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Overfitting and Underfitting With Algorithms in Machine Learning

Curve fitting is the process of determining the best fit mathematical function for a given set of data points. It examines the relationship between multiple independent variables (predictors) and a dependent variable (response) in order to determine the “best fit” line.In the figure shown, the red line represents the curve that is the best fit for the given purple data points. It can also be seen that curve fitting does not necessarily mean that the curve should pass over each and every data point. Instead, it is the most appropriate curve that represents all the data points adequately.Curve Fitting vs. Machine LearningAs discussed, curve fitting refers to finding the “best fit” curve or line for a given set of data points. Even though this is also what a part of Machine Learning or Data Science does, the applications of Machine Learning or Data Science far outweigh that of Curve Fitting.The major difference is that during Curve Fitting, the entire data is available to the developer. However, when it comes to Machine Learning, the amount of data available to the developer is only a part of the real-world data on which the Fitted Model will be applied.Even then, Machine Learning is a vast interdisciplinary field and it consists of a lot more than just “Curve Fitting”. Machine Learning can be broadly classified into Supervised, Unsupervised and Reinforcement Learning. Considering the fact that most of the real-world problems are solved by Supervised Learning, this article concentrates on Supervised Learning itself.Supervised learning can be further classified into Classification and Regression. In this case, the work done by Regression is similar to what Curve Fitting achieves. To get a broader idea, let’s look at the difference between Classification and Regression:ClassificationRegressionIt is the process of separating/classifying two or more types of data into separate categories or classes based on their characteristics.It is the process of determining the “Best Fit” curve for the given data such that, on unseen data, the data points lying on the curve accurately represent the desired result.The output values are discrete in nature (eg. 0, 1, 2, 3, etc) and are known as “Classes”.The output values are continuous in nature (eg. 0.1, 1.78, 9.54, etc).Here, the two classes (red and blue colored points) are clearly separated by the line(s) in the middle. This is an example of classification.Here, the curve represented by the magenta line is the “Best Fit” line for all the data points as shown. This is an example of Regression.Noise in DataThe data that is obtained from the real world is not ideal or noise-free. It contains a lot of noise, which needs to be filtered out before applying the Machine Learning Algorithms.As shown in the above image, the few extra data points in the top of the left graph represent unnecessary noise, which in technical terms is known as “Outliers”. As shown in the difference between the left and the right graphs, the presence of outliers makes a considerable amount of difference when it comes to the determination of the “Best Fit” line. Hence, it is of immense importance to apply preprocessing techniques in order to remove outliers from the data.Let us look at two of the most common types of noise in Data:Outliers: As already discussed, outliers are data points which do not belong to the original set of data. These data points are either too high or too low in value, such that they do not belong to the general distribution of the rest of the dataset. They are usually due to misrepresentation or an accidental entry of wrong data. There are several statistical algorithms which are used to detect and remove such outliers.Missing Data: In sharp contrast to outliers, missing data is another major challenge when it comes to the dataset. The occurrence is quite common in tabular datasets (eg. CSV files) and is a challenge if the number of missing data points exceeds 10% of the total size of the dataset. Most Machine Learning algorithms fail to perform on such datasets. However, certain algorithms such as Decision Trees are quite resilient when it comes to data with missing data and are able to provide accurate results even when supplied with such noisy datasets. Similar to Outliers, there are statistical methods to handle missing data or “NaN” (Not a Number) values. The most common of them is to remove or “drop” the row containing the missing data. Training of Data“Training” is terminology associated with Machine Learning and it basically means the “Fitting” of data or “Learning” from data. This is the step where the Model starts to learn from the given data in order to be able to predict on similar but unseen data. This step is crucial since the final output (or Prediction) of the model will be based on how well the model was able to acquire the patterns of the training data.Training in Machine Learning: Depending on the type of data, the training methodology varies. Hence, here we assume simple tabular (eg. CSV) text data. Before the model can be fitted on the data, there are a few steps that have to be followed:Data Cleaning/Preprocessing: The raw data that is thus obtained from the real-world is likely to contain a good amount of noise in it. In addition to that, the data might not be homogenous, which means, the values of different “features” might belong to different ranges. Hence, after the removal of noise, the data needs to be normalized or scaled in order to make it homogeneous.Feature Engineering: In a tabular dataset, all the columns that describe the data are called “Features”. These features are necessary to correctly predict the target value. However, data often contains columns which are irrelevant to the output of the model. Hence, these columns need to be removed or statistically processed to make sure that they do not interfere with the training of the model on features that are relevant. In addition to the removal of irrelevant features, it is often required to create new relevant features from the existing features. This allows the model to learn better and this process is also called “Feature Extraction”.Train, Validation and Test Split: After the data has been preprocessed and is ready for training, the data is split into Training Data, Validation Data and Testing Data in the ratio of 60:20:20 (usually). This ratio varies depending on the availability of data and on the application. This is done to ensure that the model does not unnecessarily “Overfit” or “Underfit”, and performs equally well when deployed in the real world.Training: Finally, as the last step,  the Training Data is fed into the model to train upon. Multiple models can be trained simultaneously and their performance can be measured against each other with the help of the Validation Set, based on which the best model is selected. This is called “Model Selection”. Finally, the selected model is used to predict on the Test Set to get a final test score, which more or less accurately defines the performance of the model on the given dataset.Training in Deep Learning: Deep Learning is a part of machine learning, but instead of relying on statistical methods, Deep Learning Techniques largely depend on calculus and aims to mimic the Neural structure of the biological brain, and hence, are often referred to as Neural Networks.The training process for Deep Learning is quite similar to that of Machine Learning except that there is no need for “Feature Engineering”. Since deep learning models largely rely on weights to specify the importance of given input (feature), the model automatically tends to learn which features are relevant and which feature is not. Hence, it assigns a “high” weight to the features that are relevant and assigns a “low” weight to the features that are not relevant. This removes the need for a separate Feature Engineering.This difference is correctly portrayed in the following figure:Improper Training of Data: As discussed above, the training of data is the most crucial step of any Machine Learning Algorithm. Improper training can lead to drastic performance degradation of the model on deployment. On a high level, there are two main types of outcomes of Improper Training: Underfitting and Overfitting.UnderfittingWhen the complexity of the model is too less for it to learn the data that is given as input, the model is said to “Underfit”. In other words, the excessively simple model fails to “Learn” the intricate patterns and underlying trends of the given dataset. Underfitting occurs for a model with Low Variance and High Bias.Underfitting data Visualization: With the initial idea out of the way, visualization of an underfitting model is important. This helps in determining if the model is underfitting the given data during training. As already discussed, supervised learning is of two types: Classification and Regression. The following graphs show underfitting for both of these cases:Classification: As shown in the figure below, the model is trained to classify between the circles and crosses. However, it is unable to do so properly due to the straight line, which fails to properly classify either of the two classes.Regression: As shown in the figure below, the data points are laid out in a given pattern, but the model is unable to “Fit” properly to the given data due to low model complexity.Detection of underfitting model: The model may underfit the data, but it is necessary to know when it does so. The following steps are the checks that are used to determine if the model is underfitting or not.Training and Validation Loss: During training and validation, it is important to check the loss that is generated by the model. If the model is underfitting, the loss for both training and validation will be significantly high. In terms of Deep Learning, the loss will not decrease at the rate that it is supposed to if the model has reached saturation or is underfitting.Over Simplistic Prediction Graph: If a