Logistic Regression in Machine Learning

What is logistic regression?

Logistic regression is a machine learning algorithm that uses supervised machine learning to calculate the outcome of a particular event using probability. It works with different types of data variables whose output is a binary(0 or 1, yes or no), and they are normally dichotomous(Having different categories) in nature. 

When working with independent variables that affect the outcome. There are several categories of logistic regression. This include:

• Continuous-it normally works with data where values can split, creating an interval or cases where the intervals get split into two equal parts, which are still meaningful. It includes temperature measurements, weight etc
• Discrete and ordinal category: This category typically follows a certain order or scale. Examples include when a specific business conducts a survey asking their customer to rate their services or products following a scale example from 1-5.
• Discrete and nominal: This type of data is generally in groups and doesn't follow any order. For example, we can group the color of the buses as blue, yellow, green, orange, etc. 

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How Logistic Regression Works

Logistic regression assumptions

Before working on any logistic regression, we make several assumptions about the data we use for training. You have to consider all of them for every project you handle. These assumptions are:

• It is good to look for large data samples to increase the reliability of the results.
• The variables(independent) should relate to log-odds (we have discussed log odds in the sections below).
• It does not work well with data with many zero values.
• We should remove or have little multicollinearity between the independent variables.
• Remove any outliers.
• The dependent variable should be dichotomous or binary. 

Logistic(Sigmoid)Function

Logistic regressions use logistic functions to change linear data into probability. It uses complex functions to provide S-shaped curves whose data ranges typically from 0 and 1. Most of the time, it fails to represent values that are more than 1.

The sigmoid function helps ensure the predicted values get mapped to the probabilities, and the values range from 0 and 1. To calculate, we use the following formula

Odds = p/(1-p)

To get rid of negative, we calculate the log odds using the following formulae.

Log odds = ln(p/(1-p))

To summarize the logistic regression, we can use this. 

Where z is an equation with a function (σ) and an output (ŷ). 

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Log odds

It's a type of formulae you can use to express probability differently. It is also known as the logit function. It helps people understand the ratio of something happening to another thing not going through and also the ratio of something happening to another thing that can go through and happen.

You first have to calculate the standard logistic function using the following formula.

We then find the logit by using the following formula, where p is the probability.

When working with these formulae, you have to understand different bases depending on the value. For instance, e   is the standard base for values greater than1, shannon represents base 2, and hartley represents base 10. Most of these bases vary depending on the values taken by the function.

For infinity numbers, we use the following formulae:

You can calculate the odds ratio by subtracting two probabilities using the following formulae.

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Types of logistic regressions

There are several types of logistic regressions. Their differences depend on the theory and how they get executed using the yes or no values. It includes:

1. Binary logistic regression
It doesn't depend on the order of categories, and it normally has two outcomes where the variables can only fall in one of the two required categories. The outcome can be in the form of 0s and 1s, True and False, Yes and No. Examples of this regression include detecting spam in health to detect diseases, finance, and sports.

2. Multinomial logistic regression
This category tests the variables in three or more levels of categories. It doesn't follow any order, and you can have more than two outputs. It's applied in fields like politics, transport, sports, text classification etc

3. Ordinal logistic regression
Their response variables work with more than three categories. They usually rely on the order of categories when looking for an output. Examples include categorizing clothes size, i.e., large, small, medium, calculating distances between two houses etc

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Applications of Logistic regression

There are several uses of linear regression. Some of the common applications of linear regression include:

1. Finance
Financial institutions like banks use predictive models to find out the credit score of their customers. The variables should be easy to read and use. They use variables that participate in the data processing procedures to help find out the variables with the best prediction. Logistic regression supports methods like recursive feature elimination to remove bad variables and improve the accuracy of the output.

2. Health and medicine
Many health companies and research groups use logistics regression to identify diseases and other health issues. They use text analysis to check the vectors by extracting the text into sentences and later converting it into 200-dimensional vectors. After extraction, you train the data and models using logistic regression and predict the outcome of the diseases with much accuracy. Some of the common diseases detected include blood tests, oncology diseases, etc.

