Machine learning
Filter

- by Priyankur Sarkar
- 14th Oct, 2019
- Last updated on 11th Mar, 2021
- 8 mins read

In today’s world, innovations happen on a daily basis, rendering all the previous versions of that product, service or skill-set outdated and obsolete. In such a dynamic and chaotic space, how can we make an informed decision without getting carried away by plain hype? To make the right decisions, we must follow a set of processes; investigate the current scenario, chart down your expectations, collect reviews from others, explore your options, select the best solution after weighing the pros and cons, make a decision and take the requisite action.

For example, if you are looking to purchase a computer, will you simply walk up to the store and pick any laptop or notebook? It’s highly unlikely that you would do so. You would probably search on Amazon, browse a few web portals where people have posted their reviews and compare different models, checking for their features, specifications and prices. You will also probably ask your friends and colleagues for their opinion. In short, you would not directly jump to a conclusion, but will instead make a decision considering the opinions and reviews of other people as well.

Ensemble models in machine learning also operate on a similar manner. They combine the decisions from multiple models to improve the overall performance. The objective of this article is to introduce the concept of ensemble learning and understand algorithms like bagging and random forest which use a similar technique.

Ensemble methods aim at improving the predictive performance of a given statistical learning or model ﬁtting technique. The general principle of ensemble methods is to construct a linear combination of some model ﬁtting method, instead of using a single ﬁt of the method.

An ensemble is itself a supervised learning algorithm, because it can be trained and then used to make predictions. Ensemble methods combine several decision trees classifiers to produce better predictive performance than a single decision tree classifier. The main principle behind the ensemble model is that a group of weak learners come together to form a strong learner, thus increasing the accuracy of the model.When we try to predict the target variable using any machine learning technique, the main causes of difference in actual and predicted values are **noise, variance, and bias**. Ensemble helps to reduce these factors (except noise, which is irreducible error). The noise-related error is mainly due to noise in the training data and can't be removed. However, the errors due to bias and variance can be reduced.

The total error can be expressed as follows:

**Total Error = Bias + Variance + Irreducible Error**

A measure such as **mean square error** (**MSE**) captures all of these errors for a continuous target variable and can be represented as follows:

*Where*, E stands for the expected mean, Y represents the actual target values and fˆ(x) is the predicted values for the target variable. It can be broken down into its components such as bias, variance and noise as shown in the following formula:

Using techniques like Bagging and Boosting helps to decrease the variance and increase the robustness of the model. Combinations of multiple classifiers decrease variance, especially in the case of unstable classifiers, and may produce a more reliable classification than a single classifier.

The goal of ensemble algorithms is to combine the predictions of several base estimators built with a given learning algorithm in order to improve generalizability / robustness over a single estimator.

There are two families of ensemble methods which are usually distinguished:

**Averaging methods.**The driving principle is to build several estimators independently and then to average their predictions. On average, the combined estimator is usually better than any of the single base estimator because its variance is reduced.|**Examples:**Bagging methods, Forests of randomized trees.**Boosting methods.**Base estimators are built sequentially and one tries to reduce the bias of the combined estimator. The motivation is to combine several weak models to produce a powerful ensemble.**Examples:**AdaBoost, Gradient Tree Boosting.

- Ensemble is a proven method for improving the accuracy of the model and works in most of the cases.
- Ensemble makes the model more robust and stable thus ensuring decent performance on the test cases in most scenarios.
- You can use ensemble to capture linear and simple as well nonlinear complex relationships in the data. This can be done by using two different models and forming an ensemble of two.

- Ensemble reduces the model interpret-ability and makes it very difficult to draw any crucial business insights at the end
- It is time-consuming and thus might not be the best idea for real-time applications
- The selection of models for creating an ensemble is an art which is really hard to master

**Max Voting:**Max-voting is one of the simplest ways of combining predictions from multiple machine learning algorithms. Each base model makes a prediction and votes for each sample. The sample class with the highest votes is considered in the final predictive class. It is mainly used for classification problems.**Averaging:**Averaging can be used while estimating the probabilities in classification tasks. But it is usually used for regression problems. Predictions are extracted from multiple models and an average of the predictions are used to make the final prediction.**Weighted Average:**Like averaging, weighted averaging is also used for regression tasks. Alternatively, it can be used while estimating probabilities in classification problems. Base learners are assigned different weights, which represent the importance of each model in the prediction.

