A Model Inspired by Human Brain!

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Today iam going to be writing about Neural Network.

Having spent my full  15 years of career in core advanced analytics  identifying the right business use case , discovering and running the  right algorithms  and representing  the final statistical output in a meaningful  form to client ,  this post will cover only Analytical and Business application side of Neural Network and not cover Technical coding aspect of it .

So if Neural Network is a  model that is inspired by the way a human brain works, then is it critical for us to understand how our brain works ? 

Model of our Brain!
Neurons are cells inside our brain and you and i have thousands of neurons inside our brain
Neurons has input wires known as dendrites which receives input
Neurons also has output wires called as Axon, through which it sends signals out to other neurons in the brain.
In simple terms a "Neuron is a computational unit which receives Inputs from Dendrites , computes something and  then send signals out via Axon and Axon of one neuron is connected to Dendrites of other neuron to pass on message"

This is how our senses work , based on this Model of our Brain Neural Network came into existence



The reason why Neural Network has become so popular today ?
Parametric Model such as Regression Analysis assumes that a certain set of X variables/Parameters will contribute to Y . In Parametric Model it is assumed that the distribution of data  to be Gaussian , Poisson or Log Linear etc. (Distribution is a known factor)

  • Logistic Regression /Linear Regression /Poisson Regression
  • Linear Discriminant Analysis
  • Perceptron
  • Naive Bayes
  • Simple Neural Networks
  • Simple Decision Trees / Cluster Analysis
While Non parametric model makes no assumption about Parameters / Variables . Example in a hidden Markov Model , at every transition stage the variables / parameters increases based on the circumstance /Stage . 

  • k-Nearest Neighbors
  • Decision Trees like CART and C4.5
  • Support Vector Machines
  • Complex Neural Networks




In the sense neural network is a non -parametric model but when you go with an assumption about layers it becomes parametric

A lot of new bees in analytics believe that neural network is an advanced model that can be replaced with parametric models isolating parametric models as a traditional model.

But the truth is neural network came into existence only to solve certain business challenges which the parametric model was unable to solve .
Ex., In a clinical trial space ,  1 patient generates 100 parameters - age , sex , diseases , symptoms , shapes and size of his body organs , tumor etc.and the data is available in the form of XRAY, CT Scan , PET Scan or MRI and if  there are 50,000 patients in a country who are suffering from  a particular disease (flu) who are unique by nature  , then we are left with 100*50,000 = 5 MM Parameters to model. 

This is when neural network is implemented , because it is impossible for parametric model to solve this challenge. The min .parameters that should exists for a neural net model to run is in the range of million which cannot be solved via parametric modeling.

Consider a simple example - if you want to model ROI and you know the parameters that influence your business , why would you want to run a neural network model and ask machine for a solution when your brain already knows the answer.

So neural network is not an advanced model in comparison with parametric model , neural network came into existence to increase labour productivity because the data has parameters that range in millions and it is impossible for your brain to calculate and tell what are the parameters that is influencing your business in a short period of time.

Lets see how neural network works

A ) How does a single neuron Model work?
The orange circle is Neuron 
X 1 , X2 and X3 are dendrites / Inputs and the 
Output is Axon





Computational steps of a single neuron model

Each Input parameter is given a weight as seen above
The equation is called Sigmoid because it uses a Logistic Equation as seen below



Neural Network Output Y is calculated by the following equation similar to the above logistic equation


Neural network with one hidden layer.
Just like how our brain work , one neuron will pass information to other neuron.
As seen below layer 2 is a hidden layer and its a 3 layer neural network model




Computational Mathematics for a Neural network with one hidden layer.



Here "a" with superscript 2 -layer 2 and subscript 1 (x1)  is the first neuron in the activation layer and its sends output to another neuron which is red in colour (above diagram)

In the figure below one can see how the output of neuron at layer 2 (a1 , a2 and a3 )  becomes input to the final neuron which is orange in colour



Instead of using the above complicated equation , one can use the below equation to calculate output very easily.


Below is the example of 4 layer neural network




How to judge the statistical significance of these models will be covered in a separate post.
In the next couple of post we will study different types of models  (parametric and non parametric) and how they are applied in Machine Learning.
Having studied financial math and economics for business , I will be posting about the mathematics and economics for business and less on the coding  - Thank God iam not an engineer , having an engineering degree and still not being able to code is a shame.


Reference : Coursera and AnalyticsVidhya


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