A practical explanation of a Naive Bayes classifier

A practical explanation of a Naive Bayes classifier

The simplest solutions are usually the most powerful ones, and Naive Bayes is a good example of that. In spite of the great advances of machine learning in the last years, it has proven to not only be simple but also fast, accurate, and reliable. It has been successfully used for many purposes, but it works particularly well with natural language processing (NLP) problems.

Naive Bayes is a family of probabilistic algorithms that take advantage of probability theory and Bayes’ Theorem to predict the tag of a text (like a piece of news or a customer review). They are probabilistic, which means that they calculate the probability of each tag for a given text, and then output the tag with the highest one. The way they get these probabilities is by using Bayes’ Theorem, which describes the probability of a feature, based on prior knowledge of conditions that might be related to that feature.

We're going to be working with an algorithm called Multinomial Naive Bayes. We’ll walk through the algorithm applied to NLP with an example, so by the end, not only will you know how this method works, but also why it works. Then, we'll lay out a few advanced techniques that can make Naive Bayes competitive with more complex Machine Learning algorithms, such as SVM and neural networks.

A Simple Example

Let’s see how this works in practice with a simple example. Suppose we are building a classifier that says whether a text is about sports or not. Our training data has 5 sentences:

"A great game"Sports
"The election was over"Not sports
"Very clean match"Sports
"A clean but forgettable game"Sports
"It was a close election"Not sports

Now, which tag does the sentence A very close game belong to?

Since Naive Bayes is a probabilistic classifier, we want to calculate the probability that the sentence "A very close game" is Sports and the probability that it’s Not Sports. Then, we take the largest one. Written mathematically, what we want is P (Sports | a very close game) — the probability that the tag of a sentence is Sports given that the sentence is “A very close game”.

That’s great, but how do we calculate these probabilities?

Let’s dig in!

Feature Engineering

The first thing we need to do when creating a machine learning model is to decide what to use as features. We call features the pieces of information that we take from the text and give to the algorithm so it can work its magic. For example, if we were doing classification on health, some features could be a person’s height, weight, gender, and so on. We would exclude things that maybe are known but aren’t useful to the model, like a person’s name or favorite color.

In this case though, we don’t even have numeric features. We just have text. We need to somehow convert this text into numbers that we can do calculations on.

So what do we do? Simple! We use word frequencies. That is, we ignore word order and sentence construction, treating every document as a set of the words it contains. Our features will be the counts of each of these words. Even though it may seem too simplistic an approach, it works surprisingly well.

Bayes’ Theorem

Now we need to transform the probability we want to calculate into something that can be calculated using word frequencies. For this, we will use some basic properties of probabilities, and Bayes’ Theorem. If you feel like your knowledge of these topics is a bit rusty, read up on it, and you'll be up to speed in a couple of minutes.

Bayes' Theorem is useful when working with conditional probabilities (like we are doing here), because it provides us with a way to reverse them:

Naive Bayes formula.

In our case, we have P (Sports | a very close game), so using this theorem we can reverse the conditional probability:

Naive Bayes example.

Since for our classifier we’re just trying to find out which tag has a bigger probability, we can discard the divisor —which is the same for both tags— and just compare

Naive Bayes example.


Naive Bayes example.

This is better, since we could actually calculate these probabilities! Just count how many times the sentence “A very close game” appears in the Sports tag, divide it by the total, and obtain P (a very close game | Sports).

There's a problem though: “A very close game” doesn’t appear in our training data, so this probability is zero. Unless every sentence that we want to classify appears in our training data, the model won’t be very useful.

Being Naive

So here comes the Naive part: we assume that every word in a sentence is independent of the other ones. This means that we’re no longer looking at entire sentences, but rather at individual words. So for our purposes, “this was a fun party” is the same as “this party was fun” and “party fun was this”.

We write this as:

Naive Bayes example.