Ensemble methods became popular as a relatively simple device to improve the predictive performance of a base procedure. There are diﬀerent reasons for this: the bagging procedure turns out to be a variance reduction scheme, at least for some base procedures. On the other hand, boosting methods are primarily reducing the (model) bias of the base procedure. This already indicates that bagging and boosting are very diﬀerent ensemble methods. From the perspective of prediction, random forests is about as good as boosting, and often better than bagging.

**B**ootstrap **Agg**regation or **Bagging** tries to implement similar learners on small sample populations and then takes a mean of all the predictions.

- It combines Bootstrapping and Aggregation to form one ensemble model
- Reduces the variance error and helps to avoid overfitting

Bagging algorithms include:

- Bagging meta-estimator
- Random forest

**Boosting** refers to a family of algorithms which converts weak learner to strong learners. Boosting is a sequential process, where each subsequent model attempts to correct the errors of the previous model. Boosting is focused on reducing the bias. It makes the boosting algorithms prone to overfitting. To avoid overfitting, parameter tuning plays an important role in boosting algorithms. Some examples of boosting are mentioned below:

- AdaBoost
- GBM
- XGBM
- Light GBM
- CatBoost

Ensemble models help in improving algorithm accuracy as well as the robustness of a model. Both Bagging and Boosting should be known by data scientists and machine learning engineers and especially people who are planning to attend data science/machine learning interviews.

Ensemble learning uses hundreds to thousands of models of the same algorithm and then work hand in hand to find the correct classification. You may also consider the fable of the blind men and the elephant to understand ensemble learning, where each blind man found a feature of the elephant and they all thought it was something different. However, if they would work together and discussed among themselves, they might have figured out what it is.

Using techniques like bagging and boosting leads to increased robustness of statistical models and decreased variance. Now the question becomes, between these different “B” words. Which is better?

There is no perfectly correct answer to that. It depends on the data, the simulation and the circumstances.

Bagging and Boosting decrease the variance of your single estimate as they combine several estimates from different models. So the result may be a model with **higher stability**.

If the problem is that the single model gets a very low performance, Bagging will rarely get a **better bias**. However, Boosting could generate a combined model with lower errors as it optimizes the advantages and reduces pitfalls of the single model.

By contrast, if the difficulty of the single model is **overfitting**, then Bagging is the best option. Boosting for its part doesn’t help to avoid over-fitting; in fact, this technique is faced with this problem itself. For this reason, Bagging is effective more often than Boosting. In this article we will discuss about Bagging, we will cover Boosting in the next post. But first, let us look into the very important concept of bootstrapping.

Sampling is the process of selecting a subset of observations from the population with the purpose of estimating some parameters about the whole population. Resampling methods, on the other hand, are used to improve the estimates of the population parameters.

In machine learning, the bootstrap method refers to random sampling with replacement. This sample is referred to as a resample. This allows the model or algorithm to get a better understanding of the various biases, variances and features that exist in the resample. Taking a sample of the data allows the resample to contain different characteristics then it might have contained as a whole. This is demonstrated in figure 1 where each sample population has different pieces, and none are identical. This would then affect the overall mean, standard deviation and other descriptive metrics of a data set. In turn, it can develop more robust models.

Bootstrapping is also great for small size data sets that can have a tendency to overfit. In fact, we recommended this to one company who was concerned because their data sets were far from “Big Data”. Bootstrapping can be a solution in this case because algorithms that utilize bootstrapping can be more robust and handle new data sets depending on the methodology chosen(boosting or bagging).

The reason behind using the bootstrap method is because it can test the stability of a solution. By using multiple sample data sets and then testing multiple models, it can increase robustness. Perhaps one sample data set has a larger mean than another, or a different standard deviation. This might break a model that was overfit, and not tested using data sets with different variations.

