Naive Bayes. What may seem like a very confusing algorithm is actually one of the simplest algorithms once understood. Part of why it’s so simple to understand and implement is because of the assumptions that it inherently makes. However, that’s not to say that it’s a poor algorithm despite the strong assumptions that it holds — in fact, Naive Bayes is widely used in the data science world and has a lot of real-life applications.
In this article, we’ll look at what Naive Bayes is, how it works with an example to make it easy to understand, the different types of Naive Bayes, the pros and cons, and some real-life applications of it…
For many of us, Bayesian statistics is voodoo magic at best, or completely subjective nonsense at worst. Among the trademarks of the Bayesian approach, Markov chain Monte Carlo methods are especially mysterious. They’re math-heavy and computationally expensive procedures for sure, but the basic reasoning behind them, like so much else in data science, can be made intuitive. That is my goal here.
So, what are Markov chain Monte Carlo (MCMC) methods? The short answer is:
MCMC methods are used to approximate the posterior distribution of a parameter of interest by random sampling in a probabilistic space.
In this article, I will explain that short answer, without any math.
There is a struggle today for the heart and minds of Artificial Intelligence. It’s a complex “Game of Thrones” conflict that involves many houses (or tribes) (see: “The Many Tribes of AI”). The two waring factions I focus on today is on the practice Cargo Cult science in the form of Bayesian statistics and in the practice of alchemy in the form of experimental Deep Learning.
For the uninitiated, let’s talk about what Cargo Cult science means. Cargo Cult science is a phrase coined by Richard Feynman to illustrate a practice in science of not working from fundamentally sound first principles. Here is Richard Feynman’s original essay on “Cargo Cult Science”. If you’ve never read it before, it great and refreshing read. I read this in my youth while studying physics. I am unsure if its required reading for physicists, but a majority of physicists are well aware of this concept.
Think Bayes is an introduction to Bayesian statistics using computational methods.
The premise of this book, and the other books in the Think X series, is that if you know how to program, you can use that skill to learn other topics.
Most books on Bayesian statistics use mathematical notation and present ideas in terms of mathematical concepts like calculus. This book uses Python code instead of math, and discrete approximations instead of continuous mathematics. As a result, what would be an integral in a math book becomes a summation, and most operations on probability distributions are simple loops.
I think this presentation is easier to understand, at least for people with programming skills. It is also more general, because when we make modeling decisions, we can choose the most appropriate model without worrying too much about whether the model lends itself to conventional analysis. Also, it provides a smooth development path from simple examples to real-world problems.
This post summarizes and links to a great multi-part tutorial series on learning the TensorFlow API for building a variety of neural networks, as well as a bonus tutorial on backpropagation from the beginning.
By Erik Hallström, Deep Learning Research Engineer.
Editor’s note: The TensorFlow API has undergone changes since this series was first published. However, the general ideas are the same, and an otherwise well-structured tutorial such as this provides a great jumping off point and opportunity to consult the API documentation to identify and implement said changes.
Schematic of a RNN processing sequential data over time.
Most tasks in Machine Learning can be reduced to classification tasks. For example, we have a medical dataset and we want to classify who has diabetes (positive class) and who doesn’t (negative class). We have a dataset from the financial world and want to know which customers will default on their credit (positive class) and which customers will not (negative class).
To do this, we can train a Classifier with a ‘training dataset’ and after such a Classifier is trained (we have determined its model parameters) and can accurately classify the training set, we can use it to classify new data (test set). If the training is done properly, the Classifier should predict the class probabilities of the new data with a similar accuracy.
There are three popular Classifiers which use three different mathematical approaches to classify data. Previously we have looked at the first two of these; Logistic Regression and the Naive Bayes classifier. Logistic Regression uses a functional approach to classify data, and the Naive Bayes classifier uses a statistical (Bayesian) approach to classify data.
Logistic Regression assumes there is some function which forms a correct model of the dataset (i.e. it maps the input values correctly to the output values). This function is defined by its parameters . We can use the gradient descent method to find the optimum values of these parameters.
The Naive Bayes method is much simpler than that; we do not have to optimize a function, but can calculate the Bayesian (conditional) probabilities directly from the training dataset. This can be done quiet fast (by creating a hash table containing the probability distributions of the features) but is generally less accurate.
Classification of data can also be done via a third way, by using a geometrical approach. The main idea is to find a line, or a plane, which can separate the two classes in their feature space. Classifiers which are using a geometrical approach are the Perceptron and the SVM (Support Vector Machines) methods.
Below we will discuss the Perceptron classification algorithm. Although Support Vector Machines is used more often, I think a good understanding of the Perceptron algorithm is essential to understanding Support Vector Machines and Neural Networks.