graph is plotted showing the data points and the fitted curve, and the curve is over-simplistic (as shown in the image above), then the model is suffering from underfitting. A more complex model is to be tried out.Classification: A lot of classes will be misclassified in the training set as well as the validation set. On data visualization, the graph would indicate that if there was a more complex model, more classes would have been correctly classified.Regression: The final “Best Fit” line will fail to fit the data points in an effective manner. On visualization, it would clearly seem that a more complex curve can fit the data better.Fix for an underfitting model: If the model is underfitting, the developer can take the following steps to recover from the underfitting state:Train Longer: Since underfitting means less model complexity, training longer can help in learning more complex patterns. This is especially true in terms of Deep Learning.Train a more complex model: The main reason behind the model to underfit is using a model of lesser complexity than required for the data. Hence, the most obvious fix is to use a more complex model. In terms of Deep Learning, a deeper network can be used.Obtain more features: If the data set lacks enough features to get a clear inference, then Feature Engineering or collecting more features will help fit the data better.Decrease Regularization: Regularization is the process that helps Generalize the model by avoiding overfitting. However, if the model is learning less or underfitting, then it is better to decrease or completely remove Regularization techniques so that the model can learn better.New Model Architecture: Finally, if none of the above approaches work, then a new model can be used, which may provide better results.OverfittingWhen the complexity of the model is too high as compared to the data that it is trying to learn from, the model is said to “Overfit”. In other words, with increasing model complexity, the model tends to fit the Noise present in data (eg. Outliers). The model learns the data too well and hence fails to Generalize. Overfitting occurs for a model with High Variance and Low Bias.Overfitting data Visualization: With the initial idea out of the way, visualization of an overfitting model is important. Similar to underfitting, overfitting can also be showcased in two forms of supervised learning: Classification and Regression. The following graphs show overfitting for both of these cases:Classification: As shown in the figure below, the model is trained to classify between the circles and crosses, and unlike last time, this time the model learns too well. It even tends to classify the noise in the data by creating an excessively complex model (right).Regression: As shown in the figure below, the data points are laid out in a given pattern, and instead of determining the least complex model that fits the data properly, the model on the right has fitted the data points too well when compared to the appropriate fitting (left).Detection of overfitting model: The parameters to look out for to determine if the model is overfitting or not is similar to those of underfitting ones. These are listed below:Training and Validation Loss: As already mentioned, it is important to measure the loss of the model during training and validation. A very low training loss but a high validation loss would signify that the model is overfitting. Additionally, in Deep Learning, if the training loss keeps on decreasing but the validation loss remains stagnant or starts to increase, it also signifies that the model is overfitting.Too Complex Prediction Graph: If a graph is plotted showing the data points and the fitted curve, and the curve is too complex to be the simplest solution which fits the data points appropriately, then the model is overfitting.Classification: If every single class is properly classified on the training set by forming a very complex decision boundary, then there is a good chance that the model is overfitting.Regression: If the final “Best Fit” line crosses over every single data point by forming an unnecessarily complex curve, then the model is likely overfitting.Fix for an overfitting model: If the model is overfitting, the developer can take the following steps to recover from the overfitting state:Early Stopping during Training: This is especially prevalent in Deep Learning. Allowing the model to train for a high number of epochs (iterations) may lead to overfitting. Hence it is necessary to stop the model from training when the model has started to overfit. This is done by monitoring the validation loss and stopping the model when the loss stops decreasing over a given number of epochs (or iterations).Train with more data: Often, the data available for training is less when compared to the model complexity. Hence, in order to get the model to fit appropriately, it is often advisable to increase the training dataset size.Train a less complex model: As mentioned earlier, the main reason behind overfitting is excessive model complexity for a relatively less complex dataset. Hence it is advisable to reduce the model complexity in order to avoid overfitting. For Deep Learning, the model complexity can be reduced by reducing the number of layers and neurons.Remove features: As a contrast to the steps to avoid underfitting, if the number of features is too many, then the model tends to overfit. Hence, reducing the number of unnecessary or irrelevant features often leads to a better and more generalized model. Deep Learning models are usually not affected by this.Regularization: Regularization is the process of simplification of the model artificially, without losing the flexibility that it gains from having a higher complexity. With the increase in regularization, the effective model complexity decreases and hence prevents overfitting.Ensembling: Ensembling is a Machine Learning method which is used to combine the predictions from multiple separate models. It reduces the model complexity and reduces the errors of each model by taking the strengths of multiple models. Out of multiple ensembling methods, two of the most commonly used are Bagging and Boosting.GeneralizationThe term “Generalization” in Machine Learning refers to the ability of a model to train on a given data and be able to predict with a respectable accuracy on similar but completely new or unseen data. Model generalization can also be considered as the prevention of overfitting of data by making sure that the model learns adequately.Generalization and its effect on an Underfitting Model: If a model is underfitting a given dataset, then all efforts to generalize that model should be avoided. Generalization should only be the goal if the model has learned the patterns of the dataset properly and needs to generalize on top of that. Any attempt to generalize an already underfitting model will lead to further underfitting since it tends to reduce model complexity.Generalization and its effect on Overfitting Model: If a model is overfitting, then it is the ideal candidate to apply generalization techniques upon. This is primarily because an overfitting model has already learned the intricate details and patterns of the dataset. Applying generalization techniques on this kind of a model will lead to a reduction of model complexity and hence prevent overfitting. In addition to that, the model will be able to predict more accurately on unseen, but similar data.Generalization Techniques: There are no separate Generalization techniques as such, but it can easily be achieved if a model performs equally well in both training and validation data. Hence, it can be said that if we apply the techniques to prevent overfitting (eg. Regularization, Ensembling, etc.) on a model that has properly acquired the complex patterns, then a successful generalization of some degree can be achieved.Relationship between Overfitting and Underfitting with Bias-Variance TradeoffBias-Variance Tradeoff: Bias denotes the simplicity of the model. A high biased model will have a simpler architecture than that of a model with a lower bias. Similarly, complementing Bias, Variance denotes how complex the model is and how well it can fit the data with a high degree of diversity.An ideal model should have Low Bias and Low Variance. However, when it comes to practical datasets and models, it is nearly impossible to achieve a “zero” Bias and Variance. These two are complementary of each other, if one decreases beyond a certain limit, then the other starts increasing. This is known as the Bias-Variance Tradeoff. Under such circumstances, there is a “sweet spot” as shown in the figure, where both bias and variance are at their optimal values.Bias-Variance and Generalization: As it is clear from the above graph, the Bias and Variance are linked to Underfitting and Overfitting.  A model with high Bias means the model is Underfitting the given data and a model with High Variance means the model is Overfitting the given data.Hence, as it can be seen, at the optimal region of the Bias-Variance tradeoff, the model is neither underfitting nor overfitting. Hence, since there is neither underfitting nor overfitting, it can also be said that the model is most Generalized, as under these conditions the model is expected to perform equally well on Training and Validation Data. Thus, the graph depicts that the Generalization Error is minimum at the optimal value of the degree of Bias and Variance.ConclusionTo summarize, the learning capabilities of a model depend on both, model complexity and data diversity. Hence, it is necessary to keep a balance between both such that the Machine Learning Models thus trained can perform equally well when deployed in the real world.In most cases, Overfitting and Underfitting can be taken care of in order to determine the most appropriate model for the given dataset. However, even though there are certain rule-based steps that can be followed to improve a model, the insight to achieve a properly Generalized model comes with experience.