One of the many reasons bootstrapping has become very common is because of the increase in computing power. This allows for many times more permutations to be done with different resamples than previously. Bootstrapping is used in both Bagging and Boosting

Let us assume we have a sample of ‘n’ values (x) and we’d like to get an estimate of the mean of the sample.

mean(x) = 1/n * sum(x)

*Consider a sample of 100 values (x) and we’d like to get an estimate of the mean of the sample. We can calculate the mean directly from the sample as:*

*We know that our sample is small and that the mean has **an **error in it. We can improve the estimate of our mean using the bootstrap procedure:*

*Create many (e.g. 1000) random sub-samples of the data set with replacement (meaning we can select the same value multiple times).**Calculate the mean of each sub-sample**Calculate the average of all of our collected means and use that as our estimated mean for the data*

E**xample:** Suppose we used 3 re-samples and got the mean values 2.3, 4.5 and 3.3. Taking the average of these we could take the estimated mean of the data to be 3.367. This process can be used to estimate other quantities like the standard deviation and even quantities used in machine learning algorithms, like learned coefficients.

While using Python, we do not have to implement the bootstrap method manually. The scikit-learn library provides an implementation that creates a single bootstrap sample of a dataset.

The resample() scikit-learn function can be used for sampling. It takes as arguments the data array, whether or not to sample with replacement, the size of the sample, and the seed for the pseudorandom number generator used prior to the sampling.

For example, let us create a bootstrap that creates a sample with replacement with 4 observations and uses a value of 1 for the pseudorandom number generator.

boot = resample(data, replace=True, n_samples=4, random_state=1)

As the bootstrap API does not allow to easily gather the out-of-bag observations that could be used as a test set to evaluate a fit model, in the univariate case we can gather the out-of-bag observations using a simple Python list comprehension.

# out of bag observations oob = [x for x in data if x not in boot]

Let us look at a small example and execute it.

# scikit-learn bootstrap from sklearn.utils import resample # data sample data = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6] # prepare bootstrap sample boot = resample(data, replace=True, n_samples=4, random_state=1) print('Bootstrap Sample: %s' % boot) # out of bag observations oob = [x for x in data if x not in boot] print('OOB Sample: %s' % oob)

The output will include the observations in the bootstrap sample and those observations in the out-of-bag sample.

Bootstrap Sample: [0.6, 0.4, 0.5, 0.1] OOB Sample: [0.2, 0.3]

**Bootstrap Aggregation**, also known as **Bagging**, is a powerful ensemble method that was proposed by Leo Breiman in 1994 to prevent overfitting. The concept behind bagging is to combine the predictions of several base learners to create a more accurate output. Bagging is the application of the Bootstrap procedure to a high-variance machine learning algorithm, typically decision trees.

- Suppose there are N observations and M features. A sample from observation is selected randomly with replacement (Bootstrapping).
- A subset of features are selected to create a model with sample of observations and subset of features.
- Feature from the subset is selected which gives the best split on the training data.
- This is repeated to create many models and every model is trained in parallel
- Prediction is given based on the aggregation of predictions from all the models.

This approach can be used with machine learning algorithms that have a high variance, such as decision trees. A separate model is trained on each bootstrap sample of data and the average output of those models used to make predictions. This technique is called bootstrap aggregation or bagging for short.

Variance means that an algorithm’s performance is sensitive to the training data, with high variance suggesting that the more the training data is changed, the more the performance of the algorithm will vary.

The performance of high variance machine learning algorithms like unpruned decision trees can be improved by training many trees and taking the average of their predictions. Results are often better than a single decision tree.

What Bagging does is help reduce variance from models that are might be very accurate, but only on the data they were trained on. This is also known as overfitting.

Overfitting is when a function fits the data too well. Typically this is because the actual equation is much too complicated to take into account each data point and outlier.

Bagging gets around this by creating its own variance amongst the data by sampling and replacing data while it tests multiple hypothesis(models). In turn, this reduces the noise by utilizing multiple samples that would most likely be made up of data with various attributes(median, average, etc).

Once each model has developed a hypothesis. The models use *voting for classification* or *averaging for regression*. This is where the “Aggregating” in “Bootstrap Aggregating” comes into play. Each hypothesis has the same weight as all the others. *When we later discuss boosting, this is one of the places the two methodologies differ.*

Essentially, all these models run at the same time, and vote on which hypothesis is the most accurate.

This helps to decrease variance i.e. reduce the overfit.

- Bagging takes advantage of ensemble learning wherein multiple weak learners outperform a single strong learner.
- It helps reduce variance and thus helps us avoid overfitting.

- There is loss of interpretability of the model.
- There can possibly be a problem of high bias if not modeled properly.
- While bagging gives us more accuracy, it is computationally expensive and may not be desirable depending on the use case.