This assumption is very strong but super useful. It's what makes this model work well with little data or data that may be mislabeled. The next step is just applying this to what we had before:

Naive Bayes example.

And now, all of these individual words actually show up several times in our training data, and we can calculate them!

Calculating Probabilities

The final step is just to calculate every probability and see which one turns out to be larger.

Calculating a probability is just counting in our training data.

First, we calculate the a priori probability of each tag: for a given sentence in our training data, the probability that it is Sports P (Sports) is ⅗. Then, P (Not Sports) is ⅖. That’s easy enough.

Then, calculating P (game | Sports) means counting how many times the word “game” appears in Sports texts (2) divided by the total number of words in sports (11). Therefore,

Naive Bayes example.

However, we run into a problem here: “close” doesn’t appear in any Sports text! That means that P (close | Sports) = 0. This is rather inconvenient since we are going to be multiplying it with the other probabilities, so we'll end up with

Naive Bayes example.

This equals 0, since in a multiplication if one of the terms is zero, the whole calculation is nullified. Doing things this way simply doesn't give us any information at all, so we have to find a way around.

How do we do it? By using something called Laplace smoothing: we add 1 to every count so it’s never zero. To balance this, we add the number of possible words to the divisor, so the division will never be greater than 1. In our case, the possible words are ['a', 'great', 'very', 'over', 'it', 'but', 'game', 'election', 'clean', 'close', 'the', 'was', 'forgettable', 'match'].

Since the number of possible words is 14 (I counted them!), applying smoothing we get that

Naive Bayes example.

The full results are:

WordP (word | Sports)P (word | Not Sports)
a(2 + 1) ÷ (11 + 14)(1 + 1) ÷ (9 + 14)
very(1 + 1) ÷ (11 + 14)(0 + 1) ÷ (9 + 14)
close(0 + 1) ÷ (11 + 14)(1 + 1) ÷ (9 + 14)
game(2 + 1) ÷ (11 + 14)(0 + 1) ÷ (9 + 14)

Now we just multiply all the probabilities, and see who is bigger:

Naive Bayes example.

Excellent! Our classifier gives “A very close game” the Sports tag.

Advanced techniques

There are many things that can be done to improve this basic model. These techniques allow Naive Bayes to perform at the same level as more advanced methods. Some of these techniques are:

  • Removing stopwords. These are common words that don’t really add anything to the classification, such as a, able, either, else, ever and so on. So for our purposes, The election was over would be election over and a very close game would be very close game.

  • Lemmatizing words. This is grouping together different inflections of the same word. So election, elections, elected, and so on would be grouped together and counted as more appearances of the same word.

  • Using n-grams. Instead of counting single words as we did here, we could count sequences of words, like “clean match” and “close election”.

  • Using TF-IDF. Instead of just counting frequency we could do something more advanced like also penalizing words that appear frequently in most of the texts.

Creating a Naive Bayes Classifier with MonkeyLearn

You now know how Naive Bayes works with a text classifier, but you’re still not quite sure where to start. Well, instead of starting from scratch, you can easily build a text classifier on MonkeyLearn, which can actually be trained with Naive Bayes.

But what is MonkeyLearn? Basically, it’s a machine learning platform that analyzes text in two ways –  by classifying it according to topic, aspect, sentiment, urgency or intent and by extracting key information such as keywords, names, and companies.

You don’t need to be a machine learning expert to use MonkeyLearn, or even know the ins and outs of Naive Bayes to build and use a text classifier.

  • It’s simple to use

You don’t need to be a machine learning expert to use MonkeyLearn, or even know the ins and outs of Naive Bayes to build and use a text classifier.

  • No setup is required:

You don’t have to worry about building the underlying infrastructure for a text analysis model. MonkeyLearn does it for you. Performance, scalability, logging, architecture, tools, etc...MonkeyLearn has it all under control!

