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## Theory of Estimation Part-I: The Introduction

The theory of estimation is a branch in statistics that provides numerical values of the unknown parameters of the population on the basis of the measured empirical data that has a random component. This is a process of guessing the underlying properties of the population by observing the sample that has been taken from the population. The idea behind this is to calculate and find out the approximate values of the population parameter on the basis of a sample statistics.

Population:- All the items in any field of inquiry constitutes to a “Population”. For example all the employees of a factory is a population of that factory and the population mean is represented and the size of the population is represented by  N.

Sample:- Selection of few items from the population constitutes to a sample and the mean of the sample is represented by  and the sample size is represented by n

Statistics:- Any statistical measure calculated on the basis of sample observations is called Statistic. Like sample mean, sample standard deviation, etc.

Estimator:- In general estimator acts as a rule, a measure computed on the basis of the sample which tells us how to calculate the values of the estimate. It is a functional form of all sample observations prorating a representative value of the collected sample.

Suppose we have a random sample x_1,x_2,…,x_n on a variable x, whose distribution in the population involves an unknown parameter. It is required to find an estimate of on the basis of sample values.

Unbiasedness:-A statistic t is said to be an unbiased estimator if E(β ̂)= βi.e. observed value is equal to the expected value. In case E(β ̂)≠ β then the estimator is biased estimator.

Consistency:- One of the most desirable property of good estimator is that its accuracy should increase when the sample becomes larger i.e. the error between the expected value and the observed value reduces as the size of the sample increases E(β ̂ )- β=0

Efficiency:-An estimator is said to be an efficient estimator if it has the smallest variance compared to all the consistent and unbiased estimators. If consistent estimator exists whose sampling variance is less than that of any other consistent estimator, it is said to be “most efficient”; and it provides a standard for the measurement of ‘efficiency’ of a statistic.

Sufficiency:- An estimator is said to be sufficient if it contains all information in the sample about .

At the end of this discussion, hopefully, you have learned what theory of estimation is. Watch the video tutorial attached below to learn more about this. DexLab Analytics is a data science training institute in gurgaon, that offers advanced courses. Follow the blog section to access more informative posts like this.

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## An Introductory Guide to NumPy

NumPy also known as numerical python, is a library consisting of multidimensional array objects and a collection of routines for processing those arrays. Using NumPy, mathematical and logical operations on arrays can be performed without it which was not possible. For example-

Multiplication of two lists will cause an error as a data structure like lists, tuple, dictionaries and sets do not allow mathematical operations.

Therefore we need NumPy to covert our data structures like lists into 1d, 2d, 3d or nd arrays so that mathematical operations can be performed. U

We can use .array() methods to create these arrays.

Now let’s check out few examples and also perform few mathematical operations to have a better understanding.

• In the above code we first import NumPy library and then use .array() method to two 1d-array a1 and b1 using the list we previously created.

• Now let’s multiply a1 and b1 array.

• Now let’s use .array() method to directly create an array.

Arrays can be created using lists, tuples and dictionaries as you can see in the above example.

Now for 2-d arrays recall that we can also make list of lists. Let’s use that to create 2d-arrays.

2d-arrays can also be created using tuples.

Remember that we are not using these as matrices because matrix multiplication is an entirely different thing we are just trying to perform mathematical operations which were otherwise not possible.

#### Random Module

Numpy also has various ways with which we can create array of random numbers which then can be used in number of ways like generating a data for practice purposes or for building beautiful graphs for a presentation.

Given below is a list of type of random numbers you can generate

.rand() :- This particular method helps you generate uniformly distributed random numbers i.e. numbers between 0 and 1 where each number between 0 and 1 will have equal probability to be in the sample dataset.

The above code generates a 2d-array with values between 0 and 1.

.randn():- This method generates normally distributed random numbers i.e. numbers between -3 and +3 where mean=median=mode and ploted gives a bell shaped curve.

Here the 20 random numbers are generated ranging between -3 and + 3.

Note:- Remember that the data is randomly picked from the normally distributed values between -3 and +3 so the graph is not bell shaped but the original data from which the values are being picked randomly is bell shaped with mean=median-mode.

.randint():-This method generates random integers between a given range.

