The naive Bayesian classification is a simple Bayesian type of probabilistic classification based on Bayes’ theorem with a strong (so-called naive) independence of assumptions. It implements a naïve Bayesian classifier, or naive classifier of Bayes, belonging to the family of linear classifiers. A naïve Bayesian classifier assumes that the existence of a characteristic for a class is independent of the existence of other characteristics. A fruit can be considered an apple if it is red, rounded, and about ten centimeters. Even if these characteristics are related in reality, a naive Bayesian classifier will determine that the fruit is an apple by independently considering these characteristics of color, shape and size. Depending on the nature of each probabilistic model, naïve Bayesian classifiers can be effectively trained in a supervised learning context. In many practical applications, parameter estimation for naive Bayesian models is based on maximum likelihood. In other words, it is possible to work with the naive Bayes model without worrying about Bayesian probability or using Bayesian methods. Despite their « naive » design model and extremely simplistic basic assumptions, naive Bayesian classifiers have been more than efficient in many complex real world situations although more recent approaches (enhanced trees, random forests) may provide better results for similar context of use. The advantage of the naïve Bayesian classifier is that it requires relatively little training data to estimate the parameters necessary for classification, namely averages and variances of the different variables.

USE CASE : CLASSIFYING BUSINESSES AS RETAIL OR HOSTELLERY/RESTAURANT/CAFE
In this use case we want to build a model that classifies a business as a retail shop or a hotel/restaurant/café according to the amount of fresh, grocery and frozen food bought during the year. The following dataset contains 5280 rows, each representing an european hotel, restaurant, café or retail shop and his annual food budget divided in three categories : budget in euros for fresh food, budget in euros for grocery food and budget in euros for frozen food. Here follows the first 40 rows of the dataset :

Dataset of businesses classification as a retail shop or a hotel/restaurant/café according to the amount of fresh, grocery and frozen food bought during the year

Here follows the dataset in CSV format :

FRESH,GROCERY,FROZEN,HOSTEL_OR_RETAIL
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