Book Image

Clojure for Data Science

By : Henry Garner
Book Image

Clojure for Data Science

By: Henry Garner

Overview of this book

Table of Contents (18 chapters)
Clojure for Data Science
Credits
About the Author
Acknowledgments
About the Reviewer
www.PacktPub.com
Preface
Index

Maximum likelihood estimation


On several occasions throughout this book, we've expressed optimization problems in terms of a cost function to be minimized. For example, in Chapter 4, Classification, we used Incanter to minimize the logistic cost function whilst building a logistic regression classifier, and in Chapter 5, Big Data, we used gradient descent to minimize a least-squares cost function when performing batch and stochastic gradient descent.

Optimization can also be expressed as a benefit to maximize, and it's sometimes more natural to think in these terms. Maximum likelihood estimation aims to find the best parameters for a model by maximizing the likelihood function.

Let's say that the probability of an observation x given model parameters β is written as:

Then, the likelihood can be expressed as:

The likelihood is a measure of the probability of the parameters, given the data. The aim of maximum likelihood estimation is to find the parameter values that make the observed data most...