So, with that we come to the end of the discussion on the Numpy. Hopefully it helped you understand Numpy, for more information you can also watch the video tutorial attached down this blog. DexLab Analytics offers machine learning courses in delhi. To keep on learning more, follow DexLab Analytics blog.

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## Linear Regression Part II: Predictive Data Analysis Using Linear Regression

In our previous blog we studied about the basic concepts of Linear Regression and its assumptions and let’s practically try to understand how it works.

Given below is a dataset for which we will try to generate a linear function i.e.

y=b0+b1Xi

Where,

y= Dependent variable

Xi= Independent variable

b0 = Intercept (coefficient)

b1 = Slope (coefficient)

To find out beta (b0& b1) coefficients we use the following formula:-

Let’s start the calculation stepwise.

1. First let’s find the mean of x and y and then find out the difference between the mean values and the Xi and Yie. (x-x ̅ ) and (y-y ̅ ).
2. Now calculate the value of (x-x ̅ )2 and (y-y ̅ )2. The variation is squared to remove the negative signs otherwise the summation of the column will be 0.
3. Next we need to see how income and consumption simultaneously variate i.e. (x-x ̅ )* (y-y ̅ )

Now all there is left is to use the above calculated values in the formula:-

As we have the value of beta coefficients we will be able to find the y ̂(dependent variable) value.

We need to now find the difference between the predicted y ̂ and observed y which is also called the error term or the error.

To remove the negative sign lets square the residual.

What is R2 and adjusted R2 ?

R2 also known as goodness of fit is the ratio of the difference between observed y and predicted  and the observed y and the mean value of y.

Hopefully, now you have understood how to solve a Linear Regression problem and would apply what you have learned in this blog. You can also follow the video tutorial attached down the blog. You can expect more such informative posts if you keep on following the DexLab Analytics blog. DexLab Analytics provides data Science certification courses in gurgaon.

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## Linear Regression Part I: A Comprehensive Guide to Linear Regression

Today’s blog explores another vital statistical concept Linear Regression, let’s begin. Linear regression is normally used in statistics for predictive modeling. It tries to model a relationship between two independent (explanatory variable) and dependent (explained variable) variables X and Y by fitting a linear equation (Y=bo+b1X+Ui) to an observed data.

#### Assumptions of linear regression

• Ui is a random real variable, where Ui is the difference between the observed dependent variable Y and predicted Y variable.
• The mean of Ui in any particular period is zero.
• The variance of Ui is constant in each period i.e for all values of X, Ui will show the same dispersion around their mean
• The variable Ui has a normal distribution i.e the value of Ui (for each Xi) have a bell shaped symmetrical distribution about their zero mean.
• The random terms of different observations are independent i.e the covariance of any Ui with any other Uj is equal to zero.
• Ui is independent of the explanatory variable X.
• Xi are a set of fixed values in the hypothesised process of repeated sampling which underlies the linear regression model.
• In case there are more than one explanatory variables then they are not perfectly linearly correlated.

Linear Regression equation can be written as:

Where,

is the dependent variable

X is the independent variable.

b0 is the intercept (where the line crosses the vertical y-axis)

b1 is the slope

Ui is the error term (difference between ) also called residual or white noise.

#### Simple linear regression follows the properties of Ordinary Least Square (OLS) which are as follows:-

1. Unbiased estimator:- E()=b ie. an estimator is unbiased if its bias is 0; E() – b = 0
2. Minimum Variance:- An estimate is best when it has the smallest variance as compared to any other estimate obtained from other econometric method.
3. Efficient estimator:- When it has both the previous properties ie.
4. Linear estimator
5. Best, Linear, Unbiased estimator (BLUE)
6. Minimum mean squared error (MSE) estimator:- It is a combination of the unbiasedness and minimum variance properties. An estimator is a minimum MSE estimator if it has the smallest mean square error.

With that the discussion on Linear Regression wraps up here, hopefully it cleared away any confusion you might have and helped you get a grasp on the concept. We have a video discussion on this same topic, which is attached below this blog, check it out for further reference.

Continue to track the DexLab Analytics blog to find informative posts related to Python for data science training.

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## Why Pursuing a Certification Course in Machine Learning Makes Sense Than Doing Self-Study?

