Gain insights into data science fundamentals, explore machine learning and big data, and delve into real-time projects. Discover systematic approaches to data acquisition, wrangling, and solving diverse problems.

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There is a lot of dispersed, and somewhat conflicting information on the internet when it comes to data science, making it tough to know where to start. Don't worry. 

This course will get you familiar with the state of data science and the related fields such as machine learning and big data. You will be going through the fundamental concepts and libraries which are essential to solve any problem in this field. 

You will work on real-time projects from Kaggle while also honing your mathematical skills which will be used extensively in most problems you face. You will also be taken through a systematic approach to learning about data acquisition to data wrangling and everything in between. This is your all-in-one guide to becoming a confident data scientist.

An Introductory Guide to Data Science and Machine Learning

# Backpropagation worked example

In this lesson we will consider the below Neural Network and update the weights and biases for one round of backpropagation. We use the sigmoid function activation function, and the learning rate l is 0.9.







We have the following initial values of inputs, weights and biases of the above neural network. 


$x_1, x_2, x_3$ are our input values with values $1$, $0$ and $1$ respectively and the corresponding class label is 1 i.e $t_j=1$. $\theta_{4}, \theta_{5}, \theta_{6}$ are the bias values of the units $4, 5$ and $6$ respectively.  

# Feedforward Process

The following table sums up the feedforward process. The first column represents the unit number from the above neural network. The second column represents the net input being computed at those units and the third column applies the sigmoid activation on the relevant net inputs and produces the output. 

<table>
  <tr>
    <th>Units, j</th>
    <th>Net input I<sub>j</sub></th>
    <th>Output, O<sub>j</sub>(Applying Sigmoid Activation)</th>
  </tr>
  <tr>
    <td>4</td>
    <td>0.2+0-0.5-0.4=-0.7</td>
    <td>0.332</td>
  </tr>
  <tr>
    <td>5</td>
    <td>-0.3+0+0.2+0.2=0.1</td>
    <td>0.525</td>
  </tr>
  <tr>
    <td>6</td>
    <td>(-0.3)(0.332)-(0.2)(0.525) + 0.1=-0.105</td>
    <td>0.474</td>
  </tr>
 
</table>
 

# Formulas for weights update

From the last lesson we have the following formulas and we will be utilizing them to update the weights and biases. 


* $w_{ij}^{new} = w_{ij}^{old} + \Delta w_{ij}$

* $\Delta w_{ij} = -\frac{\delta Error}{\delta w_{ij}}l=lE_{ij}$

* $E_{ij}=E_jz_i$

* When node $j$ is in the output layer,
<center>

$E_j = z_j(1-z_j)(t_j-z_j)$

$\Delta w_{ij}=lz_{i}z_{j}(1-z_{j})(t_{j}-z_{j})$

</center>

* When node $j$ is in the hidden layer,  

<center>

$E_j = z_j(1-z_j)\sum_{k}w_{jk}E_{k}$

$\Delta w_{ij} = lz_{i}z_{j}(1-z_{j})\sum_{k}w_{jk}E_{k}$

</center>

* For biases in the network, we can write the equation below. 

<center>

$\Delta w_j = lE_j$

</center>

## Calculation of error at each node

We calculate the errors at each node using the above formulas. The class label is 1 meaning $t_{j}=1$. Node 4 and 5 are in the hidden layer, and node 6 is in the output layer, and we will use the corresponding formulas for each node in the table below. 

<table>
  <tr>
    <th>Units, j</th>
    <th>Err<sub>j</sub></th>
    
  </tr>
  <tr>
    <td>6</td>
    <td>(0.474)(1-0.474)(1-0.474)=0.1311</td>
    
  </tr>
  <tr>
    <td>5</td>
    <td>(0.525)(1-0.525)(0.1311)(-0.2)=-0.0065</td>
    
  </tr>
  <tr>
    <td>4</td>
    <td>(0.332)(1-0.332)(0.1311)(-0.3)=-0.0087</td>
    
  </tr>
 
</table>


## Updating the weights and biases

Now we will be using the main formula to update the weights and biases in the table below. The Learning rate $l$ is 0.9.

<center>

$w_{ij}^{new} = w_{ij}^{old} + \Delta w_{ij}$

</center>


<table>
  <tr>
    <th>Weights or Bias</th>
    <th>New Value</th>
    
  </tr>
  <tr>
    <td>w<sub>46</sub></td>
    <td>-0.3+(0.9)(0.1311)(0.332)=-0.261</td>
    
  </tr>
  <tr>
    <td>w<sub>56</sub></td>
    <td>-0.2+(0.9)(0.1311)(0.525)=-0.138</td>
    
  </tr>
  <tr>
    <td>w<sub>14</sub></td>
    <td>0.2+(0.9)(-0.0087)(1)=0.192</td>
    
  </tr>
  <tr>
    <td>w<sub>15</sub></td>
    <td>-0.3+(0.9)(-0.0065)(1)=-0.306</td>
    
  </tr>
 <tr>
    <td>w<sub>24</sub></td>
    <td>0.4+(0.9)(-0.0087)(0)=0.4</td>
    
  </tr>
 <tr>
    <td>w<sub>25</sub></td>
    <td>0.1+(0.9)(-0.0065)(0)=0.1</td>
    
  </tr>
 <tr>
    <td>w<sub>34</sub></td>
    <td>-0.5+(0.9)(-0.0087)(1)=-0.508</td>
    
  </tr>
 <tr>
    <td>w<sub>35</sub></td>
    <td>0.2+(0.9)(-0.0065)(1)=0.194</td>
    
  </tr>

<tr>
    <td>&Theta;<sub>6</sub></td>
    <td>0.1+(0.9)(0.1311)=0.218</td>
    
  </tr>

<tr>
    <td>&Theta;<sub>5</sub></td>
    <td>0.1+(0.9)(-0.0065)=0.194</td>
    
  </tr>

<tr>
    <td>&Theta;<sub>4</sub></td>
    <td>-0.4+(0.9)(-0.0087)=-0.408</td>
    
  </tr>
</table>



In this lesson, we’ll continue our discussion of backpropagation.

What is Data Science ?

Applications of Data Science

Overview of Libraries

Probability and Statistics

Machine Learning Part-1

Machine Learning Part-2

Machine Learning Part-3

Deep Learning

Machine Learning Tools and Libraries

Big Data Tools and Technologies

Where to go next ?

Backpropagation Part 2

Backpropagation worked example