Overfitting and Underfitting With Algorithms in Machine Learning

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  • by Animikh Aich
  • 05th Aug, 2019
  • Last updated on 11th Mar, 2021
  • 10 mins read
Overfitting and Underfitting With Algorithms in Machine Learning

Curve fitting is the process of determining the best fit mathematical function for a given set of data points. It examines the relationship between multiple independent variables (predictors) and a dependent variable (response) in order to determine the “best fit” line.

Curve Fitting with Machine Learning Algorithms

In the figure shown, the red line represents the curve that is the best fit for the given purple data points. It can also be seen that curve fitting does not necessarily mean that the curve should pass over each and every data point. Instead, it is the most appropriate curve that represents all the data points adequately.

Curve Fitting vs. Machine Learning

As discussed, curve fitting refers to finding the “best fit” curve or line for a given set of data points. Even though this is also what a part of Machine Learning or Data Science does, the applications of Machine Learning or Data Science far outweigh that of Curve Fitting.

The major difference is that during Curve Fitting, the entire data is available to the developer. However, when it comes to Machine Learning, the amount of data available to the developer is only a part of the real-world data on which the Fitted Model will be applied.

Even then, Machine Learning is a vast interdisciplinary field and it consists of a lot more than just “Curve Fitting”. Machine Learning can be broadly classified into Supervised, Unsupervised and Reinforcement Learning. Considering the fact that most of the real-world problems are solved by Supervised Learning, this article concentrates on Supervised Learning itself.

Supervised learning can be further classified into Classification and Regression. In this case, the work done by Regression is similar to what Curve Fitting achieves. 

To get a broader idea, let’s look at the difference between Classification and Regression:

ClassificationRegression
It is the process of separating/classifying two or more types of data into separate categories or classes based on their characteristics.It is the process of determining the “Best Fit” curve for the given data such that, on unseen data, the data points lying on the curve accurately represent the desired result.
The output values are discrete in nature (eg. 0, 1, 2, 3, etc) and are known as “Classes”.The output values are continuous in nature (eg. 0.1, 1.78, 9.54, etc).
Example of classificationHere, the two classes (red and blue colored points) are clearly separated by the line(s) in the middle. This is an example of classification.example of Regression
Here, the curve represented by the magenta line is the “Best Fit” line for all the data points as shown. This is an example of Regression.

Noise in Data

The data that is obtained from the real world is not ideal or noise-free. It contains a lot of noise, which needs to be filtered out before applying the Machine Learning Algorithms.Overfitting and Underfitting With Algorithms

As shown in the above image, the few extra data points in the top of the left graph represent unnecessary noise, which in technical terms is known as “Outliers”. As shown in the difference between the left and the right graphs, the presence of outliers makes a considerable amount of difference when it comes to the determination of the “Best Fit” line. Hence, it is of immense importance to apply preprocessing techniques in order to remove outliers from the data.

Let us look at two of the most common types of noise in Data:

Outliers: As already discussed, outliers are data points which do not belong to the original set of data. These data points are either too high or too low in value, such that they do not belong to the general distribution of the rest of the dataset. They are usually due to misrepresentation or an accidental entry of wrong data. There are several statistical algorithms which are used to detect and remove such outliers.

Missing Data: In sharp contrast to outliers, missing data is another major challenge when it comes to the dataset. The occurrence is quite common in tabular datasets (eg. CSV files) and is a challenge if the number of missing data points exceeds 10% of the total size of the dataset. Most Machine Learning algorithms fail to perform on such datasets. However, certain algorithms such as Decision Trees are quite resilient when it comes to data with missing data and are able to provide accurate results even when supplied with such noisy datasets. Similar to Outliers, there are statistical methods to handle missing data or “NaN” (Not a Number) values. The most common of them is to remove or “drop” the row containing the missing data. 

Training of Data

“Training” is terminology associated with Machine Learning and it basically means the “Fitting” of data or “Learning” from data. This is the step where the Model starts to learn from the given data in order to be able to predict on similar but unseen data. This step is crucial since the final output (or Prediction) of the model will be based on how well the model was able to acquire the patterns of the training data.

Training in Machine Learning: Depending on the type of data, the training methodology varies. Hence, here we assume simple tabular (eg. CSV) text data. Before the model can be fitted on the data, there are a few steps that have to be followed:

  • Data Cleaning/Preprocessing: The raw data that is thus obtained from the real-world is likely to contain a good amount of noise in it. In addition to that, the data might not be homogenous, which means, the values of different “features” might belong to different ranges. Hence, after the removal of noise, the data needs to be normalized or scaled in order to make it homogeneous.
  • Feature Engineering: In a tabular dataset, all the columns that describe the data are called “Features”. These features are necessary to correctly predict the target value. However, data often contains columns which are irrelevant to the output of the model. Hence, these columns need to be removed or statistically processed to make sure that they do not interfere with the training of the model on features that are relevant. In addition to the removal of irrelevant features, it is often required to create new relevant features from the existing features. This allows the model to learn better and this process is also called “Feature Extraction”.
  • Train, Validation and Test Split: After the data has been preprocessed and is ready for training, the data is split into Training Data, Validation Data and Testing Data in the ratio of 60:20:20 (usually). This ratio varies depending on the availability of data and on the application. This is done to ensure that the model does not unnecessarily “Overfit” or “Underfit”, and performs equally well when deployed in the real world.
  • Training: Finally, as the last step,  the Training Data is fed into the model to train upon. Multiple models can be trained simultaneously and their performance can be measured against each other with the help of the Validation Set, based on which the best model is selected. This is called “Model Selection”. Finally, the selected model is used to predict on the Test Set to get a final test score, which more or less accurately defines the performance of the model on the given dataset.

Training in Deep Learning: Deep Learning is a part of machine learning, but instead of relying on statistical methods, Deep Learning Techniques largely depend on calculus and aims to mimic the Neural structure of the biological brain, and hence, are often referred to as Neural Networks.