If you are aware of the growth opportunities awaiting you in the Machine Learning domain, you must be in a rush to master the Machine Learning skills. Now, there are courses available that aim to sharpen the students with skills they would need to work in a challenging environment. However, some often prefer the self-study mode for developing knowledge in this highly specialized domain. No matter which way you prefer to learn, ultimately your passion and dedication would matter the most, because in both ways you need to put in the hard work and really toil hard to make any progress.

#### Is self-study a feasible option?

If you have already been through some course and want to go to the advanced level through self-study that’s a different issue, but, for those who are just starting out without any background in science, does it even make any sense to opt for self-study?

Given the way Machine Learning technology is moving fast and creating a demand for professionals with highly specialized industry knowledge, do you think self-study would be enough? Do you think a self-study plan to learn something you have no idea about would work? How much time would you need to devote? What should be your learning route? And how do you know this is the right path to follow?

Before we dive deeper into the discussion, we need to go through some prerequisites for Machine Learning study plan.

Machine learning is a broad field and assuming you are a beginner with no prior knowledge in this domain, you have to be familiar with mathematics, statistics, programming  languages, meaning undergoing a Python certification training</strong>, must be proficient in data handling including analysis and modeling, you have to work on algorithms. So, can you pick up all of these skills one by one via self-study? Add to the list the latest Machine Learning tools and applications you need to grasp.

There will be help available in the form of:

• There would be vast resources, in forms of e-books, lectures, video tutorials, most of these are free and easily accessible.
• There are forums, groups out there which you can join and access help
• You can take part in online competitions

Think it through. How long will it take for you to get from one stage to the next?

Even though there being no dearth of resources available you would be struggling with your progress and most importantly you would struggle to keep up with the pace the technology is moving ahead. Picking up a programming language, grasping and mastering concepts of linear algebra, probability, data is going to be a mammoth task.

#### What difference a certification course can make?

• To begin with these courses are designed for people coming from different backgrounds, so, you having or, not having any prior knowledge in mathematics, statistics wouldn’t matter as you would be taught everything from scratch be it math or, Machine Learning Using Python.
• The programs are designed for both working professionals as well as for beginners, all you need to do is choose the one that suits your specific level.
• These courses are designed to transform you into an industry-ready professional and you would be under the guidance of professionals who are more than familiar with the nuances of the way the industry functions.
• The modules would follow a strict schedule and your training path would be well planned out covering all the areas you need to master.
• You would learn via hands-on training and get to handle projects. Nothing makes you skilled like hands-on training.

Your journey towards a smarter future needs to be through a well mapped-out path, so, be smart about it. DexLab Analytics offers industry-ready courses on Data Science, Machine Learning course in Gurgaon and AI with Python. Take advantage of the courses that are taught by instructors who have both expertise and experience. Time is indeed money, so, stop wasting time and get down to learning.

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## Why is Data Literacy Important to Stay Relevant in Today’s Workspace?

Today’s workspace has turned volatile in trying to adjust to the new normal. Along with struggling to stay indoors while living a virtual life, adopting new manners of social distancing, people are also having to deal with issues like job loss, pay cut, or, worse, lack of vacancies. Different sectors are getting hit, except for those driven by cutting edge technology like Data Science, Artificial intelligence. The need to transition into a digital world is greater than ever. As per the World Economic Forum, there would be a greater push towards “digitization” as well as “automation”. This signifies the need for professionals with a background in Data Science, Artificial Intelligence in the future that is going to be entirely data-reliant.

So, what are you going to do? Sit back and wait till the storm passes over or are you going to utilize this downtime to upskill yourself with a Data Science course?  With the PM stressing on how the “skill, re-skill and upskill” being the need of the hour,  you can hardly afford to lose more time. Since Data Science is one of the comparatively steadier fields, that is growing despite all odds, it is time to acquire data literacy to stay relevant in a workspace that is increasingly becoming data-driven. From healthcare to manufacturing, different sectors are busy decoding the data in hand to go digital in a pandemic ridden world, and employers are looking for people who are willing to push the envelope harder to remain relevant.