There are many bagging algorithms of which perhaps the most prominent would be Random Forest.

Decision trees are simple but intuitive models. Using a top-down approach, a root node creates binary splits unless a particular criteria is fulfilled. This binary splitting of nodes results in a predicted value on the basis of the interior nodes which lead to the terminal or the final nodes. For a classification problem, a decision tree will output a predicted target class for each terminal node produced. We have covered decision tree algorithm in detail for both classification and regression in another article.

Decision trees tend to have high variance when they utilize different training and test sets of the same data, since they tend to overfit on training data. This leads to poor performance when new and unseen data is added. This limits the usage of decision trees in predictive modeling. However, using ensemble methods, models that utilize decision trees can be created as a foundation for producing powerful results.

We have already discussed about bootstrap aggregating (or bagging), we can create an ensemble (forest) of trees where multiple training sets are generated with replacement, meaning data instances. Once the training sets are created, a CART model can be trained on each subsample.

- Reduces variance by averaging the ensemble's results.
- The resulting model uses the entire feature space when considering node splits.
- Bagging trees allow the trees to grow without pruning, reducing the tree-depth sizes and resulting in high variance but lower bias, which can help improve predictive power.

The main limitation of bagging trees is that it uses the entire feature space when creating splits in the trees. Suppose some variables within the feature space are indicating certain predictions, there is a risk of having a forest of correlated trees, which actually increases bias and reduces variance.

The main objective of a machine learning model is to generalize properly to new and unseen data. When we have a flexible model, **overfitting** takes place. A flexible model is said to have high ** variance **because the learned parameters (such as the structure of the decision tree) will vary with the training data.

On the other hand, an inflexible model is said to have high ** bias** as it makes

You can through the article on one of the foundational concepts in machine learning, bias-variance tradeoff which will help you understand that the balance between creating a model that is so flexible memorizes the training data and an inflexible model cannot learn the training data.

The main reason why decision tree is prone to overfitting when we do not limit the maximum depth is because it has unlimited flexibility, which means it keeps growing unless there is one leaf node for every single observation.

Instead of limiting the depth of the tree which results in reduced variance and increase in bias, we can combine many decision trees into a single ensemble model known as the **random forest**.

Random forest is like bootstrapping algorithm with Decision tree (CART) model. Suppose we have 1000 observations in the complete population with 10 variables. Random forest will try to build multiple CART along with different samples and different initial variables. It will take a random sample of 100 observations and then chose 5 initial variables randomly to build a CART model. It will go on repeating the process say about 10 times and then make a final prediction on each of the observations. Final prediction is a function of each prediction. This final prediction can simply be the mean of each prediction.

The random forest is a model made up of many decision trees. Rather than just simply averaging the prediction of trees (which we could call a “forest”), this model uses two key concepts that gives it the name *random*:

- Random sampling of training data points when building trees
- Random subsets of features considered when splitting nodes

The basic steps involved in performing the random forest algorithm are mentioned below:

- Pick N random records from the dataset.
- Build a decision tree based on these N records.
- Choose the number of trees you want in your algorithm and repeat steps 1 and 2.
- In case of a regression problem, for a new record, each tree in the forest predicts a value for Y (output). The final value can be calculated by taking the average of all the values predicted by all the trees in the forest. Or, in the case of a classification problem, each tree in the forest predicts the category to which the new record belongs. Finally, the new record is assigned to the category that wins the majority vote.

Here we have a problem where we have to predict the gas consumption (in millions of gallons) in 48 US states based on petrol tax (in cents), per capita income (dollars), paved highways (in miles) and the proportion of population with the driving license. We will use the random forest algorithm via the Scikit-Learn Python library to solve this regression problem.

First we import the necessary libraries and our dataset.

import pandas as pd import numpy as np dataset = pd.read_csv('/content/petrol_consumption.csv') dataset.head()

Petrol_tax | Average_income | paved_Highways | Population_Driver_licence(%) | Petrol_Consumption | |
---|---|---|---|---|---|

0 | 9.0 | 3571 | 1976 | 0.525 | 541 |

1 | 9.0 | 4092 | 1250 | 0.572 | 524 |

2 | 9.0 | 3865 | 1586 | 0.580 | 561 |

3 | 7.5 | 4870 | 2351 | 0.529 | 414 |

4 | 8.0 | 4399 | 431 | 0.544 | 410 |

You will notice that the values in our dataset are not very well scaled. Let us scale them down before training the algorithm.

