Book Image

Learning Bayesian Models with R

By : Hari Manassery Koduvely
Book Image

Learning Bayesian Models with R

By: Hari Manassery Koduvely

Overview of this book

Bayesian Inference provides a unified framework to deal with all sorts of uncertainties when learning patterns form data using machine learning models and use it for predicting future observations. However, learning and implementing Bayesian models is not easy for data science practitioners due to the level of mathematical treatment involved. Also, applying Bayesian methods to real-world problems requires high computational resources. With the recent advances in computation and several open sources packages available in R, Bayesian modeling has become more feasible to use for practical applications today. Therefore, it would be advantageous for all data scientists and engineers to understand Bayesian methods and apply them in their projects to achieve better results. Learning Bayesian Models with R starts by giving you a comprehensive coverage of the Bayesian Machine Learning models and the R packages that implement them. It begins with an introduction to the fundamentals of probability theory and R programming for those who are new to the subject. Then the book covers some of the important machine learning methods, both supervised and unsupervised learning, implemented using Bayesian Inference and R. Every chapter begins with a theoretical description of the method explained in a very simple manner. Then, relevant R packages are discussed and some illustrations using data sets from the UCI Machine Learning repository are given. Each chapter ends with some simple exercises for you to get hands-on experience of the concepts and R packages discussed in the chapter. The last chapters are devoted to the latest development in the field, specifically Deep Learning, which uses a class of Neural Network models that are currently at the frontier of Artificial Intelligence. The book concludes with the application of Bayesian methods on Big Data using the Hadoop and Spark frameworks.
Table of Contents (11 chapters)
10
Index

Model overfitting and bias-variance tradeoff


The expected loss mentioned in the previous section can be written as a sum of three terms in the case of linear regression using squared loss function, as follows:

Here, Bias is the difference between the true model F(X) and average value of taken over an ensemble of datasets. Bias is a measure of how much the average prediction over all datasets in the ensemble differs from the true regression function F(X). Variance is given by . It is a measure of extent to which the solution for a given dataset varies around the mean over all datasets. Hence, Variance is a measure of how much the function is sensitive to the particular choice of dataset D. The third term Noise, as mentioned earlier, is the expectation of difference between observation and the true regression function, over all the values of X and Y. Putting all these together, we can write the following:

The objective of machine learning is to learn the function from data that minimizes...