#### What is data literacy?

Before progressing, you must understand what data literacy even means. Data literacy basically refers to having an in-depth knowledge of data that helps the employees work with data to derive actionable information from it and channelizing that to make informed decisions. However, data literacy has a wider meaning and it is not limited to the data team comprising data scientists, no, it takes all the employees in its ambit, so, that the data flow throughout the organization is seamless. Without there being employees who know their way around data, an organization can never realize its dream of initiating a data-driven culture. Having a background in Data science using Python training is the key to achieving data literacy.

#### The demand for data scientists and data analysts is soaring up

Despite the ominous presence of the pandemic, the demand for Data Science professionals is there and in August, the demand for Data Analysts and Data Scientists soared. As per a recent study, in India, a Data Science professional can expect no less than ₹9.5 lakh per annum. With prestigious institutes like Infosys, IBM India, Cognizant Technology Solutions, Accenture hiring, it is now absolutely mandatory to undergo Data Science training to grab the job opportunities.

The skill gap is there, but, that does not mean it could not be taken care of. On the contrary, it is absolutely possible and imperative that you take the necessary step of upskilling yourself to be ready for the Data Science field. Having a working knowledge of data is not enough, you must be familiar with the latest Data Science tools, must possess the knowledge to work with different models, must be familiar with data extraction, data manipulation. All of these skills and more, you would need to master before you go seeking a well-paying job.

Self-study might seem like a tempting idea, but, it is not a practical solution, if you want to be industry-ready then you must know what the industry is expecting from a Data Science professional, and only a faculty comprising industry experts can give you that knowledge while guiding you through a well designed Python for data science training course.

An institute such as DexLab Analytics understands the need of the hour and has a great team of industry professionals and experts to help aspiring Data Scientists and Data Analysts fulfill their dream. Along with offering state-of-the-art Data Science certification courses, they also provide courses like Machine Learning Using Python.

No matter which way you look, upskilling is the need of the hour as the world is busy embracing the power of Data Science. Stop procrastinating and get ready for the future.

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Internet of Things or IOT devices are a rage now, as these devices staying connected to the internet can procure data and exchange the same using the sensors embedded in those. Now the data which is being generated in copious amount needs to be processed and in comes IoT Analytics. This platform basically is concerned with analyzing the large amount of data generated by the devices. The interconnectivity of devices is helping different sectors be in sync with the world, and the timely extraction of data is of utmost significance now as it delivers actionable insights. This is a highly skilled job responsibility that could only be handled by professionals having done artificial intelligence course in delhi.

This particular domain is in the nascent stage and it is still growing, however, it is needless to point out that IoT analytics holds the clue to business success, as it enables the organizations to not only extract information from heterogeneous data but also helps in data integration. With the IoT devices generating almost 5 quintillion bytes of data, it is high time the organizations start investing in developing IoT analytics platform and building a data expert team comprising individuals having a background in Machine Learning Using Python. Now let’s have a look at the ways IoT analytics can boost business growth.

#### Optimized automated work environment

IoT analytics can optimize the automated work environment, especially the manufacturing companies can keep track of procedures without involving human employees and thereby lessening the chances of error and enhancing the accuracy of predicting machine failure, with the sensors monitoring the equipments and tracing every single issue in real-time and sending alerts to make way for predictive maintenance. The production flow goes on smoothly as a result without developing any glitch.

#### Increasing productivity

In an organization gauging the activity of the employees assumes huge significance as it directly impacts the productivity of the company, with sensors being strategically placed to monitor employee activity, performance, moods and other data points, this job gets easier. The data later gets analyzed to give the management valuable clues that enable them to make necessary modifications in policies.

#### Bettering customer experience

Regardless of the nature of your business, you would want to make sure that your customers derive  utmost satisfaction. With IoT data analytics in place you are able to trace their preferences thanks to the data streaming from devices where they have already left a digital footprint of their shopping as well as searching patterns. This in turn enables you to offer tailor-made service or products. Monitoring of customer behavior could lead to devising marketing strategies that are information based.

#### Staying ahead by predicting trends

One of the crucial aspects of IoT analytics is its ability to predict future trends. As the smart sensors keep tracking data regarding customer behavior, product performance, it becomes easier for businesses to analyze future demands and also the way trends will change to make way for emerging ones and it enables the businesses to be ready. Having access to a future estimate prepares not just businesses but industries be future ready.