We will perform two tasks in order to prepare the data. Firstly we will divide the data into ‘attributes’ and ‘label’ sets. The resultant will then be divided into training and test sets.

X = dataset.iloc[:, 0:4].values y = dataset.iloc[:, 4].values

Now let us divide the data into training and testing sets:

from sklearn.model_selection import train_test_split X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=0)

The dataset is not yet a scaled value as you will see that the Average_Income field has values in the range of thousands while Petrol_tax has values in the range of tens. It will be better if we scale our data. We will use Scikit-Learn's StandardScaler class to do the same.

# Feature Scaling from sklearn.preprocessing import StandardScaler sc = StandardScaler() X_train = sc.fit_transform(X_train) X_test = sc.transform(X_test)

Now that we have scaled our dataset, let us train the random forest algorithm to solve this regression problem.

from sklearn.ensemble import Random Forest Regressor regressor = Random Forest Regressor(n_estimators=20,random_state=0) regressor.fit(X_train, y_train) y_pred = regressor.predict(X_test)

The RandomForestRegressor is used to solve regression problems via random forest. The most important parameter of the RandomForestRegressor class is the *n_estimators* parameter. This parameter defines the number of trees in the random forest. Here we started with n_estimator=20 and check the performance of the algorithm. You can find details for all of the parameters of RandomForestRegressor here.

Let us evaluate the performance of the algorithm. For regression problems the metrics used to evaluate an algorithm are mean absolute error, mean squared error, and root mean squared error.

from sklearn import metrics print('Mean Absolute Error:', metrics.mean_absolute_error(y_test, y_pred)) print('Mean Squared Error:', metrics.mean_squared_error(y_test, y_pred)) print('Root Mean Squared Error:', np.sqrt(metrics.mean_squared_error(y_test, y_pred)))

Mean Absolute Error: 51.76500000000001 Mean Squared Error: 4216.166749999999 Root Mean Squared Error: 64.93201637097064

With 20 trees, the root mean squared error is 64.93 which is greater than 10 percent of the average petrol consumption i.e. 576.77. This may indicate, among other things, that we have not used enough estimators (trees).

Let us now change the number of estimators to 200, the results are as follows:

Mean Absolute Error: 48.33899999999999 Mean Squared Error: 3494.2330150000003 Root Mean Squared Error: 59.112037818028234

The graph below shows the decrease in the value of the root mean squared error (RMSE) with respect to number of estimators.

You will notice that the error values decrease with the increase in the number of estimators. You may consider 200 a good number for n_estimators as the rate of decrease in error diminishes. You may try playing around with other parameters to figure out a better result.

Now let us consider a classification problem to predict whether a bank currency note is authentic or not based on four attributes i.e. variance of the image wavelet transformed image, skewness, entropy, andkurtosis of the image. We will use Random Forest Classifier to solve this binary classification problem. Let’s get started.

import pandas as pd import numpy as np dataset = pd.read_csv('/content/bill_authentication.csv') dataset.head()

Variance | Skewness | Kurtosis | Entropy | Class | |
---|---|---|---|---|---|

0 | 3.62160 | 8.6661 | -2.8073 | -0.44699 | 0 |

1 | 4.54590 | 8.1674 | -2.4586 | -1.46210 | 0 |

2 | 3.86600 | -2.6383 | 1.9242 | 0.10645 | 0 |

3 | 3.45660 | 9.5228 | -4.0112 | -3.59440 | 0 |

4 | 0.32924 | -4.4552 | 4.5718 | -0.98880 | 0 |

Similar to the data we used previously for the regression problem, this data is not scaled. Let us prepare the data for training.

The following code divides data into attributes and labels:

X = dataset.iloc[:, 0:4].values y = dataset.iloc[:, 4].values

The following code divides data into training and testing sets:

from sklearn.model_selection import train_test_split X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=0)

We will do the same thing as we did for the previous problem.