The training process for Deep Learning is quite similar to that of Machine Learning except that there is no need for “Feature Engineering”. Since deep learning models largely rely on weights to specify the importance of given input (feature), the model automatically tends to learn which features are relevant and which feature is not. Hence, it assigns a “high” weight to the features that are relevant and assigns a “low” weight to the features that are not relevant. This removes the need for a separate Feature Engineering.

This difference is correctly portrayed in the following figure:

difference is correctly portrayed in Deep Learning and Machine Learning

Improper Training of Data: As discussed above, the training of data is the most crucial step of any Machine Learning Algorithm. Improper training can lead to drastic performance degradation of the model on deployment. On a high level, there are two main types of outcomes of Improper Training: Underfitting and Overfitting.

Underfitting

When the complexity of the model is too less for it to learn the data that is given as input, the model is said to “Underfit”. In other words, the excessively simple model fails to “Learn” the intricate patterns and underlying trends of the given dataset. Underfitting occurs for a model with Low Variance and High Bias.

Underfitting data Visualization: With the initial idea out of the way, visualization of an underfitting model is important. This helps in determining if the model is underfitting the given data during training. As already discussed, supervised learning is of two types: Classification and Regression. The following graphs show underfitting for both of these cases:

  • Classification: As shown in the figure below, the model is trained to classify between the circles and crosses. However, it is unable to do so properly due to the straight line, which fails to properly classify either of the two classes.

Under fitting Too simple to explain the variance

  • Regression: As shown in the figure below, the data points are laid out in a given pattern, but the model is unable to “Fit” properly to the given data due to low model complexity.

the data points are laid out in a given pattern

Detection of underfitting model: The model may underfit the data, but it is necessary to know when it does so. The following steps are the checks that are used to determine if the model is underfitting or not.

  1. Training and Validation Loss: During training and validation, it is important to check the loss that is generated by the model. If the model is underfitting, the loss for both training and validation will be significantly high. In terms of Deep Learning, the loss will not decrease at the rate that it is supposed to if the model has reached saturation or is underfitting.
  2. Over Simplistic Prediction Graph: If a graph is plotted showing the data points and the fitted curve, and the curve is over-simplistic (as shown in the image above), then the model is suffering from underfitting. A more complex model is to be tried out.
    1. Classification: A lot of classes will be misclassified in the training set as well as the validation set. On data visualization, the graph would indicate that if there was a more complex model, more classes would have been correctly classified.
    2. Regression: The final “Best Fit” line will fail to fit the data points in an effective manner. On visualization, it would clearly seem that a more complex curve can fit the data better.

Fix for an underfitting model: If the model is underfitting, the developer can take the following steps to recover from the underfitting state:

  1. Train Longer: Since underfitting means less model complexity, training longer can help in learning more complex patterns. This is especially true in terms of Deep Learning.
  2. Train a more complex model: The main reason behind the model to underfit is using a model of lesser complexity than required for the data. Hence, the most obvious fix is to use a more complex model. In terms of Deep Learning, a deeper network can be used.
  3. Obtain more features: If the data set lacks enough features to get a clear inference, then Feature Engineering or collecting more features will help fit the data better.
  4. Decrease Regularization: Regularization is the process that helps Generalize the model by avoiding overfitting. However, if the model is learning less or underfitting, then it is better to decrease or completely remove Regularization techniques so that the model can learn better.
  5. New Model Architecture: Finally, if none of the above approaches work, then a new model can be used, which may provide better results.

Overfitting

When the complexity of the model is too high as compared to the data that it is trying to learn from, the model is said to “Overfit”. In other words, with increasing model complexity, the model tends to fit the Noise present in data (eg. Outliers). The model learns the data too well and hence fails to Generalize. Overfitting occurs for a model with High Variance and Low Bias.

Overfitting data Visualization: With the initial idea out of the way, visualization of an overfitting model is important. Similar to underfitting, overfitting can also be showcased in two forms of supervised learning: Classification and Regression. The following graphs show overfitting for both of these cases:

  • Classification: As shown in the figure below, the model is trained to classify between the circles and crosses, and unlike last time, this time the model learns too well. It even tends to classify the noise in the data by creating an excessively complex model (right).

the model is trained to classify between the circles and crosses

  • Regression: As shown in the figure below, the data points are laid out in a given pattern, and instead of determining the least complex model that fits the data properly, the model on the right has fitted the data points too well when compared to the appropriate fitting (left).

the data points are laid out in a given pattern

Detection of overfitting model: The parameters to look out for to determine if the model is overfitting or not is similar to those of underfitting ones. These are listed below:

  1. Training and Validation Loss: As already mentioned, it is important to measure the loss of the model during training and validation. A very low training loss but a high validation loss would signify that the model is overfitting. Additionally, in Deep Learning, if the training loss keeps on decreasing but the validation loss remains stagnant or starts to increase, it also signifies that the model is overfitting.
  2. Too Complex Prediction Graph: If a graph is plotted showing the data points and the fitted curve, and the curve is too complex to be the simplest solution which fits the data points appropriately, then the model is overfitting.
    1. Classification: If every single class is properly classified on the training set by forming a very complex decision boundary, then there is a good chance that the model is overfitting.
    2. Regression: If the final “Best Fit” line crosses over every single data point by forming an unnecessarily complex curve, then the model is likely overfitting.

Fix for an overfitting model: If the model is overfitting, the developer can take the following steps to recover from the overfitting state:

  1. Early Stopping during Training: This is especially prevalent in Deep Learning. Allowing the model to train for a high number of epochs (iterations) may lead to overfitting. Hence it is necessary to stop the model from training when the model has started to overfit. This is done by monitoring the validation loss and stopping the model when the loss stops decreasing over a given number of epochs (or iterations).
  2. Train with more data: Often, the data available for training is less when compared to the model complexity. Hence, in order to get the model to fit appropriately, it is often advisable to increase the training dataset size.
  3. Train a less complex model: As mentioned earlier, the main reason behind overfitting is excessive model complexity for a relatively less complex dataset. Hence it is advisable to reduce the model complexity in order to avoid overfitting. For Deep Learning, the model complexity can be reduced by reducing the number of layers and neurons.
  4. Remove features: As a contrast to the steps to avoid underfitting, if the number of features is too many, then the model tends to overfit. Hence, reducing the number of unnecessary or irrelevant features often leads to a better and more generalized model. Deep Learning models are usually not affected by this.
  5. Regularization: Regularization is the process of simplification of the model artificially, without losing the flexibility that it gains from having a higher complexity. With the increase in regularization, the effective model complexity decreases and hence prevents overfitting.
  6. Ensembling: Ensembling is a Machine Learning method which is used to combine the predictions from multiple separate models. It reduces the model complexity and reduces the errors of each model by taking the strengths of multiple models. Out of multiple ensembling methods, two of the most commonly used are Bagging and Boosting.

Generalization

The term “Generalization” in Machine Learning refers to the ability of a model to train on a given data and be able to predict with a respectable accuracy on similar but completely new or unseen data. Model generalization can also be considered as the prevention of overfitting of data by making sure that the model learns adequately.

