Bayesian Average

A (work in progress) gem for adding Bayesian averages to your Rails projects. What is a Bayesian average?

tl;dr - Get rid of the issues caused by averages (means) of small datasets or datasets with outliars.

A Bayesian average is a method of estimating the mean of a population consistent with Bayesian interpretation, where instead of estimating the mean strictly from the available data set, other existing information related to that data set may also be incorporated into the calculation in order to minimize the impact of large deviations, or to assert a default value when the data set is small.

For example, in a calculation of an average review score of a book where only two reviews are available, both giving scores of 10, a normal average score would be 10. However, as only two reviews are available, 10 may not represent the true average had more reviews been available. The review site may instead calculate a Bayesian average of this score by adding the average review score of all books in the store to the calculation. For example, by adding five scores of 7 each, the Bayesian average becomes 7.86 instead of 10, which the review site would hope that it will better represent the quality of the book.

Taken from the Wikipedia article.

Currently the project is dependent on Mongoid. I might add AR support later.

Gemfile:

gem "bayesian_average", "~> 0.1.1"

In your model being ranked:

class Movie
  include Mongoid::Document
  include Mongoid::BayesianParent
  
  has_many :rankings
  
  bayesian_parent_for :ranking, weight: 100
  
  def bayesian_collection
    Movie.all
  end
end

In your model representing the rankings:

class Ranking
  include Mongoid::Document
  include Mongoid::BayesianChild
  
  belongs_to :movie
  
  field :score, type: Integer, default: 0
  
  bayesian_child_for :movie, field: :score
end

Here we define the parent and child. Let's look at the parent first.

The parent must have_many of the child objects. The line bayesian_parent_for :ranking, weight: 100 signifies that objects of the Ranking class hold the scores, and that the average of the collection will have the weight of weight objects. At this point parents can only have Bayesian scores for one class. The method definition is important. It signifies what the Bayesian score is based off of. In this case, the average of all the movies will be taken into account, but defining this method allows you to define more appropriate subsets. For example, if the Movie class has a Director, then director.movies might be a more reliable mean, since the movies by a particular director tend to be of a certain quality. Keep in mind that if this dataset is small, it will defeat the purpose of a Bayesain average, thus something like this might be better:

def bayesian_collection
  director.movies.count >= 5 ? director.movies : Movie.all
end

The child class only has one interesting line in it. bayesian_child_for :movie, field: :score simply denotes which field should be used in the average, and which class it is scoring.

This exposes the following method:

movie.bayesian_average #=> Float

Also, you will get a method to update your existing database:

Movie.all.each do { |movie| movie.update_bayesian }

Keep in mind that this will put a large load on your database. You probably want to do this a small section at a time and asynchronously with Resque or something similar.

This gem will store two fields on your parent model, num_bayesian_children and num_bayesian_points. Instead of storing a float, it will keep these fields to prevent rounding errors from propagating over the lifetime of your application.

The child model gets a before_create that increments the parent model atomically to update the number of children and number of total points.

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