi=1P(Ci)P(X|Ci)
Here P(Ci) is categorical variable and P(X|Ci) is gaussian.

Due to gaussian distribution parameter is 2k and from categorical 
P(C5) = 1-Σi=1P(Ci), from here we got k-1 and the overall parameter are 2k+k-1.

In Logistic Regression it has sigmoid representation.
                                               Z = nΣi=0βixi
                                              
                                                  y'=σ(Z)   where  σ represents activation for sigmoid


Let us assume if our data look like :




The decision boundary in above diagram will be


After transformation it will lead to neural network.



This is multilayer perceptron or Feed forward fully connected neural network 
Neural Network is learning set of based function to get output
                                      y' = σg(w) = g(f(x)) 


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