Naïve Bayes theorem is a fundamental concept in probability theory and statistics, forming the basis of the Naïve Bayes classification algorithm. Named after the Reverend Thomas Bayes, an 18th-century mathematician, the theorem provides a way to update the probability of a hypothesis (or event) based on new evidence or information. It’s particularly powerful in situations where you have initial beliefs or probabilities and then receive additional data that can impact those beliefs.
In the context of the Naïve Bayes classifier, the theorem is applied to the task of classification. It assumes that the presence of one feature is independent of the presence of any other feature, which is a simplifying but often unrealistic assumption—hence the term “naïve.” Despite this simplification, the Naïve Bayes algorithm can be surprisingly effective in many real-world applications.
In the classifier’s context, the theorem helps calculate the probability that a given data point belongs to a certain class based on the observed features. It’s achieved by calculating the posterior probability of each class given the features of the data point and then selecting the class with the highest posterior probability as the predicted class for that data point.
To study the Naïve Bayes machine learning model more, I attempted to use it to classify data from the famous breast cancer dataset in Python. This dataset contains information about various characteristics of cell nuclei present in breast cancer biopsies, and it is used for binary classification tasks to determine whether a given tumor is malignant (cancerous) or benign (non-cancerous). After creating a new column in the data set called target, I split the data using the train_test_split module into training and testing data. The x data was the features: worst radius, mean texture, worst area, and mean concavity, and the y data was the target column.
Next, I imported the GaussianNB package from sklearn, and initiated the model using the fit function. Then, I used to predict function to predict the y values based on the x test data set. Finally, I compared the accuracy of the model by using the accuracy_score function, and the model returned a 0.96491 accuracy.