  • You don’t need to code:

MonkeyLearn is ready to use straight away. All you need to do is integrate it into your codebase, made super easy thanks to MonkeyLearn’s beautiful API. It comes with SDKs for every major programming language, as well as well-written documentation.

  • Faster training:

The tagging process within MonkeyLearn is much quicker, thanks to a clean and simple interface specifically built for tagging text data. This process is also faster thanks to active learning, a machine learning technique that suggests tags within text data, as you’re training your model.

We've made a strong case for why you should create your naive bayes text classifier with MonkeyLearn, but let's see how easy it is to create your model. Here's a step-by-step guide to help you get started.

1. Create a text classifier

Sign up for free to MonkeyLearn and go to the MonkeyLearn Dashboard, select 'Create Model' and click on the 'Classifier' option:

Choose model type

2. Select 'Topic Classification'

Sentiment analysis focuses on how positive or negative a text is, while intent classification aims to categorize texts according to their purpose. In this case, we want to classify texts according to the topic, so let’s choose 'Topic Classification':

Type of classification

3. Upload your training data

You can easily upload texts from an Excel or CSV file. Remember, it’s always best to upload a large bunch of data to make sure your model has enough training data:

Import your text data

4. Create your tags

In this step, it’s important to keep the number of tags to a minimum. At MonkeyLearn, we usually recommend starting with no more than ten. Once the model is performing well, you can add more tags:

Define tags of the model

5. Train your classifier

We know what you’re thinking: what about naive bayes? We’re almost there, but first, it’s crucial to teach your classifier how to tag different text units. Just click on the correct tag for each piece of text and confirm. Soon enough, your model will start making predictions which you can confirm or correct:

Tag data

Don’t worry if more than one tag applies to a given text, just use both tags to classify it. If you start noticing that the features (pieces of information from a text that are useful for the algorithm) don’t match any tags, you can create a new tag by clicking on the add button next to 'Tags'.

6. Change to Naive Bayes

After training your model, go to the Settings section and change the algorithm from Support Vector Machines (our default algorithm) to Naive Bayes. Save your settings and go back to training your model to test it:

Select naive bayes algorithm

From that moment on, MonkeyLearn will start training your classifier with Naive Bayes.

7. Test your Naive Bayes classifier

Is it ready? This phase will show you whether it's time to put your model to work or continue training it. Click on the 'Run' tab and type something into the text box. Did your model predict the correct tag? Try a few more times to make sure you're using a classifier that's ready work for you:

Test with your own text


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Just to make sure, you can look at the classifier stats to see how accurate your Naive Bayes classifier is.

8. Start working with your model

It's time to reap what you sowed! Run brand new pieces of text through your classifier, which you can import in various ways:

  1. Using MonkeyLearn’s API with the programming language of your choice:
MonkeyLearn API

With some quick and simple coding, you can integrate MonkeyLearn into your codebase and run your classification model automatically. There are different SDKs available: Python, Ruby, PHP, Node.js, and Java.

  1. Go to the 'Batch' tab and upload a CSV or Excel file:
Batch processing

After running text data from your file through your model, you'll get a new file in return with all the tag predictions, in just a few seconds.

  1. Use third-party Integrations:

MonkeyLearn has various integrations, including Google Sheets, Zapier, Rapidminer or Zendesk, so that you can analyze data without any hassle. Just go to the 'Integrate' section and take your pick:


Final words

Hopefully, you now have a better understanding of what Naive Bayes is and how it can be used for text classification. This simple method works surprisingly well for classification problems and, computationally speaking, it’s very cheap. Creating a classifier from scratch also takes a lot of time, and that’s where MonkeyLearn’s classifier swoops in to save the day.

Whether you’re a Machine Learning expert or not, you have the tools to build your own Naive Bayes classifier. You don’t need to spend hours studying and coding – just sign up to MonkeyLearn for free or request a demo and get started.

If you’re interested in learning more about these topics, check out our guides to machine learning and natural language processing.

Bruno Stecanella

May 25th, 2017

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