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Chapter 2
The Pointwise Approach
Abstract In this chapter, we introduce the pointwise approach to learning to rank.
Specifically, we will cover the regression-based algorithms, classification-based al-
gorithms, and ordinal regression-based algorithms, and then make discussions on
their advantages and disadvantages.
2.1 Overview
When using the technologies of machine learning to solve the problem of ranking,
probably the most straightforward way is to check whether existing learning meth-
ods can be directly applied. This is exactly what the pointwise approach does. When
doing so, one assumes that the exact relevance degree of each document is what we
are going to predict, although this may not be necessary since the target is to produce
a ranked list of the documents.
According to different machine learning technologies used, the pointwise ap-
proach can be further divided into three subcategories: regression-based algo-
rithms, classification-based algorithms, and ordinal regression-based algorithms.
For regression-based algorithms, the output space contains real-valued relevance
scores; for classification-based algorithms, the output space contains non-ordered
categories; and for ordinal regression-based algorithms, the output space contains
ordered categories.
In the following, we will introduce representative algorithms in the three subcat-
egories of the pointwise approach.
2.2 Regression-Based Algorithms
In this sub-category, the problem of ranking is reduced to a regression prob-
lem [ 5 , 8 ]. Regression is a kind of supervised learning problem in which the tar-
get variable that one is trying to predict is continuous. When formalizing ranking
as regression, one regards the relevance degree given to a document as a continuous
variable, and learns the ranking function by minimizing the regret on the training set.
Here we introduce a representative algorithm as an example for this sub-category.
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