#### Smarter resource management

Efficient utilization of resources is crucial to any business, and IoT analytics can help in a big way by making predictions on the basis of real-time data. It allows companies to measure their current resource allocation plan and make adjustments to make optimal usage of the available resources and channelizing that in the right direction. It also aids in disaster planning.

Ever since we went digital the streaming of large quantity of data has become a reality and this is going to continue in the coming decades. Since, most of the data generated this way is unstructured there needs to be cutting edge platforms like IoT analytics available to manage the data and processing it to enable industries make informed decisions. Accessing Data Science training, would help individuals planning on making a career in this field.

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## Skewness and Kurtosis: A Definitive Guide

While dealing with data distribution, Skewness and Kurtosis are the two vital concepts that you need to be aware of. Today, we will be discussing both the concepts to help your gain new perspective.

Skewness gives an idea about the shape of the distribution of your data. It helps you identify the side towards which your data is inclined. In such a case, the plot of the distribution is stretched to one side than to the other. This means in case of skewness we can say that the mean, median and mode of your dataset are not equal and does not follow the assumptions of a normally distributed curve.

Positive skewness:- When the curve is stretched towards the right side more it is called a positively skewed curve. In this case mean is greater than median and median is the greater mode

(Mean>Median>Mode)

Let’s see how we can plot a positively skewed graph using python programming language.

• First we will have to import all the necessary libraries.

• Then let’s create a data using the following code:-

In the above code we first created an empty list and then created a loop where we are generating a data of 100 observations. The initial value is raised by 0.1 and then each observation is raised by the loop count.

• To get a visual representation of the above data we will be using the Seaborn library and to add more attributes to our graph we will use the Matplotlib methods.

In the above graph you can see that the data is stretched towards right, hence the data is positively skewed.

• Now let’s cross validate the notion that whether Mean>Median>Mode or not.

Since each observation in the dataset is unique mode cannot be calculated.

#### Calculation of skewness:

Formula:-

• In case we have the value of mode then skewness can be measured by Mode ─ Mean
• In case mode is ill-defined then skewness can be measured by 3(Mean ─ Median)
• To obtain relative measures of skewness, as in dispersion we use the following formula:-

When mode is defined:-
When mode is ill-defined:-

To calculate positive skewness using Python programming language we use the following code:-

Negative skewness:- When the curve is stretched towards left side more it is called a negatively skewed curve. In this case mean is less than median and median is  mode.

(Mean<Median<Mode)

Now let’s see how we can plot a negatively skewed graph using python programming language.

Since we have already imported all the necessary libraries we can head towards generating the data.|

In the above code instead of raising the value of observation we are reducing it.

• To visualize the data we have created again we will use the Seaborn and Matplotlib library.

The above graph is stretched towards left, hence it is negatively skewed.

• To check whether Mean<Median<Mode or not again we will be using the following code:-

The above result shows that the value of mean is less than mode and since each observation is unique mode cannot be calculated.

• Now let’s calculate skewness in Python.

#### Kurtosis

Kurtosis is nothing but the flatness or the peakness of a distribution curve.

• Platykurtic :- This kind of distribution has the smallest or the flattest peak.
• Misokurtic:- This kind of distribution has a medium peak.
• Leptokurtic:- This kind of distribution has the highest peak.

The video attached below will help you clear any query you might have.

So, this was the discussion on the Skewness and Kurtosis, at the end of this you have definitely become familiar with both concepts. Dexlab Analytics blog has informative posts on diverse topics such as neural network machine learning python which you need to explore to update yourself. Dexlab Analytics offers cutting edge courses like machine learning certification courses in gurgaon.

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## A Definitive Guide to Machine Learning

In a world that is riveting towards exploring the hidden potential of emerging technologies like artificial intelligence, staying aware can not only keep you in sync but can also ensure your growth. Among all the tech terms doing the rounds now, machine learning is probably the one that you have heard frequently or, it might also be the term that intrigues you the most. You might even have a friend who is pursuing a Machine Learning course in Gurgaon. So, amidst all of this hoopla why don’t you upgrade your knowledge regarding machine learning? It’s not rocket science but, it’s science and it’s really cool!