Generalization and its effect on an Underfitting Model: If a model is underfitting a given dataset, then all efforts to generalize that model should be avoided. Generalization should only be the goal if the model has learned the patterns of the dataset properly and needs to generalize on top of that. Any attempt to generalize an already underfitting model will lead to further underfitting since it tends to reduce model complexity.

Generalization and its effect on Overfitting Model: If a model is overfitting, then it is the ideal candidate to apply generalization techniques upon. This is primarily because an overfitting model has already learned the intricate details and patterns of the dataset. Applying generalization techniques on this kind of a model will lead to a reduction of model complexity and hence prevent overfitting. In addition to that, the model will be able to predict more accurately on unseen, but similar data.

Generalization Techniques: There are no separate Generalization techniques as such, but it can easily be achieved if a model performs equally well in both training and validation data. Hence, it can be said that if we apply the techniques to prevent overfitting (eg. Regularization, Ensembling, etc.) on a model that has properly acquired the complex patterns, then a successful generalization of some degree can be achieved.

Relationship between Overfitting and Underfitting with Bias-Variance Tradeoff

Bias-Variance Tradeoff: Bias denotes the simplicity of the model. A high biased model will have a simpler architecture than that of a model with a lower bias. Similarly, complementing Bias, Variance denotes how complex the model is and how well it can fit the data with a high degree of diversity.

An ideal model should have Low Bias and Low Variance. However, when it comes to practical datasets and models, it is nearly impossible to achieve a “zero” Bias and Variance. These two are complementary of each other, if one decreases beyond a certain limit, then the other starts increasing. This is known as the Bias-Variance Tradeoff. Under such circumstances, there is a “sweet spot” as shown in the figure, where both bias and variance are at their optimal values.

Relationship between Overfitting and Underfitting with Bias-Variance Tradeoff

Bias-Variance and Generalization: As it is clear from the above graph, the Bias and Variance are linked to Underfitting and Overfitting.  A model with high Bias means the model is Underfitting the given data and a model with High Variance means the model is Overfitting the given data.

Hence, as it can be seen, at the optimal region of the Bias-Variance tradeoff, the model is neither underfitting nor overfitting. Hence, since there is neither underfitting nor overfitting, it can also be said that the model is most Generalized, as under these conditions the model is expected to perform equally well on Training and Validation Data. Thus, the graph depicts that the Generalization Error is minimum at the optimal value of the degree of Bias and Variance.

Conclusion

To summarize, the learning capabilities of a model depend on both, model complexity and data diversity. Hence, it is necessary to keep a balance between both such that the Machine Learning Models thus trained can perform equally well when deployed in the real world.

In most cases, Overfitting and Underfitting can be taken care of in order to determine the most appropriate model for the given dataset. However, even though there are certain rule-based steps that can be followed to improve a model, the insight to achieve a properly Generalized model comes with experience.

Animikh

Animikh Aich

Computer Vision Engineer

Animikh Aich is a Deep Learning enthusiast, currently working as a Computer Vision Engineer. His work includes three International Conference publications and several projects based on Computer Vision and Machine Learning.

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3 comments

praveen sharma 06 Aug 2019

Thank you very much for your article, very informative and explained easy ways. This information is very helpful for my further career!

pravallika 16 Aug 2019

Nice written useful and good understanding thanks.

Krunal 20 Aug 2019

Awesome Post :) Thanks for this.

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Why Should You Start a Career in Machine Learning?