# Feature Scaling from sklearn.preprocessing import StandardScaler sc = StandardScaler() X_train = sc.fit_transform(X_train) X_test = sc.transform(X_test)

Now that we have scaled our dataset, let us train the random forest algorithm to solve this classification problem.

from sklearn.ensemble import Random Forest Classifier classifier = RandomForestClassifier(n_estimators=20, random_state=0) classifier.fit(X_train, y_train) y_pred = classifier.predict(X_test)

For classification, we have used RandomForestClassifier class of the sklearn.ensemble library. It takes n_estimators as a parameter. This parameter defines the number of trees in out random forest. Similar to the regression problem, we have started with 20 trees here. You can find details for all of the parameters of Random Forest Classifier here.

**Evaluating the Algorithm**

For evaluating classification problems, the metrics used are accuracy, confusion matrix, precision recall, and F1 values

from sklearn.metrics import classification_report, confusion_matrix, accuracy_score print(confusion_matrix(y_test,y_pred)) print(classification_report(y_test,y_pred)) print(accuracy_score(y_test, y_pred))

The output will look something like this:

**Output:**

[ [ 155 2] [ 1 117] ]

Precision | recall | f1-score | support | |

0 | 0.99 | 0.99 | 0.99 | 157 |

1 | 0.98 | 0.99 | 0.99 | 118 |

accuracy | 0.99 | 275 | ||

macro avg | 0.99 | 0.99 | 0.99 | 275 |

0.9890909090909091 | 0.99 | 0.99 | 0.99 | 275 |

The accuracy achieved by our random forest classifier with 20 trees is 98.90%. Let us change the number of trees to 200.

from sklearn.ensemble import Random Forest Classifier classifier = Random Forest Classifier(n_estimators=200, random_state=0) classifier.fit(X_train, y_train) y_pred = classifier.predict(X_test)

**Output:**

[ [ 155 2] [ 1 117] ]

Precision | recall | f1-score | support | |

0 | 0.99 | 0.99 | 0.99 | 157 |

1 | 0.98 | 0.99 | 0.99 | 118 |

accuracy | 0.99 | 275 | ||

macro avg | 0.99 | 0.99 | 0.99 | 275 |

0.9890909090909091 | 0.99 | 0.99 | 0.99 | 275 |

Unlike the regression problem, changing the number of estimators for this problem did not make any difference in the results.

An accuracy of 98.9% is pretty good. In this case, we have seen that there is not much improvement if the number of trees are increased. You may try playing around with other parameters of the RandomForestClassifier class and see if you can improve on our results.

As with any algorithm, there are advantages and disadvantages to using it. Let us look into the pros and cons of using Random Forest for classification and regression.

**Advantages**

- Random forest algorithm is unbiased as there are multiple trees and each tree is trained on a subset of data.
- Random Forest algorithm is very stable. Introducing a new data in the dataset does not affect much as the new data impacts one tree and is pretty hard to impact all the trees.
- The random forest algorithm works well when you have both categorical and numerical features.
- With missing values in the dataset, the random forest algorithm performs very well.

**Disadvantages**

- A major disadvantage of random forests lies in their complexity. More computational resources are required and also results in the large number of decision trees joined together.
- Due to their complexity, training time is more compared to other algorithms.

In this article we have covered what is ensemble learning and discussed about basic ensemble techniques. We also looked into bootstrap sampling involves iteratively resampling of a dataset with replacement which allows the model or algorithm to get a better understanding various features. Then we moved on to bagging followed by random forest. We also implemented random forest in Python for both regression and classification and came to a conclusion that increasing number of trees or estimators does not always make a difference in a classification problem. However, in regression there is an impact.

We have covered most of the topics related to algorithms in our series of machine learning blogs,click here. If you are inspired by the opportunities provided by machine learning, enrol in our Data Science and Machine Learning Courses for more lucrative career options in this landscape.

Build your own projects usingMachine Learning with Python. Practice with our industry experts on our live workshops now.

9287

- by Harsha Vardhan Garlapati
- 08 Mar 2021
- 6 mins read

If we were to list the technologies that have revo... Read More

8565

- by Priyankur Sarkar
- 20 Sep 2019
- 15 mins read

Machine Learning, being a subset of Artificial Int... Read More

6788

- by Harsha Vardhan Garlapati
- 24 Feb 2021
- 8 mins read

Machine Learning is emerging as the latest technol... Read More

Subscribe to our newsletter.

## Join the Discussion

Your email address will not be published. Required fields are marked *