Machine learning is a subset of AI that revolves round the concept of enabling a system to learn from the data automatically while finding patterns and improve the ability to predict without being explicitly programmed beforehand. One of the examples would be when you shop online from a particular site, you would notice product recommendations are lining up the page that particularly align with your preferences.  The data footprint you leave behind is being picked up and analyzed to find a pattern and machine learning algorithms work to make predictions based on that, it is a continuous process of learning that simulate human learning process.

The same experience you would go through while watching YouTube, as it would present more videos based on your recent viewing  pattern. Being such a powerful technology machine learning is gradually being implemented across different sectors and thereby pushing the demand for skilled personnel.  Pursuing machine learning certification courses in gurgaon from a reputed institute, will enable an individual to pick up the nuances of machine learning to land the perfect career.

#### What are the different types of machine learning?

When we say machines learn, it might sound like a simple concept, but, the more you delve deeper into the topic to dissect the way it works you would know that there are more to it than meets the eyes. Machine learning could be divided into categories based on the learning aspect, here we will be focusing on 3 major categories which are namely:

• Supervised Learning
• Unsupervised Learning
• Reinforcement Learning

#### Supervised Learning

Supervised learning as the name suggests involves providing the machine learning algorithm with training dataset, an example of sort to enable the system to learn to work its ways through to form the connection between input and output, the problem and the solution. The data provided for the training purposes needs to be correctly labeled so, that the algorithm is able to identify the relationship and could learn to predict output based on the input and upon finding errors could make necessary modifications. Post training when given a new dataset it should be able to analyze the input to predict a likely output for the new dataset.  This basic form of machine learning is used for facial recognition, for classifying spams.

#### Unsupervised Learning

Again the term is suggestive like the prior category we discussed above, this is also the exact opposite of supervised learning as here there is no training data available to rely on. The input is available minus the output hence the algorithm does not have a reference to learn from. Basically the algorithm has to work its way through a big mass of unclassified data and start finding patterns on its own, due to the nature of its learning which involves parsing through unclassified data the process gets complicated yet holds potential. It basically involves clustering and association to work its way through data.

#### Reinforcement Learning

Reinforcement learning could be said to have similarity with the way humans learn through trial and error method. It does not have any guidance whatsoever and involves a reward, in a given situation the algorithm needs to work its way through to find the right solution to get to the reward, and it gets there by overcoming obstacles and learning from the errors along the way. The algorithm needs to analyze and find the best solution to maximize its rewards and minimize penalties as the process involves both. Video games could be an example of reinforcement learning.

Although only 3 core categories have been mentioned here, there remains other categories which deserve as much attention, such as deep learning. Deep learning too is a comparatively new field that deserves a complete discussion solely devoted to understanding this dynamic technology, focusing on its various aspects including how to be adept at deep learning for computer vision with python.

Machine learning is a highly potent technology that has the power to predict the future course of action, industries are waking up to smell the benefits that could be derived from implementation of ML. So, let’s quickly find out what some of the applications are:

#### Malware and spam filtering

You do not have to be tech savvy to understand what email spams are or, what malware is. Application of machine learning is refining the way emails are filtered with spams being detected and sent to a separate section, the same goes for malware detection as ML powered systems are quick to detect new malware from previous patterns.

#### Virtual personal assistants

As Alexa and Siri have become a part of life, we are now used to having access to our very own virtual personal assistants. However, when we ask a question or, give a command, ML starts working its magic as it gathers the data and processes it to offer a more personalized service by predicting the pattern of commands and queries.

#### Refined search results

When you put in a search query in Google or, any of the search engines the algorithms follow and learn from the pattern of the way you conduct a search and respond to the search results being displayed. Based on the patterns it refines the search results that impact page ranking.

#### Social media feeds

Whether it is Facebook or, Pinterest , the presence of machine learning could be felt across all platforms. Your friends, your interactions, your actions all of these are monitored and analyzed by machine learning algorithms to detect a pattern and prepare friend suggestions list. Automatic Friend Tagging Suggestions is another example of ML application.

Those were a couple of examples of machine learning application, but this dynamic field stretches far. The field is evolving and in the process creating new career opportunities. However, to land a job in this field one needs to have a background in Machine Learning Using Python, to become an expert and land the right job.

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