Book Image

Clojure for Data Science

By : Garner
Book Image

Clojure for Data Science

By: Garner

Overview of this book

The term “data science” has been widely used to define this new profession that is expected to interpret vast datasets and translate them to improved decision-making and performance. Clojure is a powerful language that combines the interactivity of a scripting language with the speed of a compiled language. Together with its rich ecosystem of native libraries and an extremely simple and consistent functional approach to data manipulation, which maps closely to mathematical formula, it is an ideal, practical, and flexible language to meet a data scientist’s diverse needs. Taking you on a journey from simple summary statistics to sophisticated machine learning algorithms, this book shows how the Clojure programming language can be used to derive insights from data. Data scientists often forge a novel path, and you’ll see how to make use of Clojure’s Java interoperability capabilities to access libraries such as Mahout and Mllib for which Clojure wrappers don’t yet exist. Even seasoned Clojure developers will develop a deeper appreciation for their language’s flexibility! You’ll learn how to apply statistical thinking to your own data and use Clojure to explore, analyze, and visualize it in a technically and statistically robust way. You can also use Incanter for local data processing and ClojureScript to present interactive visualisations and understand how distributed platforms such as Hadoop sand Spark’s MapReduce and GraphX’s BSP solve the challenges of data analysis at scale, and how to explain algorithms using those programming models. Above all, by following the explanations in this book, you’ll learn not just how to be effective using the current state-of-the-art methods in data science, but why such methods work so that you can continue to be productive as the field evolves into the future.
Table of Contents (12 chapters)
11
Index

Ordinary least squares


In order to optimize the parameters of our linear model, we'd like to devise a cost function, also called a loss function, that quantifies how closely our predictions fit the data. We cannot simply sum up the residuals, positive and negative, because even large residuals will cancel each other out if their signs are in opposite directions.

We could square the values before calculating the sum so that positive and negative residuals both count towards the cost. This also has the effect of penalizing large errors more than smaller errors, but not so much that the largest residual always dominates.

Expressed as an optimization problem, we seek to identify the coefficients that minimize the sum of the residual squares. This is called Ordinary Least Squares (OLS), and the formula to calculate the slope of the regression line using OLS is:

Although this looks more complicated than the previous equations, it's really just the sum of squared residuals divided by the sum of squared...