If you are even remotely interested in technology you would have heard of machine learning. In fact machine learning is now a buzzword and there are dozens of articles and research papers dedicated to it.  Machine learning is a technique which makes the machine learn from past experiences. Complex domain problems can be resolved quickly and efficiently using Machine Learning techniques.  We are living in an age where huge amounts of data are produced every second. This explosion of data has led to creation of machine learning models which can be used to analyse data and to benefit businesses.  This article tries to answer a few important concepts related to Machine Learning and informs you about the career path in this prestigious and important domain.What is Machine Learning?So, here’s your introduction to Machine Learning. This term was coined in the year 1997. “A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P, if its performance at the tasks improves with the experiences.”, as defined in the book on ML written by Mitchell in 1997. The difference between a traditional programming and programming using Machine Learning is depicted here, the first Approach (a) is a traditional approach, and second approach (b) is a Machine Learning based approach.Machine Learning encompasses the techniques in AI which allow the system to learn automatically looking at the data available. While learning, the system tries to improve the experience without making any explicit efforts in programming. Any machine learning application follows the following steps broadlySelecting the training datasetAs the definition indicates, machine learning algorithms require past experience, that is data, for learning. So, selection of appropriate data is the key for any machine learning application.Preparing the dataset by preprocessing the dataOnce the decision about the data is made, it needs to be prepared for use. Machine learning algorithms are very susceptible to the small changes in data. To get the right insights, data must be preprocessed which includes data cleaning and data transformation.  Exploring the basic statistics and properties of dataTo understand what the data wishes to convey, the data engineer or Machine Learning engineer needs to understand the properties of data in detail. These details are understood by studying the statistical properties of data. Visualization is an important process to understand the data in detail.Selecting the appropriate algorithm to apply on the datasetOnce the data is ready and understood in detail, then appropriate Machine Learning algorithms or models are selected. The choice of algorithm depends on characteristics of data as well as type of task to be performed on the data. The choice also depends on what kind of output is required from the data.Checking the performance and fine-tuning the parameters of the algorithmThe model or algorithm chosen is fine-tuned to get improved performance. If multiple models are applied, then they are weighed against the performance. The final algorithm is again fine-tuned to get appropriate output and performance.Why Pursue a Career in Machine Learning in 2021?A recent survey has estimated that the jobs in AI and ML have grown by more than 300%. Even before the pandemic struck, Machine Learning skills were in high demand and the demand is expected to increase two-fold in the near future.A career in machine learning gives you the opportunity to make significant contributions in AI, the future of technology. All the big and small businesses are adopting Machine Learning models to improve their bottom-line margins and return on investment.  The use of Machine Learning has gone beyond just technology and it is now used in diverse industries including healthcare, automobile, manufacturing, government and more. This has greatly enhanced the value of Machine Learning experts who can earn an average salary of $112,000.  Huge numbers of jobs are expected to be created in the coming years.  Here are a few reasons why one should pursue a career in Machine Learning:The global machine learning market is expected to touch $20.83B in 2024, according to Forbes.  We are living in a digital age and this explosion of data has made the use of machine learning models a necessity. Machine Learning is the only way to extract meaning out of data and businesses need Machine Learning engineers to analyze huge data and gain insights from them to improve their businesses.If you like numbers, if you like research, if you like to read and test and if you have a passion to analyse, then machine learning is the career for you. Learning the right tools and programming languages will help you use machine learning to provide appropriate solutions to complex problems, overcome challenges and grow the business.Machine Learning is a great career option for those interested in computer science and mathematics. They can come up with new Machine Learning algorithms and techniques to cater to the needs of various business domains.As explained above, a career in machine learning is both rewarding and lucrative. There are huge number of opportunities available if you have the right expertise and knowledge. On an average, Machine Learning engineers get higher salaries, than other software developers.Years of experience in the Machine Learning domain, helps you break into data scientist roles, which is not just among the hottest careers of our generation but also a highly respected and lucrative career. Right skills in the right business domain helps you progress and make a mark for yourself in your organization. For example, if you have expertise in pharmaceutical industries and experience working in Machine learning, then you may land job roles as a data scientist consultant in big pharmaceutical companies.Statistics on Machine learning growth and the industries that use MLAccording to a research paper in AI Multiple (https://research.aimultiple.com/ml-stats/), the Machine Learning market will grow to 9 Billion USD by the end of 2022. There are various areas where Machine Learning models and solutions are getting deployed, and businesses see an overall increase of 44% investments in this area. North America is one of the leading regions in the adoption of Machine Learning followed by Asia.The Global Machine Learning market will grow by 42% which is evident from the following graph. Image sourceThere is a huge demand for Machine Learning modelling because of the large use of Cloud Based Applications and Services. The pandemic has changed the face of businesses, making them heavily dependent on Cloud and AI based services. Google, IBM, and Amazon are just some of the companies that have invested heavily in AI and Machine Learning based application development, to provide robust solutions for problems faced by small to large scale businesses. Machine Learning and Cloud based solutions are scalable and secure for all types of business.ML analyses and interprets data patterns, computing and developing algorithms for various business purposes.Advantages of Machine Learning courseNow that we have established the advantages of perusing a career in Machine Learning, let’s understand from where to start our machine learning journey. The best option would be to start with a Machine Learning course. There are various platforms which offer popular Machine Learning courses. One can always start with an online course which is both effective and safe in these COVID times.These courses start with an introduction to Machine Learning and then slowly help you to build your skills in the domain. Many courses even start with the basics of programming languages such as Python, which are important for building Machine Learning models. Courses from reputed institutions will hand hold you through the basics. Once the basics are clear, you may switch to an offline course and get the required certification.Online certifications have the same value as offline classes. They are a great way to clear your doubts and get personalized help to grow your knowledge. These courses can be completed along with your normal job or education, as most are self-paced and can be taken at a time of your convenience. There are plenty of online blogs and articles to aid you in completion of your certification.Machine Learning courses include many real time case studies which help you in understanding the basics and application aspects. Learning and applying are both important and are covered in good Machine Learning Courses. So, do your research and pick an online tutorial that is from a reputable institute.What Does the Career Path in Machine Learning Look Like?One can start their career in Machine Learning domain as a developer or application programmer. But the acquisition of the right skills and experience can lead you to various career paths. Following are some of the career options in Machine Learning (not an exhaustive list):Data ScientistA data scientist is a person with rich experience in a particular business field. A person who has a knowledge of domain, as well as machine learning modelling, is a data scientist. Data Scientists’ job is to study the data carefully and suggest accurate models to improve the business.AI and Machine Learning EngineerAn AI engineer is responsible for choosing the proper Machine Learning Algorithm based on natural language processing and neural network. They are responsible for applying it in AI applications like personalized advertising.  A Machine Learning Engineer is responsible for creating the appropriate models for improvement of the businessData EngineerA Data Engineer, as the name suggests, is responsible to collect data and make it ready for the application of Machine Learning models. Identification of the right data and making it ready for extraction of further insights is the main work of a data engineer.Business AnalystA person who studies the business and analyzes the data to get insights from it is a Business Analyst. He or she is responsible for extracting the insights from the data at hand.Business Intelligence (BI) DeveloperA BI developer uses Machine Learning and Data Analytics techniques to work on a large amount of data. Proper representation of data to suit business decisions, using the latest tools for creation of intuitive dashboards is the role of a BI developer.  Human Machine Interface learning engineerCreating tools using machine learning techniques to ease the human machine interaction or automate decisions, is the role of a Human Machine Interface learning engineer. This person helps in generating choices for users to ease their work.Natural Language Processing (NLP) engineer or developerAs the name suggests, this person develops various techniques to process Natural Language constructs. Building applications or systems using machine learning techniques to build Natural Language based applications is their main task. They create multilingual Chatbots for use in websites and other applications.Why are Machine Learning Roles so popular?As mentioned above, the market growth of AI and ML has increased tremendously over the past years. The Machine Learning Techniques are applied in every domain including marketing, sales, product recommendations, brand retention, creating advertising, understanding the sentiments of customer, security, banking and more. Machine learning algorithms are also used in emails to ease the users work. This says a lot, and proves that a career in Machine Learning is in high demand as all businesses are incorporating various machine learning techniques and are improving their business.One can harness this popularity by skilling up with Machine Learning skills. Machine Learning models are now being used by every company, irrespective of their size--small or big, to get insights on their data and use these insights to improve the business. As every company wishes to grow faster, they are deploying more machine learning engineers to get their work done on time. Also, the migration of businesses to Cloud services for better security and scalability, has increased their requirement for more Machine Learning algorithms and models to cater to their needs.Introducing the Machine learning techniques and solutions has brought huge returns for businesses.  Machine Learning solution providers like Google, IBM, Microsoft etc. are investing in human resources for development of Machine Learning models and algorithms. The tools developed by them are popularly used by businesses to get early returns. It has been observed that there is significant increase in patents in Machine Learning domains since the past few years, indicating the quantum of work happening in this domain.Machine Learning SkillsLet’s visit a few important skills one must acquire to work in the domain of Machine Learning.Programming languagesKnowledge of programming is very important for a career in Machine Learning. Languages like Python and R are popularly used to develop applications using Machine Learning models and algorithms. Python, being the simplest and most flexible language, is very popular for AI and Machine Learning applications. These languages provide rich support of libraries for implementation of Machine Learning Algorithms. A person who is good in programming can work very efficiently in this domain.Mathematics and StatisticsThe base for Machine Learning is mathematics and statistics. Statistics applied to data help in understanding it in micro detail. Many machine learning models are based on the probability theory and require knowledge of linear algebra, transformations etc. A good understanding of statistics and probability increases the early adoption to Machine Learning domain.Analytical toolsA plethora of analytical tools are available where machine learning models are already implemented and made available for use. Also, these tools are very good for visualization purposes. Tools like IBM Cognos, PowerBI, Tableue etc are important to pursue a career as a  Machine Learning engineer.Machine Learning Algorithms and librariesTo become a master in this domain, one must master the libraries which are provided with various programming languages. The basic understanding of how machine learning algorithms work and are implemented is crucial.Data Modelling for Machine Learning based systemsData lies at the core of any Machine Learning application. So, modelling the data to suit the application of Machine Learning algorithms is an important task. Data modelling experts are the heart of development teams that develop machine learning based systems. SQL based solutions like Oracle, SQL Server, and NoSQL solutions are important for modelling data required for Machine Learning applications. MongoDB, DynamoDB, Riak are some important NOSQL based solutions available to process unstructured data for Machine Learning applications.Other than these skills, there are two other skills that may prove to be beneficial for those planning on a career in the Machine Learning domain:Natural Language processing techniquesFor E-commerce sites, customer feedback is very important and crucial in determining the roadmap of future products. Many customers give reviews for the products that they have used or give suggestions for improvement. These feedbacks and opinions are analyzed to gain more insights about the customers buying habits as well as about the products. This is part of natural language processing using Machine Learning. The likes of Google, Facebook, Twitter are developing machine learning algorithms for Natural Language Processing and are constantly working on improving their solutions. Knowledge of basics of Natural Language Processing techniques and libraries is must in the domain of Machine Learning.Image ProcessingKnowledge of Image and Video processing is very crucial when a solution is required to be developed in the area of security, weather forecasting, crop prediction etc. Machine Learning based solutions are very effective in these domains. Tools like Matlab, Octave, OpenCV are some important tools available to develop Machine Learning based solutions which require image or video processing.ConclusionMachine Learning is a technique to automate the tasks based on past experiences. This is among the most lucrative career choices right now and will continue to remain so in the future. Job opportunities are increasing day by day in this domain. Acquiring the right skills by opting for a proper Machine Learning course is important to grow in this domain. You can have an impressive career trajectory as a machine learning expert, provided you have the right skills and expertise.
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Why Should You Start a Career in Machine Learning?