3. Text editing
In the current technology, many companies use natural language processing. It involves extracting and processing to provide clear texts and help in other activities. Some of the common applications of logistic regression using natural language processing include detecting hate speech, customer support, sorting emails, etc.

Many companies that handle a lot of PDF documents use logistic regression to extract texts using the OCR system. They later change the text into useful, using different tricks like character training. Character training involves the use of logistic regression to change the lines, identify where punctuation starts, the first and last character of a sentence etc

4. Hotel Industry
Most hotel booking sites across the world have deployed different machine learning algorithms to help them with the different functionalities of their sites. They help gauge the customer's behavior and try to recommend to them what they are up to. Logistic regression uses the data given to evaluate how users interact with the site and when to change the user interface. One of the common examples of this application is booking.com. 

5. Gaming industry
Most gamers like games with speed and options like in-app purchases that change different aspects of the game, i.e., characters, communication, etc. Logistic regression uses customers' data by analyzing their behavior and recommending games according to how they play. The algorithm normally recommends them using customers who had the same behavior, the type of games customers put in their account profile, or both factors.

6. Marketing
Many companies use logistic regression to measure customers' probability of continuing the subscription or canceling it. It is through monitoring the customer’s behavior using probability. It is common in SAAS businesses.

7. Politics
It can predict which candidate the voter will vote for using their age, voting pattern in the past years, place of residence, income, and race, among others. It forces the politicians to employ data scientists to deploy this algorithm to help in finding out how many votes they can manage.

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 Advantages of using logistic regression

• It's easier to use a logistic regression machine learning algorithm. When training models using logistic regression, they are easier to implement, and they require less computation power making them suitable for machine learning models training.
• When working with high dimensional datasets, it accepts several techniques like using L1 and L2 techniques to prevent the dataset from overfitting during training.
• Logistic regression works and performs well when working with linearly separable datasets, making it efficient for machine learning.
• It provides both directions (positive or negative), and the predictor produced gets measured based on relevancy(coefficient size). It helps the parameters provide interferences that show the importance of the features.
• You can easily update the models when you want them to have a new data reflection. You can use methods like stochastic gradient descent to achieve the result.
• When working with the logistic regression, their outputs have better probabilities that match well with the classification results.
• It works well with neural networks, especially during the stacking of neural classifiers.
• It uses less training time, i.e., during the interpretation, it uses little time than other methods like Artificial Neural networks.
• You can extend the algorithms to support multi-class classification using classifiers like softmax.
• It's easier to interpret the output weights after using the logistic regressions to train the models. 

Disadvantages of using logistic regression

Some of the disadvantages of using logistic regression include:

• It does not support non-linear problems since it's not easy to find non-linear data that will need many features to change the data into linear dimensions.
• When working with high dimensional models, the probability outcome may not be accurate. It is due to the cases where people train and model less data using many features.
• When training independent variables, there are cases of repetition that occur due to the lack of multicollinearity between the variables making it provide inaccurate training parameters.
• All the variables used in logistic regression have to be linearly related using the log odds (log(p/(1-p)) formula both for the dependent and independent variables.
• Users should provide large datasets and category examples to use in identification.
• Presence of outliers where the data values deviations from the expected ranges may lead to erroneous results. 
• We should have different training examples per category. You are likely to get repeated results when you have related examples because the model gives too much attention to specific training examples.
• When handling complex relationships, it's sometimes hard to use them. 

Conclusion

Many businesses have embraced linear regression, and there is a high demand for machine learning specialists. You have to learn how to use it and apply it in real-life scenarios. Most of them are easier to use and need time to learn and master. To work better with the models, you have to ensure you use the best training methods for better accuracy.

Many professionals are now using algorithms in different fields to help them discover different uses for their data. They can use them to improve and get more customers, which leads to more conversion. Many data scientists use the principles to implement them in their daily activities. It has good levels of accuracy that make it a good use to add to your skillset. 

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