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Types of Probability Distributions Every Data Science Expert Should know

Data Science has become one of the most popular interdisciplinary fields. It uses scientific approaches, methods, algorithms, and operations to obtain facts and insights from unstructured, semi-structured, and structured datasets. Organizations use these collected facts and insights for efficient production, business growth, and to predict user requirements. Probability distribution plays a significant role in performing data analysis equipping a dataset for training a model. In this article, you will learn about the types of Probability Distribution, random variables, types of discrete distributions, and continuous distribution.  What is Probability Distribution? A Probability Distribution is a statistical method that determines all the probable values and possibilities that a random variable can deliver from a particular range. 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The density function and distribution techniques can also help in plotting data, thus supporting data analysts to visualize data and extract meaning. General Properties of Probability Distributions Probability distribution determines the likelihood of any outcome. The mathematical expression takes a specific value of x and shows the possibility of a random variable with p(x). Some general properties of the probability distribution are – The total of all probabilities for any possible value becomes equal to 1. In a probability distribution, the possibility of finding any specific value or a range of values must lie between 0 and 1. Probability distributions tell us the dispersal of the values from the random variable. Consequently, the type of variable also helps determine the type of probability distribution.Common Data Types Before jumping directly into explaining the different probability distributions, let us first understand the different types of probability distributions or the main categories of the probability distribution. Data analysts and data engineers have to deal with a broad spectrum of data, such as text, numerical, image, audio, voice, and many more. Each of these have a specific means to be represented and analyzed. Data in a probability distribution can either be discrete or continuous. Numerical data especially takes one of the two forms. Discrete data: They take specific values where the outcome of the data remains fixed. Like, for example, the consequence of rolling two dice or the number of overs in a T-20 match. In the first case, the result lies between 2 and 12. In the second case, the event will be less than 20. Different types of discrete distributions that use discrete data are: Binomial Distribution Hypergeometric Distribution Geometric Distribution Poisson Distribution Negative Binomial Distribution Multinomial Distribution  Continuous data: It can obtain any value irrespective of bound or limit. Example: weight, height, any trigonometric value, age, etc. Different types of continuous distributions that use continuous data are: Beta distribution Cauchy distribution Exponential distribution Gamma distribution Logistic distribution Weibull distribution Types of Probability Distribution explained Here are some of the popular types of Probability distributions used by data science professionals. (Try all the code using Jupyter Notebook) Normal Distribution: It is also known as Gaussian distribution. It is one of the simplest types of continuous distribution. This probability distribution is symmetrical around its mean value. It also shows that data at close proximity of the mean is frequently occurring, compared to data that is away from it. Here, mean = 0, variance = finite valueHere, you can see 0 at the center is the Normal Distribution for different mean and variance values. Here is a code example showing the use of Normal Distribution: from scipy.stats import norm  import matplotlib.pyplot as mpl  import numpy as np  def normalDist() -> None:      fig, ax = mpl.subplots(1, 1)      mean, var, skew, kurt = norm.stats(moments = 'mvsk')      x = np.linspace(norm.ppf(0.01),  norm.ppf(0.99), 100)      ax.plot(x, norm.pdf(x),          'r-', lw = 5, alpha = 0.6, label = 'norm pdf')      ax.plot(x, norm.cdf(x),          'b-', lw = 5, alpha = 0.6, label = 'norm cdf')      vals = norm.ppf([0.001, 0.5, 0.999])      np.allclose([0.001, 0.5, 0.999], norm.cdf(vals))      r = norm.rvs(size = 1000)      ax.hist(r, normed = True, histtype = 'stepfilled', alpha = 0.2)      ax.legend(loc = 'best', frameon = False)      mpl.show()  normalDist() Output: Bernoulli Distribution: It is the simplest type of probability distribution. It is a particular case of Binomial distribution, where n=1. It means a binomial distribution takes 'n' number of trials, where n > 1 whereas, the Bernoulli distribution takes only a single trial.   Probability Mass Function of a Bernoulli’s Distribution is:  where p = probability of success and q = probability of failureHere is a code example showing the use of Bernoulli Distribution: from scipy.stats import bernoulli  import seaborn as sb    def bernoulliDist():      data_bern = bernoulli.rvs(size=1200, p = 0.7)      ax = sb.distplot(          data_bern,           kde = True,           color = 'g',           hist_kws = {'alpha' : 1},          kde_kws = {'color': 'y', 'lw': 3, 'label': 'KDE'})      ax.set(xlabel = 'Bernouli Values', ylabel = 'Frequency Distribution')  bernoulliDist() Output:Continuous Uniform Distribution: In this type of continuous distribution, all outcomes are equally possible; each variable gets the same probability of hit as a consequence. This symmetric probabilistic distribution has random variables at an equal interval, with the probability of 1/(b-a). Here is a code example showing the use of Uniform Distribution: from numpy import random  import matplotlib.pyplot as mpl  import seaborn as sb  def uniformDist():      sb.distplot(random.uniform(size = 1200), hist = True)      mpl.show()  uniformDist() Output: Log-Normal Distribution: A Log-Normal distribution is another type of continuous distribution of logarithmic values that form a normal distribution. We can transform a log-normal distribution into a normal distribution. Here is a code example showing the use of Log-Normal Distribution import matplotlib.pyplot as mpl  def lognormalDist():      muu, sig = 3, 1      s = np.random.lognormal(muu, sig, 1000)      cnt, bins, ignored = mpl.hist(s, 80, normed = True, align ='mid', color = 'y')      x = np.linspace(min(bins), max(bins), 10000)      calc = (np.exp( -(np.log(x) - muu) **2 / (2 * sig**2))             / (x * sig * np.sqrt(2 * np.pi)))      mpl.plot(x, calc, linewidth = 2.5, color = 'g')      mpl.axis('tight')      mpl.show()  lognormalDist() Output: Pareto Distribution: It is one of the most critical types of continuous distribution. The Pareto Distribution is a skewed statistical distribution that uses power-law to describe quality control, scientific, social, geophysical, actuarial, and many other types of observable phenomena. The distribution shows slow or heavy-decaying tails in the plot, where much of the data reside at its extreme end. Here is a code example showing the use of Pareto Distribution – import numpy as np  from matplotlib import pyplot as plt  from scipy.stats import pareto  def paretoDist():      xm = 1.5        alp = [2, 4, 6]       x = np.linspace(0, 4, 800)      output = np.array([pareto.pdf(x, scale = xm, b = a) for a in alp])      plt.plot(x, output.T)      plt.show()  paretoDist() Output:Exponential Distribution: It is a type of continuous distribution that determines the time elapsed between events (in a Poisson process). Let’s suppose, that you have the Poisson distribution model that holds the number of events happening in a given period. We can model the time between each birth using an exponential distribution.Here is a code example showing the use of Pareto Distribution – from numpy import random  import matplotlib.pyplot as mpl  import seaborn as sb  def expDist():      sb.distplot(random.exponential(size = 1200), hist = True)      mpl.show()   expDist()Output:Types of the Discrete probability distribution – There are various types of Discrete Probability Distribution a Data science aspirant should know about. Some of them are – Binomial Distribution: It is one of the popular discrete distributions that determine the probability of x success in the 'n' trial. We can use Binomial distribution in situations where we want to extract the probability of SUCCESS or FAILURE from an experiment or survey which went through multiple repetitions. A Binomial distribution holds a fixed number of trials. Also, a binomial event should be independent, and the probability of obtaining failure or success should remain the same. Here is a code example showing the use of Binomial Distribution – from numpy import random  import matplotlib.pyplot as mpl  import seaborn as sb    def binomialDist():      sb.distplot(random.normal(loc = 50, scale = 6, size = 1200), hist = False, label = 'normal')      sb.distplot(random.binomial(n = 100, p = 0.6, size = 1200), hist = False, label = 'binomial')      plt.show()    binomialDist() Output:Geometric Distribution: The geometric probability distribution is one of the crucial types of continuous distributions that determine the probability of any event having likelihood ‘p’ and will happen (occur) after 'n' number of Bernoulli trials. Here 'n' is a discrete random variable. In this distribution, the experiment goes on until we encounter either a success or a failure. The experiment does not depend on the number of trials. Here is a code example showing the use of Geometric Distribution – import matplotlib.pyplot as mpl  def probability_to_occur_at(attempt, probability):      return (1-p)**(attempt - 1) * probability  p = 0.3  attempt = 4  attempts_to_show = range(21)[1:]  print('Possibility that this event will occur on the 7th try: ', probability_to_occur_at(attempt, p))  mpl.xlabel('Number of Trials')  mpl.ylabel('Probability of the Event')  barlist = mpl.bar(attempts_to_show, height=[probability_to_occur_at(x, p) for x in attempts_to_show], tick_label=attempts_to_show)  barlist[attempt].set_color('g')  mpl.show() Output:Poisson Distribution: Poisson distribution is one of the popular types of discrete distribution that shows how many times an event has the possibility of occurrence in a specific set of time. We can obtain this by limiting the Bernoulli distribution from 0 to infinity. Data analysts often use the Poisson distributions to comprehend independent events occurring at a steady rate in a given time interval. Here is a code example showing the use of Poisson Distribution from scipy.stats import poisson  import seaborn as sb  import numpy as np  import matplotlib.pyplot as mpl  def poissonDist():       mpl.figure(figsize = (10, 10))      data_binom = poisson.rvs(mu = 3, size = 5000)      ax = sb.distplot(data_binom, kde=True, color = 'g',                       bins=np.arange(data_binom.min(), data_binom.max() + 1),                       kde_kws={'color': 'y', 'lw': 4, 'label': 'KDE'})      ax.set(xlabel = 'Poisson Distribution', ylabel='Data Frequency')      mpl.show()      poissonDist() Output:Multinomial Distribution: A multinomial distribution is another popular type of discrete probability distribution that calculates the outcome of an event having two or more variables. The term multi means more than one. The Binomial distribution is a particular type of multinomial distribution with two possible outcomes - true/false or heads/tails. Here is a code example showing the use of Multinomial Distribution – import numpy as np  import matplotlib.pyplot as mpl  np.random.seed(99)   n = 12                      pvalue = [0.3, 0.46, 0.22]     s = []  p = []     for size in np.logspace(2, 3):      outcomes = np.random.multinomial(n, pvalue, size=int(size))        prob = sum((outcomes[:,0] == 7) & (outcomes[:,1] == 2) & (outcomes[:,2] == 3))/len(outcomes)      p.append(prob)      s.append(int(size))  fig1 = mpl.figure()  mpl.plot(s, p, 'o-')  mpl.plot(s, [0.0248]*len(s), '--r')  mpl.grid()  mpl.xlim(xmin = 0)  mpl.xlabel('Number of Events')  mpl.ylabel('Function p(X = K)') Output:Negative Binomial Distribution: It is also a type of discrete probability distribution for random variables having negative binomial events. It is also known as the Pascal distribution, where the random variable tells us the number of repeated trials produced during a specific number of experiments.  Here is a code example showing the use of Negative Binomial Distribution – import matplotlib.pyplot as mpl   import numpy as np   from scipy.stats import nbinom    x = np.linspace(0, 6, 70)   gr, kr = 0.3, 0.7        g = nbinom.ppf(x, gr, kr)   s = nbinom.pmf(x, gr, kr)   mpl.plot(x, g, "*", x, s, "r--") Output: Apart from these mentioned distribution types, various other types of probability distributions exist that data science professionals can use to extract reliable datasets. In the next topic, we will understand some interconnections & relationships between various types of probability distributions. Relationship between various Probability distributions – It is surprising to see that different types of probability distributions are interconnected. In the chart shown below, the dashed line is for limited connections between two families of distribution, whereas the solid lines show the exact relationship between them in terms of transformation, variable, type, etc. Conclusion  Probability distributions are prevalent among data analysts and data science professionals because of their wide usage. Today, companies and enterprises hire data science professionals in many sectors, namely, computer science, health, insurance, engineering, and even social science, where probability distributions appear as fundamental tools for application. It is essential for Data analysts and data scientists. to know the core of statistics. Probability Distributions perform a requisite role in analyzing data and cooking a dataset to train the algorithms efficiently. If you want to learn more about data science - particularly probability distributions and their uses, check out KnowledgeHut's comprehensive Data science course. 
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Types of Probability Distributions Every Data Scie...

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